





Internet Research Task Force (IRTF)                   S. Smyshlyaev, Ed.
Request for Comments: 8645                                     CryptoPro
Category: Informational                                      August 2019
ISSN: 2070-1721


                Re-keying Mechanisms for Symmetric Keys

Abstract

   A certain maximum amount of data can be safely encrypted when
   encryption is performed under a single key.  This amount is called
   the "key lifetime".  This specification describes a variety of
   methods for increasing the lifetime of symmetric keys.  It provides
   two types of re-keying mechanisms based on hash functions and block
   ciphers that can be used with modes of operations such as CTR, GCM,
   CBC, CFB, and OMAC.

   This document is a product of the Crypto Forum Research Group (CFRG)
   in the IRTF.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Research Task Force
   (IRTF).  The IRTF publishes the results of Internet-related research
   and development activities.  These results might not be suitable for
   deployment.  This RFC represents the consensus of the Crypto Forum
   Research Group of the Internet Research Task Force (IRTF).  Documents
   approved for publication by the IRSG are not candidates for any level
   of Internet Standard; see Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   https://www.rfc-editor.org/info/rfc8645.














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Copyright Notice

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   4
   2.  Conventions Used in This Document . . . . . . . . . . . . . .   7
   3.  Basic Terms and Definitions . . . . . . . . . . . . . . . . .   7
   4.  Choosing Constructions and Security Parameters  . . . . . . .   9
   5.  External Re-keying Mechanisms . . . . . . . . . . . . . . . .  11
     5.1.  Methods of Key Lifetime Control . . . . . . . . . . . . .  14
     5.2.  Parallel Constructions  . . . . . . . . . . . . . . . . .  14
       5.2.1.  Parallel Construction Based on a KDF on a Block
               Cipher  . . . . . . . . . . . . . . . . . . . . . . .  15
       5.2.2.  Parallel Construction Based on a KDF on a Hash
               Function  . . . . . . . . . . . . . . . . . . . . . .  16
       5.2.3.  Tree-Based Construction . . . . . . . . . . . . . . .  16
     5.3.  Serial Constructions  . . . . . . . . . . . . . . . . . .  17
       5.3.1.  Serial Construction Based on a KDF on a Block Cipher   19
       5.3.2.  Serial Construction Based on a KDF on a Hash Function  19
     5.4.  Using Additional Entropy during Re-keying . . . . . . . .  19
   6.  Internal Re-keying Mechanisms . . . . . . . . . . . . . . . .  20
     6.1.  Methods of Key Lifetime Control . . . . . . . . . . . . .  22
     6.2.  Constructions that Do Not Require a Master Key  . . . . .  23
       6.2.1.  ACPKM Re-keying Mechanisms  . . . . . . . . . . . . .  23
       6.2.2.  CTR-ACPKM Encryption Mode . . . . . . . . . . . . . .  25
       6.2.3.  GCM-ACPKM Authenticated Encryption Mode . . . . . . .  26
     6.3.  Constructions that Require a Master Key . . . . . . . . .  29
       6.3.1.  ACPKM-Master Key Derivation from the Master Key . . .  29
       6.3.2.  CTR-ACPKM-Master Encryption Mode  . . . . . . . . . .  31
       6.3.3.  GCM-ACPKM-Master Authenticated Encryption Mode  . . .  33
       6.3.4.  CBC-ACPKM-Master Encryption Mode  . . . . . . . . . .  37
       6.3.5.  CFB-ACPKM-Master Encryption Mode  . . . . . . . . . .  39
       6.3.6.  OMAC-ACPKM-Master Authentication Mode . . . . . . . .  40
   7.  Joint Usage of External and Internal Re-keying  . . . . . . .  42
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  43
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  43
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  44
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  44
     10.2.  Informative References . . . . . . . . . . . . . . . . .  45
   Appendix A.  Test Examples  . . . . . . . . . . . . . . . . . . .  48
     A.1.  Test Examples for External Re-keying  . . . . . . . . . .  48
       A.1.1.  External Re-keying with a Parallel Construction . . .  48
       A.1.2.  External Re-keying with a Serial Construction . . . .  49
     A.2.  Test Examples for Internal Re-keying  . . . . . . . . . .  52
       A.2.1.  Internal Re-keying Mechanisms that Do Not
               Require a Master Key  . . . . . . . . . . . . . . . .  52
       A.2.2.  Internal Re-keying Mechanisms with a Master Key . . .  56
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  69
   Contributors  . . . . . . . . . . . . . . . . . . . . . . . . . .  69
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  69



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1.  Introduction

   A certain maximum amount of data can be safely encrypted when
   encryption is performed under a single key.  Hereinafter, this amount
   will be referred to as the "key lifetime".  The need for such a
   limitation is dictated by the following methods of cryptanalysis:

   1.  Methods based on the combinatorial properties of the used block
       cipher mode of operation

          These methods do not depend on the underlying block cipher.
          Common mode restrictions derived from such methods are of
          order 2^{n/2}, where n is a block size defined in Section 3.
          [Sweet32] includes an example of an attack that is based on
          such methods.

   2.  Methods based on side-channel analysis issues

          In most cases, these methods do not depend on the used
          encryption modes and weakly depend on the used cipher
          features.  Limitations resulting from these considerations are
          usually the most restrictive ones.  [TEMPEST] is an example of
          an attack that is based on such methods.

   3.  Methods based on the properties of the used block cipher

          The most common methods of this type are linear and
          differential cryptanalysis [LDC].  In most cases, these
          methods do not depend on the used modes of operation.  In the
          case of secure block ciphers, bounds resulting from such
          methods are roughly the same as the natural bounds of 2^n and
          are dominated by the other bounds above.  Therefore, they can
          be excluded from the considerations here.

   As a result, it is important to replace a key when the total size of
   the processed plaintext under that key approaches the lifetime
   limitation.  A specific value of the key lifetime should be
   determined in accordance with some safety margin for protocol
   security and the methods outlined above.

   Suppose L is a key lifetime limitation in some protocol P.  For
   simplicity, assume that all messages have the same length m.  Hence,
   the number of messages q that can be processed with a single key K
   should be such that m * q <= L.  This can be depicted graphically as
   a rectangle with sides m and q enclosed by area L (see Figure 1).






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                      +------------------------+
                      |                      L |
                      | +--------m---------+   |
                      | |==================|   |
                      | |==================|   |
                      | q==================|   |       m * q <= L
                      | |==================|   |
                      | |==================|   |
                      | +------------------+   |
                      +------------------------+

         Figure 1: Graphic Display of the Key Lifetime Limitation

   In practice, the amount of data that corresponds to limitation L may
   not be enough.  The simplest and obvious solution in this situation
   is a regular renegotiation of an initial key after processing this
   threshold amount of data L.  However, this reduces the total
   performance, since it usually entails termination of application data
   transmission, additional service messages, the use of a random number
   generator, and many other additional calculations, including
   resource-intensive public key cryptography.

   For protocols based on block ciphers or stream ciphers, a more
   efficient way to increase the key lifetime is to use various
   re-keying mechanisms.  This specification considers re-keying
   mechanisms for block ciphers only; re-keying mechanisms typical for
   stream ciphers (e.g., [Pietrzak2009], [FPS2012]) are beyond the scope
   of this document.

   Re-keying mechanisms can be applied at the different protocol levels:
   the block cipher level (this approach is known as fresh re-keying and
   is described, for instance, in [FRESHREKEYING]; the block cipher mode
   of operation level (see Section 6); and the protocol level above the
   block cipher mode of operation (see Section 5).  The usage of the
   first approach is highly inefficient due to the key changing after
   each message block is processed.  Moreover, fresh re-keying
   mechanisms can change the block cipher internal structure and,
   consequently, can require an additional security analysis for each
   particular block cipher.  As a result, this approach depends on
   particular primitive properties and cannot be applied to any
   arbitrary block cipher without additional security analysis.
   Therefore, fresh re-keying mechanisms go beyond the scope of this
   document.

   Thus, this document contains the list of recommended re-keying
   mechanisms that can be used in the symmetric encryption schemes based
   on the block ciphers.  These mechanisms are independent from the




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   particular block cipher specification, and their security properties
   rely only on the standard block cipher security assumption.

   This specification presents two basic approaches to extending the
   lifetime of a key while avoiding renegotiation, which were introduced
   in [AAOS2017]:

   1.  External re-keying

      External re-keying is performed by a protocol, and it is
      independent of the underlying block cipher and the mode of
      operation.  External re-keying can use parallel and serial
      constructions.  In the parallel case, data processing keys K^1,
      K^2, ... are generated directly from the initial key K
      independently of each other.  In the serial case, every data-
      processing key depends on the state that is updated after the
      generation of each new data-processing key.

      As a generalization of external parallel re-keying, an external
      tree-based mechanism can be considered.  It is specified in
      Section 5.2.3 and can be viewed as the tree generalization in
      [GGM].  Similar constructions are used in the one-way tree
      mechanism ([OWT]) and [AESDUKPT] standard.

   2.  Internal re-keying

      Internal re-keying is built into the mode, and it depends heavily
      on the properties of the mode of operation and the block size.

   The re-keying approaches extend the key lifetime for a single initial
   key by allowing the leakages to be limited (via side channels) and by
   improving the combinatorial properties of the used block cipher mode
   of operation.

   In practical applications, re-keying can be useful for protocols that
   need to operate in hostile environments or under restricted resource
   conditions (e.g., those that require lightweight cryptography, where
   ciphers have a small block size that imposes strict combinatorial
   limitations).  Moreover, mechanisms that use external or internal
   re-keying may provide some protection against possible future attacks
   (by limiting the number of plaintext-ciphertext pairs that an
   adversary can collect) and some properties of forward or backward
   security (meaning that past or future data-processing keys remain
   secure even if the current key is compromised; see [AbBell] for more
   details).  External or internal re-keying can be used in network
   protocols as well as in the systems for data-at-rest encryption.





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   Depending on the concrete protocol characteristics, there might be
   situations in which both external and internal re-keying mechanisms
   (see Section 7) can be applied.  For example, a similar approach was
   used in Taha's tree construction (see [TAHA]).

   Note that there are key-updating (key regression) algorithms (e.g.,
   [FKK2005] and [KMNT2003]) that are called "re-keying" as well, but
   they pursue goals other than increasing the key lifetime.  Therefore,
   key regression algorithms are excluded from the considerations here.

   This document represents the consensus of the Crypto Forum Research
   Group (CFRG).

2.  Conventions Used in This Document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

3.  Basic Terms and Definitions

   This document uses the following terms and definitions for the sets
   and operations on the elements of these sets:

   V*      the set of all bit strings of a finite length (hereinafter
           referred to as strings), including the empty string;

   V_s     the set of all bit strings of length s, where s is a
           non-negative integer;

   |X|     the bit length of the bit string X;

   A | B   the concatenation of strings A and B both belonging to V*,
           i.e., a string in V_{|A|+|B|}, where the left substring in
           V_|A| is equal to A and the right substring in V_|B| is equal
           to B;

   (xor)   the exclusive-or of two bit strings of the same length;

   Z_{2^n} the ring of residues modulo 2^n;

   Int_s: V_s -> Z_{2^s}
           the transformation that maps the string a = (a_s, ... , a_1)
           in V_s into the integer Int_s(a) = 2^{s-1} * a_s + ... + 2 *
           a_2 + a_1 (the interpretation of the binary string as an
           integer);



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   Vec_s: Z_{2^s} -> V_s
           the transformation inverse to the mapping Int_s (the
           interpretation of an integer as a binary string);

   MSB_i: V_s -> V_i
           the transformation that maps the string a = (a_s, ... , a_1)
           in V_s into the string MSB_i(a) = (a_s, ... , a_{s-i+1}) in
           V_i (most significant bits);

   LSB_i: V_s -> V_i
           the transformation that maps the string a = (a_s, ... , a_1)
           in V_s into the string LSB_i(a) = (a_i, ... , a_1) in V_i
           (least significant bits);

   Inc_c: V_s -> V_s
           the transformation that maps the string a = (a_s, ... , a_1)
           in V_s into the string Inc_c(a) = MSB_{|a|-c}(a) |
           Vec_c(Int_c(LSB_c(a)) + 1(mod 2^c)) in V_s (incrementing the
           least significant c bits of the bit string, regarded as the
           binary representation of an integer);

   a^s     the string in V_s that consists of s 'a' bits;

   E_{K}: V_n -> V_n
           the block cipher permutation under the key K in V_k;

   ceil(x) the smallest integer that is greater than or equal to x;

   floor(x)
           the biggest integer that is less than or equal to x;

   k       the bit length of the K; k is assumed to be divisible by 8;

   n       the block size of the block cipher (in bits); n is assumed to
           be divisible by 8;

   b       the number of data blocks in the plaintext P (b =
           ceil(|P|/n));

   N       the section size (the number of bits that are processed with
           one section key before this key is transformed).

   A plaintext message P and the corresponding ciphertext C are divided
   into b = ceil(|P|/n) blocks, denoted as P = P_1 | P_2 | ... | P_b and
   C = C_1 | C_2 | ... | C_b, respectively.  The first b-1 blocks P_i
   and C_i are in V_n for i = 1, 2, ... , b-1.  The b-th blocks P_b and
   C_b may be incomplete blocks, i.e., in V_r, where r <= n if not
   otherwise specified.



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4.  Choosing Constructions and Security Parameters

   External re-keying is an approach assuming that a key is transformed
   after encrypting a limited number of entire messages.  The external
   re-keying method is chosen at the protocol level, regardless of the
   underlying block cipher or the encryption mode.  External re-keying
   is recommended for protocols that process relatively short messages
   or protocols that have a way to divide a long message into manageable
   pieces.  Through external re-keying, the number of messages that can
   be securely processed with a single initial key K is substantially
   increased without a loss of message length.

   External re-keying has the following advantages

   1.  It increases the lifetime of an initial key by increasing the
       number of messages processed with this key.

   2.  It has minimal impact on performance when the number of messages
       processed under one initial key is sufficiently large.

   3.  It provides forward and backward security of data-processing
       keys.

   However, the use of external re-keying has the following
   disadvantage: in cases with restrictive key lifetime limitations, the
   message sizes can become obstructive due to the impossibility of
   processing sufficiently large messages, so it may be necessary to
   perform additional fragmentation at the protocol level.  For example,
   if the key lifetime L is 1 GB and the message length m = 3 GB, then
   this message cannot be processed as a whole, and it should be divided
   into three fragments that will be processed separately.

   Internal re-keying is an approach assuming that a key is transformed
   during each separate message processing.  Such procedures are
   integrated into the base modes of operations, so every internal
   re-keying mechanism is defined for the particular operation mode and
   the block size of the used cipher.  Internal re-keying is recommended
   for protocols that process long messages: the size of each single
   message can be substantially increased without loss in the number of
   messages that can be securely processed with a single initial key.

   Internal re-keying has the following advantages:

   1.  It increases the lifetime of an initial key by increasing the
       size of the messages processed with one initial key.

   2.  It has minimal impact on performance.




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   3.  Internal re-keying mechanisms without a master key do not affect
       short-message transformation at all.

   4.  It is transparent (works like any mode of operation): it does not
       require changes of initialization vectors (IVs) and a restart of
       MACing.

   However, the use of internal re-keying has the following
   disadvantages:

   1.  a specific method must not be chosen independently of a mode of
       operation.

   2.  internal re-keying mechanisms without a master key do not provide
       backward security of data-processing keys.

   Any block cipher modes of operations with internal re-keying can be
   jointly used with any external re-keying mechanisms.  Such joint
   usage increases both the number of messages processed with one
   initial key and their maximum possible size.

   If the adversary has access to the data-processing interface, the use
   of the same cryptographic primitives both for data-processing and
   re-keying transformation decreases the code size but can lead to some
   possible vulnerabilities (the possibility of mounting a chosen-
   plaintext attack may lead to the compromise of the following keys).
   This vulnerability can be eliminated by using different primitives
   for data processing and re-keying, e.g., block cipher for data
   processing and hash for re-keying (see Section 5.2.2 and
   Section 5.3.2).  However, in this case, the security of the whole
   scheme cannot be reduced to standard notions like a pseudorandom
   function (PRF) or pseudorandom permutation (PRP), so security
   estimations become more difficult and unclear.

   Summing up the abovementioned issues briefly:

   1.  If a protocol assumes processing of long records (e.g., [CMS]),
       internal re-keying should be used.  If a protocol assumes
       processing of a significant number of ordered records, which can
       be considered as a single data stream (e.g., [TLS], [SSH]),
       internal re-keying may also be used.

   2.  For protocols that allow out-of-order delivery and lost records
       (e.g., [DTLS], [ESP]), external re-keying should be used as, in
       this case, records cannot be considered as a single data stream.
       If the records are also long enough, internal re-keying should
       also be used during each separate message processing.




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   For external re-keying:

   1.  If it is desirable to separate transformations used for data
       processing and key updates, hash function-based re-keying should
       be used.

   2.  If parallel data processing is required, then parallel external
       re-keying should be used.

   3.  If restrictive key lifetime limitations are present, external
       tree-based re-keying should be used.

   For internal re-keying:

   1.  If the property of forward and backward security is desirable for
       data-processing keys and if additional key material can be easily
       obtained for the data-processing stage, internal re-keying with a
       master key should be used.

5.  External Re-keying Mechanisms

   This section presents an approach to increasing the initial key
   lifetime by using a transformation of a data-processing key (frame
   key) after processing a limited number of entire messages (frame).
   The approach provides external parallel and serial re-keying
   mechanisms (see [AbBell]).  These mechanisms use initial key K only
   for frame key generation and never use it directly for data
   processing.  Such mechanisms operate outside of the base modes of
   operations and do not change them at all; therefore, they are called
   "external re-keying" mechanisms in this document.

   External re-keying mechanisms are recommended for usage in protocols
   that process quite small messages, since the maximum gain in
   increasing the initial key lifetime is achieved by increasing the
   number of messages.

   External re-keying increases the initial key lifetime through the
   following approach.  Suppose there is a protocol P with some mode of
   operation (base encryption or authentication mode).  Let L1 be a key
   lifetime limitation induced by side-channel analysis methods (side-
   channel limitation), let L2 be a key lifetime limitation induced by
   methods based on the combinatorial properties of a used mode of
   operation (combinatorial limitation), and let q1, q2 be the total
   numbers of messages of length m that can be safely processed with an
   initial key K according to these limitations.






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   Let L = min(L1, L2), q = min(q1, q2), and q * m <= L.  As the L1
   limitation is usually much stronger than the L2 limitation (L1 < L2),
   the final key lifetime restriction is equal to the most restrictive
   limitation L1.  Thus, as displayed in Figure 2, without re-keying,
   only q1 (q1 * m <= L1) messages can be safely processed.

                         <--------m------->
                         +----------------+ ^ ^
                         |================| | |
                         |================| | |
                     K-->|================| q1|
                         |================| | |
                         |==============L1| | |
                         +----------------+ v |
                         |                |   |
                         |                |   |
                         |                |   q2
                         |                |   |
                         |                |   |
                         |                |   |
                         |                |   |
                         |                |   |
                         |                |   |
                         |                |   |
                         |                |   |
                         |              L2|   |
                         +----------------+   v

             Figure 2: Basic Principles of Message Processing
                        without External Re-keying

   Suppose that the safety margin for the protocol P is fixed and the
   external re-keying approach is applied to the initial key K to
   generate the sequence of frame keys.  The frame keys are generated in
   such a way that the leakage of a previous frame key does not have any
   impact on the following one, so the side-channel limitation L1 is
   switched off.  Thus, the resulting key lifetime limitation of the
   initial key K can be calculated on the basis of a new combinatorial
   limitation L2'.  It is proven (see [AbBell]) that the security of the
   mode of operation that uses external re-keying leads to an increase
   when compared to base mode without re-keying (thus, L2 < L2').
   Hence, as displayed in Figure 3, the resulting key lifetime
   limitation if using external re-keying can be increased up to L2'.








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                         <--------m------->
                   K     +----------------+
                   |     |================|
                   v     |================|
                  K^1--> |================|
                   |     |================|
                   |     |==============L1|
                   |     +----------------+
                   |     |================|
                   v     |================|
                  K^2--> |================|
                   |     |================|
                   |     |==============L1|
                   |     +----------------+
                   |     |================|
                   v     |================|
                  ...    |      . . .     |
                         |                |
                         |                |
                         |              L2|
                         +----------------+
                         |                |
                        ...              ...
                         |             L2'|
                         +----------------+

             Figure 3: Basic Principles of Message Processing
                          with External Re-keying

   Note: The key transformation process is depicted in a simplified
   form.  A specific approach (parallel and serial) is described below.

   Consider an example.  Let the message size in a protocol P be equal
   to 1 KB.  Suppose L1 = 128 MB and L2 = 1 TB.  Thus, if an external
   re-keying mechanism is not used, the initial key K must be
   renegotiated after processing 128 MB / 1 KB = 131072 messages.

   If an external re-keying mechanism is used, the key lifetime
   limitation L1 goes off.  Hence, the resulting key lifetime limitation
   L2' can be set to more than 1 TB.  Thus, if an external re-keying
   mechanism is used, more than 1 TB / 1 KB = 2^30 messages can be
   processed before the initial key K is renegotiated.  This is 8192
   times greater than the number of messages that can be processed when
   an external re-keying mechanism is not used.







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5.1.  Methods of Key Lifetime Control

   Suppose L is an amount of data that can be safely processed with one
   frame key.  For i in {1, 2, ... , t}, the frame key K^i (see Figures
   4 and 6) should be transformed after processing q_i messages, where
   q_i can be calculated in accordance with one of the following
   approaches:

   Explicit approach:

      q_i is such that |M^{i,1}| + ... + |M^{i,q_i}| <= L, |M^{i,1}| +
      ... + |M^{i,q_i+1}| > L.
      This approach allows use of the frame key K^i in an almost optimal
      way, but it can be applied only when messages cannot be lost or
      reordered (e.g., TLS records).

   Implicit approach:

      q_i = L / m_max, i = 1, ... , t.
      The amount of data processed with one frame key K^i is calculated
      under the assumption that every message has the maximum length
      m_max.  Hence, this amount can be considerably less than the key
      lifetime limitation L.  On the other hand, this approach can be
      applied when messages may be lost or reordered (e.g., DTLS
      records).

   Dynamic key changes:

      We can organize the key change using the Protected Point to Point
      ([P3]) solution by building a protected tunnel between the
      endpoints in which the information about frame key updating can be
      safely passed across.  This can be useful, for example, when we
      want the adversary to not detect the key change during the
      protocol evaluation.

5.2.  Parallel Constructions

   External parallel re-keying mechanisms generate frame keys K^1, K^2,
   ... directly from the initial key K independently of each other.

   The main idea behind external re-keying with a parallel construction
   is presented in Figure 4:









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   Maximum message size = m_max.
   _____________________________________________________________

                                   m_max
                             <---------------->
                   M^{1,1}   |===             |
                   M^{1,2}   |=============== |
         +->K^1-->   ...            ...
         |         M^{1,q_1} |========        |
         |
         |
         |         M^{2,1}   |================|
         |         M^{2,2}   |=====           |
   K-----|->K^2-->   ...            ...
         |         M^{2,q_2} |==========      |
         |
        ...
         |         M^{t,1}   |============    |
         |         M^{t,2}   |=============   |
         +->K^t-->   ...            ...
                   M^{t,q_t} |==========      |

   _____________________________________________________________

             Figure 4: External Parallel Re-keying Mechanisms

   The frame key K^i, i = 1, ... , t - 1 is updated after processing a
   certain number of messages (see Section 5.1).

5.2.1.  Parallel Construction Based on a KDF on a Block Cipher

   The ExtParallelC re-keying mechanism is based on the key derivation
   function on a block cipher and is used to generate t frame keys as
   follows:

      K^1 | K^2 | ... | K^t = ExtParallelC(K, t * k) = MSB_{t *
      k}(E_{K}(Vec_n(0)) |
      E_{K}(Vec_n(1)) | ... | E_{K}(Vec_n(R - 1))),

   where R = ceil(t * k/n).











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5.2.2.  Parallel Construction Based on a KDF on a Hash Function

   The ExtParallelH re-keying mechanism is based on the key derivation
   function HKDF-Expand, described in [RFC5869], and is used to generate
   t frame keys as follows:

      K^1 | K^2 | ... | K^t = ExtParallelH(K, t * k) = HKDF-Expand(K,
      label, t * k),

   where label is a string (may be a zero-length string) that is defined
   by a specific protocol.

5.2.3.  Tree-Based Construction

   The application of an external tree-based mechanism leads to the
   construction of the key tree with the initial key K (root key) at the
   0 level and the frame keys K^1, K^2, ... at the last level, as
   described in Figure 5.

                            K_root = K
                      ___________|___________
                     |          ...          |
                     V                       V
                    K{1,1}                K{1,W1}
               ______|______           ______|______
              |     ...     |         |     ...     |
              V             V         V             V
           K{2,1}       K{2,W2}  K{2,(W1-1)*W2+1} K{2,W1*W2}
            __|__         __|__     __|__         __|__
           | ... |       | ... |   | ... |       | ... |
           V     V       V     V   V     V       V     V
        K{3,1}  ...     ...   ... ...   ...     ...   K{3,W1*W2*W3}

         ...                                           ...
        __|__                   ...                   __|__
       | ... |                                       | ... |
       V     V                                       V     V
   K{h,1}   K{h,Wh}         K{h,(W1*...*W{h-1}-1)*Wh+1}  K{h,W1*...*Wh}
     //       \\                                  //       \\
   K^1       K^{Wh}        K^{(W1*...*W{h-1}-1)*Wh+1}     K^{W1*...*Wh}
   ____________________________________________________________________

                  Figure 5: External Tree-Based Mechanism

   The tree height h and the number of keys Wj, j in {1, ... , h}, which
   can be partitioned from the "parent" key, are defined in accordance
   with a specific protocol and key lifetime limitations for the used
   derivation functions.



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   Each j-level key K{j,w}, where j in {1, ... , h}, w in {1, ... , W1 *
   ... * Wj}, is derived from the (j-1)-level "parent" key K{j-1,
   ceil(w/Wi)} (and other appropriate input data) using the j-th level
   derivation function.  This function can be based on the block cipher
   function or on the hash function and is defined in accordance with a
   specific protocol.

   The i-th frame K^i, i in {1, 2, ... , W1*...*Wh}, can be calculated
   as follows:

      K^i = ExtKeyTree(K, i) = KDF_h(KDF_{h-1}(... KDF_1(K, ceil(i / (W2
      * ... * Wh)) ... , ceil(i / Wh)), i),

   where KDF_j is the j-th level derivation function that takes two
   arguments (the parent key value and the integer in a range from 1 to
   W1 * ... * Wj) and outputs the j-th level key value.

   The frame key K^i is updated after processing a certain number of
   messages (see Section 5.1).

   In order to create an efficient implementation, during frame key K^i
   generation, the derivation functions KDF_j, j in {1, ... , h-1}
   should be used only when ceil(i / (W{j+1} * ... * Wh)) != ceil((i -
   1) / (W{j+1} * ... * Wh)); otherwise, it is necessary to use a
   previously generated value.  This approach also makes it possible to
   take countermeasures against side-channel attacks.

   Consider an example.  Suppose h = 3, W1 = W2 = W3 = W, and KDF_1,
   KDF_2, KDF_3 are key derivation functions based on the
   KDF_GOSTR3411_2012_256 (hereafter simply KDF) function described in
   [RFC7836].  The resulting ExtKeyTree function can be defined as
   follows:

      ExtKeyTree(K, i) = KDF(KDF(KDF(K, "level1", ceil(i / W^2)),
      "level2", ceil(i / W)), "level3", i).

   where i in {1, 2, ... , W^3}.

   A structure similar to the external tree-based mechanism can be found
   in Section 6 of [NISTSP800-108].

5.3.  Serial Constructions

   External serial re-keying mechanisms generate frame keys, each of
   which depends on the secret state (K*_1, K*_2, ...) that is updated
   after the generation of each new frame key; see Figure 6.  Similar
   approaches are used in the [SIGNAL] protocol and the [TLS] updating




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   traffic key mechanism and were proposed for use in the [U2F]
   protocol.

   External serial re-keying mechanisms have the obvious disadvantage of
   being impossible to implement in parallel, but they may be the
   preferred option if additional forward secrecy is desirable.  If all
   keys are securely deleted after usage, the compromise of a current
   secret state at some point does not lead to a compromise of all
   previous secret states and frame keys.  In terms of [TLS], compromise
   of application_traffic_secret_N does not compromise all previous
   application_traffic_secret_i, i < N.

   The main idea behind external re-keying with a serial construction is
   presented in Figure 6:

   Maximum message size = m_max.
   _____________________________________________________________
                                        m_max
                                  <---------------->
                        M^{1,1}   |===             |
                        M^{1,2}   |=============== |
   K*_1 = K --->K^1-->    ...            ...
     |                  M^{1,q_1} |========        |
     |
     |
     |                  M^{2,1}   |================|
     v                  M^{2,2}   |=====           |
   K*_2 ------->K^2-->    ...            ...
     |                  M^{2,q_2} |==========      |
     |
    ...
     |                  M^{t,1}   |============    |
     v                  M^{t,2}   |=============   |
   K*_t ------->K^t-->    ...            ...
                        M^{t,q_t} |==========      |


   _____________________________________________________________

              Figure 6: External Serial Re-keying Mechanisms

   The frame key K^i, i = 1, ... , t - 1, is updated after processing a
   certain number of messages (see Section 5.1).








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5.3.1.  Serial Construction Based on a KDF on a Block Cipher

   The frame key K^i is calculated using the ExtSerialC transformation
   as follows:

      K^i = ExtSerialC(K, i) =
      MSB_k(E_{K*_i}(Vec_n(0)) |E_{K*_i}(Vec_n(1)) | ... |
      E_{K*_i}(Vec_n(J - 1))),

   where J = ceil(k / n), i = 1, ... , t, K*_i is calculated as follows:

      K*_1 = K,

      K*_{j+1} = MSB_k(E_{K*_j}(Vec_n(J)) | E_{K*_j}(Vec_n(J + 1)) |
      ... |
      E_{K*_j}(Vec_n(2 * J - 1))),

   where j = 1, ... , t - 1.

5.3.2.  Serial Construction Based on a KDF on a Hash Function

   The frame key K^i is calculated using the ExtSerialH transformation
   as follows:

      K^i = ExtSerialH(K, i) = HKDF-Expand(K*_i, label1, k),

   where i = 1, ... , t; HKDF-Expand is the HMAC-based key derivation
   function, as described in [RFC5869]; and K*_i is calculated as
   follows:

      K*_1 = K,

      K*_{j+1} = HKDF-Expand(K*_j, label2, k), where j = 1, ... , t - 1,

   where label1 and label2 are different strings from V* that are
   defined by a specific protocol (see, for example, the algorithm for
   updating traffic keys in TLS 1.3 [TLS]).

5.4.  Using Additional Entropy during Re-keying

   In many cases, using additional entropy during re-keying won't
   increase security but may give a false sense of that.  Therefore, one
   can rely on additional entropy only after conducting a deep security
   analysis.  For example, good PRF constructions do not require
   additional entropy for the quality of keys, so, in most cases, there
   is no need to use additional entropy with external re-keying
   mechanisms based on secure KDFs.  However, in some situations, mixed-
   in entropy can still increase security in the case of a time-limited



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   but complete breach of the system when an adversary can access the
   frame-key generation interface but cannot reveal the master keys
   (e.g., when the master keys are stored in a Hardware Security Module
   (HSM)).

   For example, an external parallel construction based on a KDF on a
   hash function with a mixed-in entropy can be described as follows:

      K^i = HKDF-Expand(K, label_i, k),

   where label_i is additional entropy that must be sent to the
   recipient (e.g., sent jointly with an encrypted message).  The
   entropy label_i and the corresponding key K^i must be generated
   directly before message processing.

6.  Internal Re-keying Mechanisms

   This section presents an approach to increasing the key lifetime by
   using a transformation of a data-processing key (section key) during
   each separate message processing.  Each message is processed starting
   with the same key (the first section key), and each section key is
   updated after processing N bits of the message (section).

   This section provides internal re-keying mechanisms called ACPKM
   (Advanced Cryptographic Prolongation of Key Material) and ACPKM-
   Master that do not use a master key and use a master key,
   respectively.  Such mechanisms are integrated into the base modes of
   operation and actually form new modes of operation.  Therefore, they
   are called "internal re-keying" mechanisms in this document.

   Internal re-keying mechanisms are recommended to be used in protocols
   that process large single messages (e.g., CMS messages), since the
   maximum gain in increasing the key lifetime is achieved by increasing
   the length of a message, while it provides almost no increase in the
   number of messages that can be processed with one initial key.

   Internal re-keying increases the key lifetime through the following
   approach.  Suppose protocol P uses some base mode of operation.  Let
   L1 and L2 be a side channel and combinatorial limitations,
   respectively, and for some fixed number of messages q, let m1, m2 be
   the lengths of messages that can be safely processed with a single
   initial key K according to these limitations.

   Thus, the approach without re-keying (analogous to Section 5) yields
   a final key lifetime restriction equal to L1, and only q messages of
   the length m1 can be safely processed; see Figure 7.





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                K
                |
                v
      ^ +----------------+------------------------------------+
      | |==============L1|                                  L2|
      | |================|                                    |
      q |================|                                    |
      | |================|                                    |
      | |================|                                    |
      v +----------------+------------------------------------+
        <-------m1------->
        <----------------------------m2----------------------->

             Figure 7: Basic Principles of Message Processing
                        without Internal Re-keying

   Suppose that the safety margin for the protocol P is fixed and the
   internal re-keying approach is applied to the base mode of operation.
   Suppose further that every message is processed with a section key,
   which is transformed after processing N bits of data, where N is a
   parameter.  If q * N does not exceed L1, then the side-channel
   limitation L1 goes off, and the resulting key lifetime limitation of
   the initial key K can be calculated on the basis of a new
   combinatorial limitation L2'.  The security of the mode of operation
   that uses internal re-keying increases when compared to the base mode
   of operation without re-keying (thus, L2 < L2').  Hence, as displayed
   in Figure 8, the resulting key lifetime limitation if using internal
   re-keying can be increased up to L2'.

     K-----> K^1-------------> K^2 -----------> . . .
             |                 |
             v                 v
   ^ +---------------+---------------+------------------+--...--+
   | |=============L1|=============L1|======          L2|    L2'|
   | |===============|===============|======            |       |
   q |===============|===============|====== . . .      |       |
   | |===============|===============|======            |       |
   | |===============|===============|======            |       |
   v +---------------+---------------+------------------+--...--+
     <-------N------->

             Figure 8: Basic Principles of Message Processing
                          with Internal Re-keying

   Note: The key transformation process is depicted in a simplified
   form.  A specific approach (ACPKM and ACPKM-Master re-keying
   mechanisms) is described below.




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   Since the performance of encryption can slightly decrease for rather
   small values of N, the maximum possible value should be selected for
   parameter N for a particular protocol in order to provide the
   necessary key lifetime for the considered security models.

   Consider an example.  Suppose L1 = 128 MB and L2 = 10 TB.  Let the
   message size in the protocol be large/unlimited (which may exhaust
   the whole key lifetime L2).  The most restrictive resulting key
   lifetime limitation is equal to 128 MB.

   Thus, there is a need to put a limit on the maximum message size
   m_max.  For example, if m_max = 32 MB, it may happen that the
   renegotiation of initial key K would be required after processing
   only four messages.

   If an internal re-keying mechanism with section size N = 1 MB is
   used, more than L1 / N = 128 MB / 1 MB = 128 messages can be
   processed before the renegotiation of initial key K (instead of four
   messages when an internal re-keying mechanism is not used).  Note
   that only one section of each message is processed with the section
   key K^i, and, consequently, the key lifetime limitation L1 goes off.
   Hence, the resulting key lifetime limitation L2' can be set to more
   than 10 TB (in cases when a single large message is processed using
   the initial key K).

6.1.  Methods of Key Lifetime Control

   Suppose L is an amount of data that can be safely processed with one
   section key and N is a section size (fixed parameter).  Suppose
   M^{i}_1 is the first section of message M^{i}, i = 1, ... , q (see
   Figures 9 and 10); the parameter q can then be calculated in
   accordance with one of the following two approaches:

   o  Explicit approach:
      q_i is such that |M^{1}_1| + ... + |M^{q}_1| <= L, |M^{1}_1| + ...
      + |M^{q+1}_1| > L
      This approach allows use of the section key K^i in an almost
      optimal way, but it can be applied only when messages cannot be
      lost or reordered (e.g., TLS records).

   o  Implicit approach:
      q = L / N.
      The amount of data processed with one section key K^i is
      calculated under the assumption that the length of every message
      is equal to or greater than section size N and thus can be
      considerably less than the key lifetime limitation L.  On the
      other hand, this approach can be applied when messages may be lost
      or reordered (e.g., DTLS records).



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6.2.  Constructions that Do Not Require a Master Key

   This section describes the block cipher modes that use the ACPKM
   re-keying mechanism, which does not use a master key; an initial key
   is used directly for the data encryption.

6.2.1.  ACPKM Re-keying Mechanisms

   This section defines a periodical key transformation without a master
   key, which is called the ACPKM re-keying mechanism.  This mechanism
   can be applied to one of the base encryption modes (CTR and GCM block
   cipher modes) to get an extension of this encryption mode that uses
   periodical key transformation without a master key.  This extension
   can be considered as a new encryption mode.

   An additional parameter that defines the functioning of base
   encryption modes with the ACPKM re-keying mechanism is the section
   size N.  The value of N is measured in bits and is fixed within a
   specific protocol based on the requirements of the system capacity
   and the key lifetime.  The section size N MUST be divisible by the
   block size n.

   The main idea behind internal re-keying without a master key is
   presented in Figure 9:

   Section size = const = N,
   maximum message size = m_max.
   ____________________________________________________________________

                 ACPKM       ACPKM              ACPKM
          K^1 = K ---> K^2 ---...-> K^{l_max-1} ----> K^{l_max}
              |          |                |           |
              |          |                |           |
              v          v                v           v
   M^{1} |==========|==========| ... |==========|=======:  |
   M^{2} |==========|==========| ... |===       |       :  |
     .        .          .        .       .          .  :
     :        :          :        :       :          :  :
   M^{q} |==========|==========| ... |==========|=====  :  |
                      section                           :
                    <---------->                      m_max
                       N bit
   ___________________________________________________________________
   l_max = ceil(m_max/N).

             Figure 9: Internal Re-keying without a Master Key





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   During the processing of the input message M with the length m in
   some encryption mode that uses the ACPKM key transformation of the
   initial key K, the message is divided into l = ceil(m / N) sections
   (denoted as M = M_1 | M_2 | ... | M_l, where M_i is in V_N for i in
   {1, 2, ... , l - 1} and M_l is in V_r, r <= N).  The first section of
   each message is processed with the section key K^1 = K.  To process
   the (i + 1)-th section of each message, the section key K^{i+1} is
   calculated using the ACPKM transformation as follows:

      K^{i+1} = ACPKM(K^i) = MSB_k(E_{K^i}(D_1) | ... | E_{K^i}(D_J)),

   where J = ceil(k/n) and D_1, D_2, ... , D_J are in V_n and are
   calculated as follows:

      D_1 | D_2 | ... | D_J = MSB_{J * n}(D),

   where D is the following constant in V_{1024}:

             D = ( 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87
                 | 88 | 89 | 8a | 8b | 8c | 8d | 8e | 8f
                 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97
                 | 98 | 99 | 9a | 9b | 9c | 9d | 9e | 9f
                 | a0 | a1 | a2 | a3 | a4 | a5 | a6 | a7
                 | a8 | a9 | aa | ab | ac | ad | ae | af
                 | b0 | b1 | b2 | b3 | b4 | b5 | b6 | b7
                 | b8 | b9 | ba | bb | bc | bd | be | bf
                 | c0 | c1 | c2 | c3 | c4 | c5 | c6 | c7
                 | c8 | c9 | ca | cb | cc | cd | ce | cf
                 | d0 | d1 | d2 | d3 | d4 | d5 | d6 | d7
                 | d8 | d9 | da | db | dc | dd | de | df
                 | e0 | e1 | e2 | e3 | e4 | e5 | e6 | e7
                 | e8 | e9 | ea | eb | ec | ed | ee | ef
                 | f0 | f1 | f2 | f3 | f4 | f5 | f6 | f7
                 | f8 | f9 | fa | fb | fc | fd | fe | ff)

   Note: The constant D is such that D_1, ... , D_J are pairwise
   different for any allowed n and k values.

   Note: The highest bit of each octet of the constant D is equal to 1.
   This condition is important as, in conjunction with a certain mode
   message length limitation, it allows prevention of collisions of
   block cipher permutation inputs in cases with key transformation and
   message processing (for more details, see Section 4.4 of [AAOS2017]).








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6.2.2.  CTR-ACPKM Encryption Mode

   This section defines a CTR-ACPKM encryption mode that uses the ACPKM
   internal re-keying mechanism for the periodical key transformation.

   The CTR-ACPKM mode can be considered as the base encryption mode CTR
   (see [MODES]) extended by the ACPKM re-keying mechanism.

   The CTR-ACPKM encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512.

   o  128 <= k <= 512.

   o  The number c of bits in a specific part of the block to be
      incremented is such that 32 <= c <= 3 / 4 n, where c is a multiple
      of 8.

   o  The maximum message size m_max = n * 2^{c-1}.

   The CTR-ACPKM mode encryption and decryption procedures are defined
   as follows:

   +----------------------------------------------------------------+
   |  CTR-ACPKM-Encrypt(N, K, ICN, P)                               |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - section size N,                                             |
   |  - initial key K,                                              |
   |  - initial counter nonce ICN in V_{n-c},                       |
   |  - plaintext P = P_1 | ... | P_b, |P| <= m_max.                |
   |  Output:                                                       |
   |  - ciphertext C.                                               |
   |----------------------------------------------------------------|
   |  1. CTR_1 = ICN | 0^c                                          |
   |  2. For j = 2, 3, ... , b do                                   |
   |         CTR_{j} = Inc_c(CTR_{j-1})                             |
   |  3. K^1 = K                                                    |
   |  4. For i = 2, 3, ... , ceil(|P| / N)                          |
   |         K^i = ACPKM(K^{i-1})                                   |
   |  5. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j * n / N),                                   |
   |         G_j = E_{K^i}(CTR_j)                                   |
   |  6. C = P (xor) MSB_{|P|}(G_1 | ... | G_b)                     |
   |  7. Return C                                                   |
   +----------------------------------------------------------------+




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   +----------------------------------------------------------------+
   |  CTR-ACPKM-Decrypt(N, K, ICN, C)                               |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - section size N,                                             |
   |  - initial key K,                                              |
   |  - initial counter nonce ICN in V_{n-c},                       |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= m_max.               |
   |  Output:                                                       |
   |  - plaintext P.                                                |
   |----------------------------------------------------------------|
   |  1. P = CTR-ACPKM-Encrypt(N, K, ICN, C)                        |
   |  2. Return P                                                   |
   +----------------------------------------------------------------+

   The initial counter nonce (ICN) value for each message that is
   encrypted under the given initial key K must be chosen in a unique
   manner.

6.2.3.  GCM-ACPKM Authenticated Encryption Mode

   This section defines the GCM-ACPKM authenticated encryption mode that
   uses the ACPKM internal re-keying mechanism for the periodical key
   transformation.

   The GCM-ACPKM mode can be considered as the base authenticated
   encryption mode GCM (see [GCM]) extended by the ACPKM re-keying
   mechanism.

   The GCM-ACPKM authenticated encryption mode can be used with the
   following parameters:

   o  n in {128, 256}.

   o  128 <= k <= 512.

   o  The number c of bits in a specific part of the block to be
      incremented is such that 1 / 4 n <= c <= 1 / 2 n, c is a multiple
      of 8.

   o  Authentication tag length t.

   o  The maximum message size m_max = min{n * (2^{c-1} - 2), 2^{n/2} -
      1}.







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   The GCM-ACPKM mode encryption and decryption procedures are defined
   as follows:

   +-------------------------------------------------------------------+
   |  GHASH(X, H)                                                      |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - bit string X = X_1 | ... | X_m, X_1, ... , X_m in V_n.         |
   |  Output:                                                          |
   |  - block GHASH(X, H) in V_n.                                      |
   |-------------------------------------------------------------------|
   |  1. Y_0 = 0^n                                                     |
   |  2. For i = 1, ... , m do                                         |
   |         Y_i = (Y_{i-1} (xor) X_i) * H                             |
   |  3. Return Y_m                                                    |
   +-------------------------------------------------------------------+

   +-------------------------------------------------------------------+
   |  GCTR(N, K, ICB, X)                                               |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - section size N,                                                |
   |  - initial key K,                                                 |
   |  - initial counter block ICB,                                     |
   |  - X = X_1 | ... | X_b.                                           |
   |  Output:                                                          |
   |  - Y in V_{|X|}.                                                  |
   |-------------------------------------------------------------------|
   |  1. If X in V_0, then return Y, where Y in V_0                    |
   |  2. GCTR_1 = ICB                                                  |
   |  3. For i = 2, ... , b do                                         |
   |         GCTR_i = Inc_c(GCTR_{i-1})                                |
   |  4. K^1 = K                                                       |
   |  5. For j = 2, ... , ceil(|X| / N)                                |
   |         K^j = ACPKM(K^{j-1})                                      |
   |  6. For i = 1, ... , b do                                         |
   |         j = ceil(i * n / N),                                      |
   |         G_i = E_{K_j}(GCTR_i)                                     |
   |  7. Y = X (xor) MSB_{|X|}(G_1 | ... | G_b)                        |
   |  8. Return Y                                                      |
   +-------------------------------------------------------------------+










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   +-------------------------------------------------------------------+
   |  GCM-ACPKM-Encrypt(N, K, ICN, P, A)                               |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - section size N,                                                |
   |  - initial key K,                                                 |
   |  - initial counter nonce ICN in V_{n-c},                          |
   |  - plaintext P = P_1 | ... | P_b, |P| <= m_max,                   |
   |  - additional authenticated data A.                               |
   |  Output:                                                          |
   |  - ciphertext C,                                                  |
   |  - authentication tag T.                                          |
   |-------------------------------------------------------------------|
   |  1. H = E_{K}(0^n)                                                |
   |  2. ICB_0 = ICN | 0^{c-1} | 1                                     |
   |  3. C = GCTR(N, K, Inc_c(ICB_0), P)                               |
   |  4. u = n * ceil(|C| / n) - |C|                                   |
   |     v = n * ceil(|A| / n) - |A|                                   |
   |  5. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) |                |
   |               | Vec_{n/2}(|C|), H)                                |
   |  6. T = MSB_t(E_{K}(ICB_0) (xor) S)                               |
   |  7. Return C | T                                                  |
   +-------------------------------------------------------------------+

   +-------------------------------------------------------------------+
   |  GCM-ACPKM-Decrypt(N, K, ICN, A, C, T)                            |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - section size N,                                                |
   |  - initial key K,                                                 |
   |  - initial counter block ICN,                                     |
   |  - additional authenticated data A,                               |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= m_max,                  |
   |  - authentication tag T.                                          |
   |  Output:                                                          |
   |  - plaintext P or FAIL.                                           |
   |-------------------------------------------------------------------|
   |  1. H = E_{K}(0^n)                                                |
   |  2. ICB_0 = ICN | 0^{c-1} | 1                                     |
   |  3. P = GCTR(N, K, Inc_c(ICB_0), C)                               |
   |  4. u = n * ceil(|C| / n) - |C|                                   |
   |     v = n * ceil(|A| / n) - |A|                                   |
   |  5. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) |                |
   |               | Vec_{n/2}(|C|), H)                                |
   |  6. T' = MSB_t(E_{K}(ICB_0) (xor) S)                              |
   |  7. If T = T', then return P; else return FAIL                    |
   +-------------------------------------------------------------------+




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   The * operation on (pairs of) the 2^n possible blocks corresponds to
   the multiplication operation for the binary Galois (finite) field of
   2^n elements defined by the polynomial f as follows (analogous to
   [GCM]):

   n = 128:  f = a^128 + a^7 + a^2 + a^1 + 1,

   n = 256:  f = a^256 + a^10 + a^5 + a^2 + 1.

   The initial counter nonce ICN value for each message that is
   encrypted under the given initial key K must be chosen in a unique
   manner.

   The key for computing values E_{K}(ICB_0) and H is not updated and is
   equal to the initial key K.

6.3.  Constructions that Require a Master Key

   This section describes the block cipher modes that use the ACPKM-
   Master re-keying mechanism, which use the initial key K as a master
   key, so K is never used directly for data processing but is used for
   key derivation.

6.3.1.  ACPKM-Master Key Derivation from the Master Key

   This section defines periodical key transformation with a master key,
   which is called the ACPKM-Master re-keying mechanism.  This mechanism
   can be applied to one of the base modes of operation (CTR, GCM, CBC,
   CFB, OMAC modes) for getting an extension that uses periodical key
   transformation with a master key.  This extension can be considered
   as a new mode of operation.

   Additional parameters that define the functioning of modes of
   operation that use the ACPKM-Master re-keying mechanism are the
   section size N, the change frequency T* of the master keys K*_1,
   K*_2, ... (see Figure 10), and the size d of the section key
   material.  The values of N and T* are measured in bits and are fixed
   within a specific protocol based on the requirements of the system
   capacity and the key lifetime.  The section size N MUST be divisible
   by the block size n.  The master key frequency T* MUST be divisible
   by d and by n.










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   The main idea behind internal re-keying with a master key is
   presented in Figure 10:

   Master key frequency T*,
   section size N,
   maximum message size = m_max.
   _____________________________________________________________________

                           ACPKM                 ACPKM
                K*_1 = K----------> K*_2 ---------...-----> K*_l_max
               ___|___            ___|___                 ___|___
              |       |          |       |               |       |
              v  ...  v          v  ...  v               v  ...  v
            K[1]     K[t]     K[t+1]  K[2*t]  K[(l_max-1)t+1] K[l_max*t]
              |       |          |       |               |       |
              |       |          |       |               |       |
              v       v          v       v               v       v
   M^{1}||======|...|======||======|...|======||...||======|...|==  : ||
   M^{2}||======|...|======||======|...|======||...||======|...|====: ||
    ... ||      |   |      ||      |   |      ||   ||      |   |    : ||
   M^{q}||======|...|======||====  |...|      ||...||      |...|    : ||
          section                                                   :
         <------>                                                   :
           N bit                                                  m_max
   _____________________________________________________________________
   |K[i]| = d,
   t = T* / d,
   l_max = ceil(m_max / (N * t)).


              Figure 10: Internal Re-keying with a Master Key

   During the processing of the input message M with the length m in
   some mode of operation that uses ACPKM-Master key transformation with
   the initial key K and the master key frequency T*, the message M is
   divided into l = ceil(m / N) sections (denoted as M = M_1 | M_2 |
   ... | M_l, where M_i is in V_N for i in {1, 2, ... , l - 1} and M_l
   is in V_r, r <= N).  The j-th section of each message is processed
   with the key material K[j], j in {1, ... , l}, |K[j]| = d, which is
   calculated with the ACPKM-Master algorithm as follows:

      K[1] | ... | K[l] = ACPKM-Master(T*, K, d, l) = CTR-ACPKM-Encrypt
      (T*, K, 1^{n/2}, 0^{d*l}).

   Note: The parameters d and l MUST be such that d * l <= n *
   2^{n/2-1}.





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6.3.2.  CTR-ACPKM-Master Encryption Mode

   This section defines a CTR-ACPKM-Master encryption mode that uses the
   ACPKM-Master internal re-keying mechanism for the periodical key
   transformation.

   The CTR-ACPKM-Master encryption mode can be considered as the base
   encryption mode CTR (see [MODES]) extended by the ACPKM-Master
   re-keying mechanism.

   The CTR-ACPKM-Master encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512.

   o  128 <= k <= 512.

   o  The number c of bits in a specific part of the block to be
      incremented is such that 32 <= c <= 3 / 4 n, c is a multiple of 8.

   o  The maximum message size m_max = min{N * (n * 2^{n/2-1} / k), n *
      2^c}.

   The key material K[j] that is used for one-section processing is
   equal to K^j, where |K^j| = k bits.


























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   The CTR-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:

   +----------------------------------------------------------------+
   |  CTR-ACPKM-Master-Encrypt(N, K, T*, ICN, P)                    |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - section size N,                                             |
   |  - initial key K,                                              |
   |  - master key frequency T*,                                    |
   |  - initial counter nonce ICN in V_{n-c},                       |
   |  - plaintext P = P_1 | ... | P_b, |P| <= m_max.                |
   |  Output:                                                       |
   |  - ciphertext C.                                               |
   |----------------------------------------------------------------|
   |  1. CTR_1 = ICN | 0^c                                          |
   |  2. For j = 2, 3, ... , b do                                   |
   |         CTR_{j} = Inc_c(CTR_{j-1})                             |
   |  3. l = ceil(|P| / N)                                          |
   |  4. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l)                |
   |  5. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j * n / N),                                   |
   |         G_j = E_{K^i}(CTR_j)                                   |
   |  6. C = P (xor) MSB_{|P|}(G_1 | ... |G_b)                      |
   |  7. Return C                                                   |
   |----------------------------------------------------------------+

   +----------------------------------------------------------------+
   |  CTR-ACPKM-Master-Decrypt(N, K, T*, ICN, C)                    |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - section size N,                                             |
   |  - initial key K,                                              |
   |  - master key frequency T*,                                    |
   |  - initial counter nonce ICN in V_{n-c},                       |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= m_max.               |
   |  Output:                                                       |
   |  - plaintext P.                                                |
   |----------------------------------------------------------------|
   |  1. P = CTR-ACPKM-Master-Encrypt(N, K, T*, ICN, C)             |
   |  1. Return P                                                   |
   +----------------------------------------------------------------+

   The initial counter nonce ICN value for each message that is
   encrypted under the given initial key must be chosen in a unique
   manner.





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6.3.3.  GCM-ACPKM-Master Authenticated Encryption Mode

   This section defines a GCM-ACPKM-Master authenticated encryption mode
   that uses the ACPKM-Master internal re-keying mechanism for the
   periodical key transformation.

   The GCM-ACPKM-Master authenticated encryption mode can be considered
   as the base authenticated encryption mode GCM (see [GCM]) extended by
   the ACPKM-Master re-keying mechanism.

   The GCM-ACPKM-Master authenticated encryption mode can be used with
   the following parameters:

   o  n in {128, 256}.

   o  128 <= k <= 512.

   o  The number c of bits in a specific part of the block to be
      incremented is such that 1 / 4 n <= c <= 1 / 2 n, c is a multiple
      of 8.

   o  authentication tag length t.

   o  the maximum message size m_max = min{N * ( n * 2^{n/2-1} / k), n *
      (2^c - 2), 2^{n/2} - 1}.

   The key material K[j] that is used for the j-th section processing is
   equal to K^j, |K^j| = k bits.

   The GCM-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:

   +-------------------------------------------------------------------+
   |  GHASH(X, H)                                                      |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - bit string X = X_1 | ... | X_m, X_i in V_n for i in {1, ... ,m}|
   |  Output:                                                          |
   |  - block GHASH(X, H) in V_n                                       |
   |-------------------------------------------------------------------|
   |  1. Y_0 = 0^n                                                     |
   |  2. For i = 1, ... , m do                                         |
   |         Y_i = (Y_{i-1} (xor) X_i) * H                             |
   |  3. Return Y_m                                                    |
   +-------------------------------------------------------------------+






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   +-------------------------------------------------------------------+
   |  GCTR(N, K, T*, ICB, X)                                           |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - section size N,                                                |
   |  - initial key K,                                                 |
   |  - master key frequency T*,                                       |
   |  - initial counter block ICB,                                     |
   |  - X = X_1 | ... | X_b.                                           |
   |  Output:                                                          |
   |  - Y in V_{|X|}.                                                  |
   |-------------------------------------------------------------------|
   |  1. If X in V_0, then return Y, where Y in V_0                    |
   |  2. GCTR_1 = ICB                                                  |
   |  3. For i = 2, ... , b do                                         |
   |         GCTR_i = Inc_c(GCTR_{i-1})                                |
   |  4. l = ceil(|X| / N)                                             |
   |  5. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l)                   |
   |  6. For j = 1, ... , b do                                         |
   |         i = ceil(j * n / N),                                      |
   |         G_j = E_{K^i}(GCTR_j)                                     |
   |  7. Y = X (xor) MSB_{|X|}(G_1 | ... | G_b)                        |
   |  8. Return Y                                                      |
   +-------------------------------------------------------------------+



























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   +-------------------------------------------------------------------+
   |  GCM-ACPKM-Master-Encrypt(N, K, T*, ICN, P, A)                    |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - section size N,                                                |
   |  - initial key K,                                                 |
   |  - master key frequency T*,                                       |
   |  - initial counter nonce ICN in V_{n-c},                          |
   |  - plaintext P = P_1 | ... | P_b, |P| <= m_max.                   |
   |  - additional authenticated data A.                               |
   |  Output:                                                          |
   |  - ciphertext C,                                                  |
   |  - authentication tag T.                                          |
   |-------------------------------------------------------------------|
   |  1. K^1 = ACPKM-Master(T*, K, k, 1)                               |
   |  2. H = E_{K^1}(0^n)                                              |
   |  3. ICB_0 = ICN | 0^{c-1} | 1                                     |
   |  4. C = GCTR(N, K, T*, Inc_c(ICB_0), P)                           |
   |  5. u = n * ceil(|C| / n) - |C|                                   |
   |     v = n * ceil(|A| / n) - |A|                                   |
   |  6. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) |                |
   |               | Vec_{n/2}(|C|), H)                                |
   |  7. T = MSB_t(E_{K^1}(ICB_0) (xor) S)                             |
   |  8. Return C | T                                                  |
   +-------------------------------------------------------------------+


























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   +-------------------------------------------------------------------+
   |  GCM-ACPKM-Master-Decrypt(N, K, T*, ICN, A, C, T)                 |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - section size N,                                                |
   |  - initial key K,                                                 |
   |  - master key frequency T*,                                       |
   |  - initial counter nonce ICN in V_{n-c},                          |
   |  - additional authenticated data A.                               |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= m_max,                  |
   |  - authentication tag T.                                          |
   |  Output:                                                          |
   |  - plaintext P or FAIL.                                           |
   |-------------------------------------------------------------------|
   |  1. K^1 = ACPKM-Master(T*, K, k, 1)                               |
   |  2. H = E_{K^1}(0^n)                                              |
   |  3. ICB_0 = ICN | 0^{c-1} | 1                                     |
   |  4. P = GCTR(N, K, T*, Inc_c(ICB_0), C)                           |
   |  5. u = n * ceil(|C| / n) - |C|                                   |
   |     v = n * ceil(|A| / n) - |A|                                   |
   |  6. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) |                |
   |               | Vec_{n/2}(|C|), H)                                |
   |  7. T' = MSB_t(E_{K^1}(ICB_0) (xor) S)                            |
   |  8. If T = T', then return P; else return FAIL.                   |
   +-------------------------------------------------------------------+

   The * operation on (pairs of) the 2^n possible blocks corresponds to
   the multiplication operation for the binary Galois (finite) field of
   2^n elements defined by the polynomial f as follows (by analogy with
   [GCM]):

   n = 128:  f = a^128 + a^7 + a^2 + a^1 + 1,

   n = 256:  f = a^256 + a^10 + a^5 + a^2 + 1.

   The initial counter nonce ICN value for each message that is
   encrypted under the given initial key must be chosen in a unique
   manner.













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6.3.4.  CBC-ACPKM-Master Encryption Mode

   This section defines a CBC-ACPKM-Master encryption mode that uses the
   ACPKM-Master internal re-keying mechanism for the periodical key
   transformation.

   The CBC-ACPKM-Master encryption mode can be considered as the base
   encryption mode CBC (see [MODES]) extended by the ACPKM-Master
   re-keying mechanism.

   The CBC-ACPKM-Master encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512.

   o  128 <= k <= 512.

   o  The maximum message size m_max = N * (n * 2^{n/2-1} / k).

   In the specification of the CBC-ACPKM-Master mode, the plaintext and
   ciphertext must be a sequence of one or more complete data blocks.
   If the data string to be encrypted does not initially satisfy this
   property, then it MUST be padded to form complete data blocks.  The
   padding methods are out of the scope of this document.  An example of
   a padding method can be found in Appendix A of [MODES].

   The key material K[j] that is used for the j-th section processing is
   equal to K^j, |K^j| = k bits.

   We use D_{K} to denote the decryption function that is a permutation
   inverse to E_{K}.




















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   The CBC-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:

   +----------------------------------------------------------------+
   |  CBC-ACPKM-Master-Encrypt(N, K, T*, IV, P)                     |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - section size N,                                             |
   |  - initial key K,                                              |
   |  - master key frequency T*,                                    |
   |  - initialization vector IV in V_n,                            |
   |  - plaintext P = P_1 | ... | P_b, |P_b| = n, |P| <= m_max.     |
   |  Output:                                                       |
   |  - ciphertext C.                                               |
   |----------------------------------------------------------------|
   |  1. l = ceil(|P| / N)                                          |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l)                |
   |  3. C_0 = IV                                                   |
   |  4. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j * n / N),                                   |
   |         C_j = E_{K^i}(P_j (xor) C_{j-1})                       |
   |  5. Return C = C_1 | ... | C_b                                 |
   |----------------------------------------------------------------+

   +----------------------------------------------------------------+
   |  CBC-ACPKM-Master-Decrypt(N, K, T*, IV, C)                     |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - section size N,                                             |
   |  - initial key K,                                              |
   |  - master key frequency T*,                                    |
   |  - initialization vector IV in V_n,                            |
   |  - ciphertext C = C_1 | ... | C_b, |C_b| = n, |C| <= m_max.    |
   |  Output:                                                       |
   |  - plaintext P.                                                |
   |----------------------------------------------------------------|
   |  1. l = ceil(|C| / N)                                          |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l)                |
   |  3. C_0 = IV                                                   |
   |  4. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j * n / N)                                    |
   |         P_j = D_{K^i}(C_j) (xor) C_{j-1}                       |
   |  5. Return P = P_1 | ... | P_b                                 |
   +----------------------------------------------------------------+

   The initialization vector IV for any particular execution of the
   encryption process must be unpredictable.




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6.3.5.  CFB-ACPKM-Master Encryption Mode

   This section defines a CFB-ACPKM-Master encryption mode that uses the
   ACPKM-Master internal re-keying mechanism for the periodical key
   transformation.

   The CFB-ACPKM-Master encryption mode can be considered as the base
   encryption mode CFB (see [MODES]) extended by the ACPKM-Master
   re-keying mechanism.

   The CFB-ACPKM-Master encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512.

   o  128 <= k <= 512.

   o  The maximum message size m_max = N * (n * 2^{n/2-1} / k).

   The key material K[j] that is used for the j-th section processing is
   equal to K^j, |K^j| = k bits.

   The CFB-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:

   +-------------------------------------------------------------+
   |  CFB-ACPKM-Master-Encrypt(N, K, T*, IV, P)                  |
   |-------------------------------------------------------------|
   |  Input:                                                     |
   |  - section size N,                                          |
   |  - initial key K,                                           |
   |  - master key frequency T*,                                 |
   |  - initialization vector IV in V_n,                         |
   |  - plaintext P = P_1 | ... | P_b, |P| <= m_max.             |
   |  Output:                                                    |
   |  - ciphertext C.                                            |
   |-------------------------------------------------------------|
   |  1. l = ceil(|P| / N)                                       |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l)             |
   |  3. C_0 = IV                                                |
   |  4. For j = 1, 2, ... , b - 1 do                            |
   |         i = ceil(j * n / N),                                |
   |         C_j = E_{K^i}(C_{j-1}) (xor) P_j                    |
   |  5. C_b = MSB_{|P_b|}(E_{K^l}(C_{b-1})) (xor) P_b           |
   |  6. Return C = C_1 | ... | C_b                              |
   |-------------------------------------------------------------+





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   +-------------------------------------------------------------+
   |  CFB-ACPKM-Master-Decrypt(N, K, T*, IV, C)                  |
   |-------------------------------------------------------------|
   |  Input:                                                     |
   |  - section size N,                                          |
   |  - initial key K,                                           |
   |  - master key frequency T*,                                 |
   |  - initialization vector IV in V_n,                         |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= m_max.            |
   |  Output:                                                    |
   |  - plaintext P.                                             |
   |-------------------------------------------------------------|
   |  1. l = ceil(|C| / N)                                       |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l)             |
   |  3. C_0 = IV                                                |
   |  4. For j = 1, 2, ... , b - 1 do                            |
   |         i = ceil(j * n / N),                                |
   |         P_j = E_{K^i}(C_{j-1}) (xor) C_j                    |
   |  5. P_b = MSB_{|C_b|}(E_{K^l}(C_{b-1})) (xor) C_b           |
   |  6. Return P = P_1 | ... | P_b                              |
   +-------------------------------------------------------------+

   The initialization vector IV for any particular execution of the
   encryption process must be unpredictable.

6.3.6.  OMAC-ACPKM-Master Authentication Mode

   This section defines an OMAC-ACPKM-Master message authentication code
   calculation mode that uses the ACPKM-Master internal re-keying
   mechanism for the periodical key transformation.

   The OMAC-ACPKM-Master mode can be considered as the base message
   authentication code calculation mode OMAC1, which is also known as
   CMAC (see [RFC4493]), extended by the ACPKM-Master re-keying
   mechanism.

   The OMAC-ACPKM-Master message authentication code calculation mode
   can be used with the following parameters:

   o  n in {64, 128, 256}.

   o  128 <= k <= 512.

   o  The maximum message size m_max = N * (n * 2^{n/2-1} / (k + n)).

   The key material K[j] that is used for one-section processing is
   equal to K^j | K^j_1, where |K^j| = k bits and |K^j_1| = n bits.




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   The following is a specification of the subkey generation process of
   OMAC:

   +-------------------------------------------------------------------+
   | Generate_Subkey(K1, r)                                            |
   |-------------------------------------------------------------------|
   | Input:                                                            |
   |  - key K1.                                                        |
   |  Output:                                                          |
   |  - key SK.                                                        |
   |-------------------------------------------------------------------|
   |   1. If r = n, then return K1                                     |
   |   2. If r < n, then                                               |
   |          if MSB_1(K1) = 0                                         |
   |              return K1 << 1                                       |
   |          else                                                     |
   |              return (K1 << 1) (xor) R_n                           |
   +-------------------------------------------------------------------+

   Here, R_n takes the following values:

   o  n = 64: R_{64} = 0^{59} | 11011.

   o  n = 128: R_{128} = 0^{120} | 10000111.

   o  n = 256: R_{256} = 0^{145} | 10000100101.

























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   The OMAC-ACPKM-Master message authentication code calculation mode is
   defined as follows:

   +-------------------------------------------------------------------+
   | OMAC-ACPKM-Master(K, N, T*, M)                                    |
   |-------------------------------------------------------------------|
   | Input:                                                            |
   |  - section size N,                                                |
   |  - initial key K,                                                 |
   |  - master key frequency T*,                                       |
   |  - plaintext M = M_1 | ... | M_b, |M| <= m_max.                   |
   |  Output:                                                          |
   |  - message authentication code T.                                 |
   |-------------------------------------------------------------------|
   | 1. C_0 = 0^n                                                      |
   | 2. l = ceil(|M| / N)                                              |
   | 3. K^1 | K^1_1 | ... | K^l | K^l_1 =                              |
                     = ACPKM-Master(T*, K, (k + n), l)                 |
   | 4. For j = 1, 2, ... , b - 1 do                                   |
   |        i = ceil(j * n / N),                                       |
   |        C_j = E_{K^i}(M_j (xor) C_{j-1})                           |
   | 5. SK = Generate_Subkey(K^l_1, |M_b|)                             |
   | 6. If |M_b| = n, then M*_b = M_b                                  |
   |                  else M*_b = M_b | 1 | 0^{n - 1 -|M_b|}           |
   | 7. T = E_{K^l}(M*_b (xor) C_{b-1} (xor) SK)                       |
   | 8. Return T                                                       |
   +-------------------------------------------------------------------+

7.  Joint Usage of External and Internal Re-keying

   Both external re-keying and internal re-keying have their own
   advantages and disadvantages, which are discussed in Section 1.  For
   instance, using external re-keying can essentially limit the message
   length, while in the case of internal re-keying, the section size,
   which can be chosen as the maximal possible for operational
   properties, limits the number of separate messages.  Therefore, the
   choice of re-keying mechanism (either external or internal) depends
   on particular protocol features.  However, some protocols may have
   features that require the advantages of both the external and
   internal re-keying mechanisms: for example, the protocol mainly
   transmits short messages, but it must additionally support processing
   of very long messages.  In such situations, it is necessary to use
   external and internal re-keying jointly, since these techniques
   negate each other's disadvantages.

   For composition of external and internal re-keying techniques, any
   mechanism described in Section 5 can be used with any mechanism
   described in Section 6.



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   For example, consider the GCM-ACPKM mode with external serial
   re-keying based on a KDF on a hash function.  Denote the number of
   messages in each frame (in the case of the implicit approach to the
   key lifetime control) for external re-keying as a frame size.

   Let L be a key lifetime limitation.  The section size N for internal
   re-keying and the frame size q for external re-keying must be chosen
   in such a way that q * N must not exceed L.

   Suppose that t messages (ICN_i, P_i, A_i), with initial counter nonce
   ICN_i, plaintext P_i, and additional authenticated data A_i will be
   processed before renegotiation.

   For authenticated encryption of each message (ICN_i, P_i, A_i), i =
   1, ..., t, the following algorithm can be applied:

   1. j = ceil(i / q),
   2. K^j = ExtSerialH(K, j),
   3. C_i | T_i = GCM-ACPKM-Encrypt(N, K^j, ICN_i, P_i, A_i).

   Note that nonces ICN_i that are used under the same frame key must be
   unique for each message.

8.  Security Considerations

   Re-keying should be used to increase a priori security properties of
   ciphers in hostile environments (e.g., with side-channel
   adversaries).  If efficient attacks on a cipher are known, the cipher
   must not be used.  Thus, re-keying cannot be used as a patch for
   vulnerable ciphers.  Base cipher properties must be well analyzed
   because the security of re-keying mechanisms is based on the security
   of a block cipher as a pseudorandom function.

   Re-keying is not intended to solve any postquantum security issues
   for symmetric cryptography, since the reduction of security caused by
   Grover's algorithm is not connected with a size of plaintext
   transformed by a cipher -- only a negligible (sufficient for key
   uniqueness) material is needed -- and the aim of re-keying is to
   limit the size of plaintext transformed under one initial key.

   Re-keying can provide backward security only if previous key material
   is securely deleted after usage by all parties.

9.  IANA Considerations

   This document has no IANA actions.





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10.  References

10.1.  Normative References

   [CMS]      Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
              RFC 5652, DOI 10.17487/RFC5652, September 2009,
              <https://www.rfc-editor.org/info/rfc5652>.

   [DTLS]     Rescorla, E. and N. Modadugu, "Datagram Transport Layer
              Security Version 1.2", RFC 6347, DOI 10.17487/RFC6347,
              January 2012, <https://www.rfc-editor.org/info/rfc6347>.

   [ESP]      Kent, S., "IP Encapsulating Security Payload (ESP)",
              RFC 4303, DOI 10.17487/RFC4303, December 2005,
              <https://www.rfc-editor.org/info/rfc4303>.

   [GCM]      Dworkin, M., "Recommendation for Block Cipher Modes of
              Operation: Galois/Counter Mode (GCM) and GMAC", NIST
              Special Publication 800-38D, DOI 10.6028/NIST.SP.800-38D,
              November 2007,
              <http://nvlpubs.nist.gov/nistpubs/Legacy/SP/
              nistspecialpublication800-38d.pdf>.

   [MODES]    Dworkin, M., "Recommendation for Block Cipher Modes of
              Operation: Methods and Techniques", NIST Special
              Publication 800-38A, DOI 10.6028/NIST.SP.800-38A, December
              2001.

   [NISTSP800-108]
              National Institute of Standards and Technology,
              "Recommendation for Key Derivation Using Pseudorandom
              Functions", NIST Special Publication 800-108, October
              2009, <http://nvlpubs.nist.gov/nistpubs/Legacy/SP/
              nistspecialpublication800-108.pdf>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC4493]  Song, JH., Poovendran, R., Lee, J., and T. Iwata, "The
              AES-CMAC Algorithm", RFC 4493, DOI 10.17487/RFC4493, June
              2006, <https://www.rfc-editor.org/info/rfc4493>.

   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869,
              DOI 10.17487/RFC5869, May 2010,
              <https://www.rfc-editor.org/info/rfc5869>.



Smyshlyaev                    Informational                    [Page 44]

RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   [RFC7836]  Smyshlyaev, S., Ed., Alekseev, E., Oshkin, I., Popov, V.,
              Leontiev, S., Podobaev, V., and D. Belyavsky, "Guidelines
              on the Cryptographic Algorithms to Accompany the Usage of
              Standards GOST R 34.10-2012 and GOST R 34.11-2012",
              RFC 7836, DOI 10.17487/RFC7836, March 2016,
              <https://www.rfc-editor.org/info/rfc7836>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [SSH]      Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253,
              January 2006, <https://www.rfc-editor.org/info/rfc4253>.

   [TLS]      Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
              <https://www.rfc-editor.org/info/rfc8446>.

10.2.  Informative References

   [AAOS2017] Ahmetzyanova, L., Alekseev, E., Oshkin, I., and S.
              Smyshlyaev, "Increasing the Lifetime of Symmetric Keys for
              the GCM Mode by Internal Re-keying", Cryptology ePrint
              Archive, Report 2017/697, 2017,
              <https://eprint.iacr.org/2017/697.pdf>.

   [AbBell]   Abdalla, M. and M. Bellare, "Increasing the Lifetime of a
              Key: A Comparative Analysis of the Security of Re-keying
              Techniques", ASIACRYPT 2000, Lecture Notes in Computer
              Science, Volume 1976, pp. 546-559,
              DOI 10.1007/3-540-44448-3_42, October 2000.

   [AESDUKPT] American National Standards Institute, "Retail Financial
              Services Symmetric Key Management - Part 3: Derived Unique
              Key Per Transaction", ANSI X9.24-3-2017, October 2017.

   [FKK2005]  Fu, K., Kamara, S., and T. Kohno, "Key Regression:
              Enabling Efficient Key Distribution for Secure Distributed
              Storage", November 2005, <https://homes.cs.washington.edu/
              ~yoshi/papers/KR/NDSS06.pdf>.










Smyshlyaev                    Informational                    [Page 45]

RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   [FPS2012]  Faust, S., Pietrzak, K., and J. Schipper, "Practical
              Leakage-Resilient Symmetric Cryptography", Cryptographic
              Hardware and Embedded Systems (CHES), Lecture Notes in
              Computer Science, Volume 7428, pp. 213-232,
              DOI 10.1007/978-3-642-33027-8_13, 2012,
              <https://link.springer.com/content/
              pdf/10.1007%2F978-3-642-33027-8_13.pdf>.

   [FRESHREKEYING]
              Dziembowski, S., Faust, S., Herold, G., Journault, A.,
              Masny, D., and F. Standaert, "Towards Sound Fresh
              Re-Keying with Hard (Physical) Learning Problems",
              Cryptology ePrint Archive, Report 2016/573, June 2016,
              <https://eprint.iacr.org/2016/573>.

   [GGM]      Goldreich, O., Goldwasser, S., and S. Micali, "How to
              Construct Random Functions", Journal of the Association
              for Computing Machinery, Volume 33, No. 4, pp. 792-807,
              DOI 10.1145/6490.6503, October 1986,
              <https://dl.acm.org/citation.cfm?doid=6490.6503>.

   [KMNT2003] Kim, Y., Maino, F., Narasimha, M., and G. Tsudik, "Secure
              Group Services for Storage Area Networks",
              IEEE Communications Magazine 41, Number 8, pp. 92-99,
              DOI 10.1109/SISW.2002.1183514, August 2003,
              <https://ieeexplore.ieee.org/document/1183514>.

   [LDC]      Heys, H., "A Tutorial on Linear and Differential
              Cryptanalysis", 2001, <https://citeseerx.ist.psu.edu/
              viewdoc/citations?doi=10.1.1.2.2759>.

   [OWT]      Joye, M. and S. Yen, "One-Way Cross-Trees and Their
              Applications", Public Key Cryptography (PKC), Lecture
              Notes in Computer Science, Volume 2274,
              DOI 10.1007/3-540-45664-3_25, February 2002,
              <https://link.springer.com/content/
              pdf/10.1007%2F3-540-45664-3_25.pdf>.

   [P3]       Alexander, P., "Subject: [Cfrg] Dynamic Key Changes on
              Encrypted Sessions. - Draft I-D Attached", message to
              the CFRG mailing list, 4 November 2017,
              <https://mailarchive.ietf.org/arch/msg/cfrg/
              ecTR3Hb-DFfrPCVmY0ghyYOEcxU>.








Smyshlyaev                    Informational                    [Page 46]

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   [Pietrzak2009]
              Pietrzak, K., "A Leakage-Resilient Mode of Operation",
              EUROCRYPT 2009, Lecture Notes in Computer Science, Volume
              5479, pp. 462-482, DOI 10.1007/978-3-642-01001-9_27, April
              2009, <https://iacr.org/archive/eurocrypt2009/
              54790461/54790461.pdf>.

   [SIGNAL]   Perrin, T., Ed. and M. Marlinspike, "The Double Ratchet
              Algorithm", November 2016, <https://signal.org/docs/
              specifications/doubleratchet/doubleratchet.pdf>.

   [Sweet32]  Bhargavan, K. and G. Leurent, "On the Practical
              (In-)Security of 64-bit Block Ciphers: Collision Attacks
              on HTTP over TLS and OpenVPN", Proceedings of the 2016 ACM
              SIGSAC Conference on Computer and Communications
              Security, pp. 456-467, DOI 10.1145/2976749.2978423,
              October 2016, <https://sweet32.info/SWEET32_CCS16.pdf>.

   [TAHA]     Taha, M. and P. Schaumont, "Key Updating for Leakage
              Resiliency With Application to AES Modes of Operation",
              IEEE Transactions on Information Forensics and Security,
              DOI 10.1109/TIFS.2014.2383359, December 2014,
              <http://ieeexplore.ieee.org/document/6987331/>.

   [TEMPEST]  Ramsay, C. and J. Lohuis, "TEMPEST attacks against AES.
              Covertly stealing keys for 200 euro", June 2017,
              <https://www.fox-it.com/en/wp-content/uploads/sites/11/
              Tempest_attacks_against_AES.pdf>.

   [U2F]      Chang, D., Mishra, S., Sanadhya, S., and A. Singh, "On
              Making U2F Protocol Leakage-Resilient via Re-keying",
              Cryptology ePrint Archive, Report 2017/721, August 2017,
              <https://eprint.iacr.org/2017/721.pdf>.


















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Appendix A.  Test Examples

A.1.  Test Examples for External Re-keying

A.1.1.  External Re-keying with a Parallel Construction

   External re-keying with a parallel construction based on AES-256
   ****************************************************************
   k = 256
   t = 128

   Initial key:
   00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00

   K^1:
   51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86
   64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1

   K^2:
   6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15
   B8 02 92 32 D8 D3 8D 73 FE DC DD C6 C8 36 78 BD

   K^3:
   B6 40 24 85 A4 24 BD 35 B4 26 43 13 76 26 70 B6
   5B F3 30 3D 3B 20 EB 14 D1 3B B7 91 74 E3 DB EC

   ...

   K^126:
   2F 3F 15 1B 53 88 23 CD 7D 03 FC 3D FD B3 57 5E
   23 E4 1C 4E 46 FF 6B 33 34 12 27 84 EF 5D 82 23

   K^127:
   8E 51 31 FB 0B 64 BB D0 BC D4 C5 7B 1C 66 EF FD
   97 43 75 10 6C AF 5D 5E 41 E0 17 F4 05 63 05 ED

   K^128:
   77 4F BF B3 22 60 C5 3B A3 8E FE B1 96 46 76 41
   94 49 AF 84 2D 84 65 A7 F4 F7 2C DC A4 9D 84 F9

   External re-keying with a parallel construction based on SHA-256
   ****************************************************************
   k = 256
   t = 128

   label:
   SHA2label



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   Initial key:
   00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00

   K^1:
   C1 A1 4C A0 30 29 BE 43 9F 35 3C 79 1A 51 48 57
   26 7A CD 5A E8 7D E7 D1 B2 E2 C7 AF A4 29 BD 35

   K^2:
   03 68 BB 74 41 2A 98 ED C4 7B 94 CC DF 9C F4 9E
   A9 B8 A9 5F 0E DC 3C 1E 3B D2 59 4D D1 75 82 D4

   K^3:
   2F D3 68 D3 A7 8F 91 E6 3B 68 DC 2B 41 1D AC 80
   0A C3 14 1D 80 26 3E 61 C9 0D 24 45 2A BD B1 AE

   ...

   K^126:
   55 AC 2B 25 00 78 3E D4 34 2B 65 0E 75 E5 8B 76
   C8 04 E9 D3 B6 08 7D C0 70 2A 99 A4 B5 85 F1 A1

   K^127:
   77 4D 15 88 B0 40 90 E5 8C 6A D7 5D 0F CF 0A 4A
   6C 23 F1 B3 91 B1 EF DF E5 77 64 CD 09 F5 BC AF

   K^128:
   E5 81 FF FB 0C 90 88 CD E5 F4 A5 57 B6 AB D2 2E
   94 C3 42 06 41 AB C1 72 66 CC 2F 59 74 9C 86 B3

A.1.2.  External Re-keying with a Serial Construction

   External re-keying with a serial construction based on AES-256
   **************************************************************
   AES 256 examples:
   k = 256
   t = 128

   Initial key:
   00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00

   K*_1:
   00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00






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   K^1:
   66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
   51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86

   K*_2:
   64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
   6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15

   K^2:
   66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
   51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86

   K*_3:
   64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
   6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15

   K^3:
   66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
   51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86

   ...

   K*_126:
   64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
   6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15

   K^126:
   66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
   51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86

   K*_127:
   64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
   6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15

   K^127:
   66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
   51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86

   K*_128:
   64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
   6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15

   K^128:
   66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
   51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86






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   External re-keying with a serial construction based on SHA-256
   **************************************************************
   k = 256
   t = 128

   Initial key:
   00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00

   label1:
   SHA2label1

   label2:
   SHA2label2

   K*_1:
   00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00

   K^1:
   2D A8 D1 37 6C FD 52 7F F7 36 A4 E2 81 C6 0A 9B
   F3 8E 66 97 ED 70 4F B5 FB 10 33 CC EC EE D5 EC

   K*_2:
   14 65 5A D1 7C 19 86 24 9B D3 56 DF CC BE 73 6F
   52 62 4A 9D E3 CC 40 6D A9 48 DA 5C D0 68 8A 04

   K^2:
   2F EA 8D 57 2B EF B8 89 42 54 1B 8C 1B 3F 8D B1
   84 F9 56 C7 FE 01 11 99 1D FB 98 15 FE 65 85 CF

   K*_3:
   18 F0 B5 2A D2 45 E1 93 69 53 40 55 43 70 95 8D
   70 F0 20 8C DF B0 5D 67 CD 1B BF 96 37 D3 E3 EB

   K^3:
   53 C7 4E 79 AE BC D1 C8 24 04 BF F6 D7 B1 AC BF
   F9 C0 0E FB A8 B9 48 29 87 37 E1 BA E7 8F F7 92

   ...

   K*_126:
   A3 6D BF 02 AA 0B 42 4A F2 C0 46 52 68 8B C7 E6
   5E F1 62 C3 B3 2F DD EF E4 92 79 5D BB 45 0B CA

   K^126:
   6C 4B D6 22 DC 40 48 0F 29 C3 90 B8 E5 D7 A7 34
   23 4D 34 65 2C CE 4A 76 2C FE 2A 42 C8 5B FE 9A



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   K*_127:
   84 5F 49 3D B8 13 1D 39 36 2B BE D3 74 8F 80 A1
   05 A7 07 37 BA 15 72 E0 73 49 C2 67 5D 0A 28 A1

   K^127:
   57 F0 BD 5A B8 2A F3 6B 87 33 CF F7 22 62 B4 D0
   F0 EE EF E1 50 74 E5 BA 13 C1 23 68 87 36 29 A2

   K*_128:
   52 F2 0F 56 5C 9C 56 84 AF 69 AD 45 EE B8 DA 4E
   7A A6 04 86 35 16 BA 98 E4 CB 46 D2 E8 9A C1 09

   K^128:
   9B DD 24 7D F3 25 4A 75 E0 22 68 25 68 DA 9D D5
   C1 6D 2D 2B 4F 3F 1F 2B 5E 99 82 7F 15 A1 4F A4

A.2.  Test Examples for Internal Re-keying

A.2.1.  Internal Re-keying Mechanisms that Do Not Require a Master Key

   CTR-ACPKM mode with AES-256
   ***************************
   k = 256
   n = 128
   c = 64
   N = 256

   Initial key K:
   00000:   88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
   00010:   FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF

   Plaintext P:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
   00010:   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
   00020:   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
   00030:   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
   00040:   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
   00050:   44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
   00060:   55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44

   ICN:
   12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12
   23 34 45 56 67 78 89 90 12 13 14 15 16 17 18 19

   D_1:
   00000:   80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F





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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   D_2:
   00000:   90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F

   Section_1

   Section key K^1:
   00000:   88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
   00010:   FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF

   Input block CTR_1:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 00

   Output block G_1:
   00000:   FD 7E F8 9A D9 7E A4 B8 8D B8 B5 1C 1C 9D 6D D0

   Input block CTR_2:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 01

   Output block G_2:
   00000:   19 98 C5 71 76 37 FB 17 11 E4 48 F0 0C 0D 60 B2

   Section_2

   Section key K^2:
   00000:   F6 80 D1 21 2F A4 3D F4 EC 3A 91 DE 2A B1 6F 1B
   00010:   36 B0 48 8A 4F C1 2E 09 98 D2 E4 A8 88 E8 4F 3D

   Input block CTR_3:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02

   Output block G_3:
   00000:   E4 88 89 4F B6 02 87 DB 77 5A 07 D9 2C 89 46 EA

   Input block CTR_4:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03

   Output block G_4:
   00000:   BC 4F 87 23 DB F0 91 50 DD B4 06 C3 1D A9 7C A4

   Section_3

   Section key K^3:
   00000:   8E B9 7E 43 27 1A 42 F1 CA 8E E2 5F 5C C7 C8 3B
   00010:   1A CE 9E 5E D0 6A A5 3B 57 B9 6A CF 36 5D 24 B8

   Input block CTR_5:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04




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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   Output block G_5:
   00000:   68 6F 22 7D 8F B2 9C BD 05 C8 C3 7D 22 FE 3B B7

   Input block CTR_6:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05

   Output block G_6:
   00000:   C0 1B F9 7F 75 6E 12 2F 80 59 55 BD DE 2D 45 87

   Section_4

   Section key K^4:
   00000:   C5 71 6C C9 67 98 BC 2D 4A 17 87 B7 8A DF 94 AC
   00010:   E8 16 F8 0B DB BC AD 7D 60 78 12 9C 0C B4 02 F5

   Block number 7:

   Input block CTR_7:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06

   Output block G_7:
   00000:   03 DE 34 74 AB 9B 65 8A 3B 54 1E F8 BD 2B F4 7D


   The result G = G_1 | G_2 | G_3 | G_4 | G_5 | G_6 | G_7:
   00000:   FD 7E F8 9A D9 7E A4 B8 8D B8 B5 1C 1C 9D 6D D0
   00010:   19 98 C5 71 76 37 FB 17 11 E4 48 F0 0C 0D 60 B2
   00020:   E4 88 89 4F B6 02 87 DB 77 5A 07 D9 2C 89 46 EA
   00030:   BC 4F 87 23 DB F0 91 50 DD B4 06 C3 1D A9 7C A4
   00040:   68 6F 22 7D 8F B2 9C BD 05 C8 C3 7D 22 FE 3B B7
   00050:   C0 1B F9 7F 75 6E 12 2F 80 59 55 BD DE 2D 45 87
   00060:   03 DE 34 74 AB 9B 65 8A 3B 54 1E F8 BD 2B F4 7D

   The result ciphertext C = P (xor) MSB_{|P|}(G):
   00000:   EC 5C CB DE 8C 18 D3 B8 72 56 68 D0 A7 37 F4 58
   00010:   19 89 E7 42 32 62 9D 60 99 7D E2 4B C0 E3 9F B8
   00020:   F5 AA BA 0B E3 64 F0 53 EE F0 BC 15 C2 76 4C EA
   00030:   9E 7C C3 76 BD 87 19 C9 77 0F CA 2D E2 A3 7C B5
   00040:   5B 2B 77 1B F8 3A 05 17 BE 04 2D 82 28 FE 2A 95
   00050:   84 4E 9F 08 FD F7 B8 94 4C B7 AA B7 DE 3C 67 B4
   00060:   56 B8 43 FC 32 31 DE 46 D5 AB 14 F8 AC 09 C7 39










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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   GCM-ACPKM mode with AES-128
   ***************************
   k = 128
   n = 128
   c = 32
   N = 256

   Initial key K:
   00000:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Additional data A:
   00000:   11 22 33

   Plaintext:
   00000:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   00010:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   00020:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   ICN:
   00000:   00 00 00 00 00 00 00 00 00 00 00 00

   Number of sections: 2

   Section key K^1:
   00000:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Section key K^2:
   00000:   15 1A 9F B0 B6 AC C5 97 6A FB 50 31 D1 DE C8 41

   Encrypted GCTR_1 | GCTR_2 | GCTR_3:
   00000:   03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78
   00010:   F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0
   00020:   D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD

   Ciphertext C:
   00000:   03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78
   00010:   F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0
   00020:   D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD

   GHASH input:
   00000:   11 22 33 00 00 00 00 00 00 00 00 00 00 00 00 00
   00010:   03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78
   00020:   F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0
   00030:   D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD
   00040:   00 00 00 00 00 00 00 18 00 00 00 00 00 00 01 80

   GHASH output S:
   00000:   E8 ED E9 94 9A DD 55 30 B0 F4 4E F5 00 FC 3E 3C



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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   Authentication tag  T:
   00000:   B0 0F 15 5A 60 A3 65 51 86 8B 53 A2 A4 1B 7B 66

   The result C | T:
   00000:   03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78
   00010:   F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0
   00020:   D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD
   00030:   B0 0F 15 5A 60 A3 65 51 86 8B 53 A2 A4 1B 7B 66

A.2.2.  Internal Re-keying Mechanisms with a Master Key

   CTR-ACPKM-Master mode with AES-256
   **********************************
   k = 256
   n = 128
   c for CTR-ACPKM mode = 64
   c for CTR-ACPKM-Master mode = 64
   N = 256
   T* = 512

   Initial key K:
   00000:   88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
   00010:   FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF

   Initial vector ICN:
   00000:   12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12

   Plaintext P:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
   00010:   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
   00020:   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
   00030:   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
   00040:   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
   00050:   44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
   00060:   55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44

   K^1 | K^2 | K^3 | K^4:
   00000:   9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
   00010:   39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
   00020:   77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
   00030:   AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
   00040:   E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
   00050:   60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
   00060:   F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
   00070:   2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12






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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   Section_1

   K^1:
   00000:   9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
   00010:   39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60

   Input block CTR_1:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 00

   Output block G_1:
   00000:   8C A2 B6 82 A7 50 65 3F 8E BF 08 E7 9F 99 4D 5C

   Input block CTR_2:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 01

   Output block G_2:
   00000:   F6 A6 A5 BA 58 14 1E ED 23 DC 31 68 D2 35 89 A1


   Section_2

   K^2:
   00000:   77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
   00010:   AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3

   Input block CTR_3:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02

   Output block G_3:
   00000:   4A 07 5F 86 05 87 72 94 1D 8E 7D F8 32 F4 23 71

   Input block CTR_4:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03

   Output block G_4:
   00000:   23 35 66 AF 61 DD FE A7 B1 68 3F BA B0 52 4A D7


   Section_3

   K^3:
   00000:   E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
   00010:   60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94

   Input block CTR_5:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04





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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   Output block G_5:
   00000:   A8 09 6D BC E8 BB 52 FC DE 6E 03 70 C1 66 95 E8

   Input block CTR_6:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05

   Output block G_6:
   00000:   C6 E3 6E 8E 5B 82 AA C4 A6 6C 14 8D B1 F6 9B EF


   Section_4

   K^4:
   00000:   F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
   00010:   2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12

   Input block CTR_7:
   00000:   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06

   Output block G_7:
   00000:   82 2B E9 07 96 37 44 95 75 36 3F A7 07 F8 40 22


   The result G = G_1 | G_2 | G_3 | G_4 | G_5 | G_6 | G_7:
   00000:   8C A2 B6 82 A7 50 65 3F 8E BF 08 E7 9F 99 4D 5C
   00010:   F6 A6 A5 BA 58 14 1E ED 23 DC 31 68 D2 35 89 A1
   00020:   4A 07 5F 86 05 87 72 94 1D 8E 7D F8 32 F4 23 71
   00030:   23 35 66 AF 61 DD FE A7 B1 68 3F BA B0 52 4A D7
   00040:   A8 09 6D BC E8 BB 52 FC DE 6E 03 70 C1 66 95 E8
   00050:   C6 E3 6E 8E 5B 82 AA C4 A6 6C 14 8D B1 F6 9B EF
   00060:   82 2B E9 07 96 37 44 95 75 36 3F A7 07 F8 40 22

   The result ciphertext C = P (xor) MSB_{|P|}(G):
   00000:   9D 80 85 C6 F2 36 12 3F 71 51 D5 2B 24 33 D4 D4
   00010:   F6 B7 87 89 1C 41 78 9A AB 45 9B D3 1E DB 76 AB
   00020:   5B 25 6C C2 50 E1 05 1C 84 24 C6 34 DC 0B 29 71
   00030:   01 06 22 FA 07 AA 76 3E 1B D3 F3 54 4F 58 4A C6
   00040:   9B 4D 38 DA 9F 33 CB 56 65 A2 ED 8F CB 66 84 CA
   00050:   82 B6 08 F9 D3 1B 00 7F 6A 82 EB 87 B1 E7 B9 DC
   00060:   D7 4D 9E 8F 0F 9D FF 59 9B C9 35 A7 16 DA 73 66











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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   GCM-ACPKM-Master mode with AES-256
   **********************************
   k = 192
   n = 128
   c for the CTR-ACPKM mode = 64
   c for the GCM-ACPKM-Master mode = 32
   T* = 384
   N = 256

   Initial key K:
   00000:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   00010:   00 00 00 00 00 00 00 00

   Additional data A:
   00000:   11 22 33

   Plaintext:
   00000:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   00010:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   00020:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   00030:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   00040:   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   ICN:
   00000:   00 00 00 00 00 00 00 00 00 00 00 00

   Number of sections: 3

   K^1 | K^2 | K^3:
   00000:   93 BA AF FB 35 FB E7 39 C1 7C 6A C2 2E EC F1 8F
   00010:   7B 89 F0 BF 8B 18 07 05 96 48 68 9F 36 A7 65 CC
   00020:   CD 5D AC E2 0D 47 D9 18 D7 86 D0 41 A8 3B AB 99
   00030:   F5 F8 B1 06 D2 71 78 B1 B0 08 C9 99 0B 72 E2 87
   00040:   5A 2D 3C BE F1 6E 67 3C

   Encrypted GCTR_1 | ... | GCTR_5
   00000:   43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52
   00010:   69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8
   00020:   11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE
   00030:   4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14
   00040:   40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08

   Ciphertext C:
   00000:   43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52
   00010:   69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8
   00020:   11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE
   00030:   4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14
   00040:   40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08



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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   GHASH input:
   00000:   11 22 33 00 00 00 00 00 00 00 00 00 00 00 00 00
   00010:   43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52
   00020:   69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8
   00030:   11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE
   00040:   4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14
   00050:   40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08
   00060:   00 00 00 00 00 00 00 18 00 00 00 00 00 00 02 80

   GHASH output S:
   00000:   6E A3 4B D5 6A C5 40 B7 3E 55 D5 86 D1 CC 09 7D

   Authentication tag  T:
   00050:   CC 3A BA 11 8C E7 85 FD 77 78 94 D4 B5 20 69 F8

   The result C | T:
   00000:   43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52
   00010:   69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8
   00020:   11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE
   00030:   4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14
   00040:   40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08
   00050:   CC 3A BA 11 8C E7 85 FD 77 78 94 D4 B5 20 69 F8


   CBC-ACPKM-Master mode with AES-256
   **********************************
   k = 256
   n = 128
   c for the CTR-ACPKM mode = 64
   N = 256
   T* = 512

   Initial key K:
   00000:   88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
   00010:   FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF

   Initial vector IV:
   00000:   12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12

   Plaintext P:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
   00010:   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
   00020:   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
   00030:   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
   00040:   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
   00050:   44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
   00060:   55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44




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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   K^1 | K^2 | K^3 | K^4:
   00000:   9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
   00010:   39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
   00020:   77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
   00030:   AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
   00040:   E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
   00050:   60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
   00060:   F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
   00070:   2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12

   Section_1

   K^1:
   00000:   9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
   00010:   39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60

   Plaintext block P_1:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88

   Input block P_1 (xor) C_0:
   00000:   03 16 65 3C C5 CD B9 F0 5E 5C 1E 18 5E 5A 98 9A

   Output block C_1:
   00000:   59 CB 5B CA C2 69 2C 60 0D 46 03 A0 C7 40 C9 7C

   Plaintext block P_2:
   00000:   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A

   Input block P_2 (xor) C_1:
   00000:   59 DA 79 F9 86 3C 4A 17 85 DF A9 1B 0B AE 36 76

   Output block C_2:
   00000:   80 B6 02 74 54 8B F7 C9 78 1F A1 05 8B F6 8B 42

   Section_2

   K^2:
   00000:   77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
   00010:   AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3

   Plaintext block P_3:
   00000:   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00

   Input block P_3 (xor) C_2:
   00000:   91 94 31 30 01 ED 80 41 E1 B5 1A C9 65 09 81 42

   Output block C_3:
   00000:   8C 24 FB CF 68 15 B1 AF 65 FE 47 75 95 B4 97 59



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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   Plaintext block P_4:
   00000:   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11

   Input block P_4 (xor) C_3:
   00000:   AE 17 BF 9A 0E 62 39 36 CF 45 8B 9B 6A BE 97 48

   Output block C_4:
   00000:   19 65 A5 00 58 0D 50 23 72 1B E9 90 E1 83 30 E9

   Section_3

   K^3:
   00000:   E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
   00010:   60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94

   Plaintext block P_5:
   00000:   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22

   Input block P_5 (xor) C_4:
   00000:   2A 21 F0 66 2F 85 C9 89 C9 D7 07 6F EB 83 21 CB

   Output block C_5:
   00000:   56 D8 34 F4 6F 0F 4D E6 20 53 A9 5C B5 F6 3C 14

   Plaintext block P_6:
   00000:   44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33

   Input block P_6 (xor) C_5:
   00000:   12 8D 52 83 E7 96 E7 5D EC BD 56 56 B5 E7 1E 27

   Output block C_6:
   00000:   66 68 2B 8B DD 6E B2 7E DE C7 51 D6 2F 45 A5 45

   Section_4

   K^4:
   00000:   F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
   00010:   2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12

   Plaintext block P_7:
   00000:   55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44

   Input block P_7 (xor) C_6:
   00000:   33 0E 5C 03 44 C4 09 B2 30 38 5B D6 3E 67 96 01

   Output block C_7:
   00000:   7F 4D 87 F9 CA E9 56 09 79 C4 FA FE 34 0B 45 34




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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   Ciphertext C:
   00000:   59 CB 5B CA C2 69 2C 60 0D 46 03 A0 C7 40 C9 7C
   00010:   80 B6 02 74 54 8B F7 C9 78 1F A1 05 8B F6 8B 42
   00020:   8C 24 FB CF 68 15 B1 AF 65 FE 47 75 95 B4 97 59
   00030:   19 65 A5 00 58 0D 50 23 72 1B E9 90 E1 83 30 E9
   00040:   56 D8 34 F4 6F 0F 4D E6 20 53 A9 5C B5 F6 3C 14
   00050:   66 68 2B 8B DD 6E B2 7E DE C7 51 D6 2F 45 A5 45
   00060:   7F 4D 87 F9 CA E9 56 09 79 C4 FA FE 34 0B 45 34


   CFB-ACPKM-Master mode with AES-256
   **********************************
   k = 256
   n = 128
   c for the CTR-ACPKM mode = 64
   N = 256
   T* = 512

   Initial key K:
   00000:   88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
   00010:   FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF

   Initial vector IV:
   00000:   12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12

   Plaintext P:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
   00010:   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
   00020:   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
   00030:   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
   00040:   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
   00050:   44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
   00060:   55 66 77 88 99 AA BB CC

   K^1 | K^2 | K^3 | K^4
   00000:   9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
   00010:   39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
   00020:   77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
   00030:   AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
   00040:   E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
   00050:   60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
   00060:   F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
   00070:   2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12








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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   Section_1

   K^1:
   00000:   9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
   00010:   39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60

   Plaintext block P_1:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88

   Encrypted block E_{K^1}(C_0):
   00000:   1C 39 9D 59 F8 5D 91 91 A9 D2 12 9F 63 15 90 03

   Output block C_1 = E_{K^1}(C_0) (xor) P_1:
   00000:   0D 1B AE 1D AD 3B E6 91 56 3C CF 53 D8 BF 09 8B

   Plaintext block P_2:
   00000:   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A

   Encrypted block E_{K^1}(C_1):
   00000:   6B A2 C5 42 52 69 C6 0B 15 14 06 87 90 46 F6 2E

   Output block C_2 = E_{K^1}(C_1) (xor) P_2:
   00000:   6B B3 E7 71 16 3C A0 7C 9D 8D AC 3C 5C A8 09 24

   Section_2

   K^2:
   00000:   77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
   00010:   AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3

   Plaintext block P_3:
   00000:   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00

   Encrypted block E_{K^2}(C_2):
   00000:   95 45 5F DB C3 9E 0A 13 9F CB 10 F5 BD 79 A3 88

   Output block C_3 = E_{K^2}(C_2) (xor) P_3:
   00000:   84 67 6C 9F 96 F8 7D 9B 06 61 AB 39 53 86 A9 88

   Plaintext block P_4:
   00000:   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11

   Encrypted block E_{K^2}(C_3):
   00000:   E0 AA 32 5D 80 A4 47 95 BA 42 BF 63 F8 4A C8 B2

   Output block C_4 = E_{K^2}(C_3) (xor) P_4:
   00000:   C2 99 76 08 E6 D3 CF 0C 10 F9 73 8D 07 40 C8 A3




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   Section_3

   K^3:
   00000:   E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
   00010:   60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94

   Plaintext block P_5:
   00000:   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22

   Encrypted block E_{K^3}(C_4):
   00000:   FE 42 8C 70 C2 51 CE 13 36 C1 BF 44 F8 49 66 89

   Output block C_5 = E_{K^3}(C_4) (xor) P_5:
   00000:   CD 06 D9 16 B5 D9 57 B9 8D 0D 51 BB F2 49 77 AB

   Plaintext block P_6:
   00000:   44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33

   Encrypted block E_{K^3}(C_5):
   00000:   01 24 80 87 86 18 A5 43 11 0A CC B5 0A E5 02 A3

   Output block C_6 = E_{K^3}(C_5) (xor) P_6:
   00000:   45 71 E6 F0 0E 81 0F F8 DD E4 33 BF 0A F4 20 90

   Section_4

   K^4:
   00000:   F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
   00010:   2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12

   Plaintext block P_7:
   00000:   55 66 77 88 99 AA BB CC

   Encrypted block MSB_{|P_7|}(E_{K^4}(C_6)):
   00000:   97 5C 96 37 55 1E 8C 7F

   Output block C_7 = MSB_{|P_7|}(E_{K^4}(C_6)) (xor) P_7
   00000:   C2 3A E1 BF CC B4 37 B3

   Ciphertext C:
   00000:   0D 1B AE 1D AD 3B E6 91 56 3C CF 53 D8 BF 09 8B
   00010:   6B B3 E7 71 16 3C A0 7C 9D 8D AC 3C 5C A8 09 24
   00020:   84 67 6C 9F 96 F8 7D 9B 06 61 AB 39 53 86 A9 88
   00030:   C2 99 76 08 E6 D3 CF 0C 10 F9 73 8D 07 40 C8 A3
   00040:   CD 06 D9 16 B5 D9 57 B9 8D 0D 51 BB F2 49 77 AB
   00050:   45 71 E6 F0 0E 81 0F F8 DD E4 33 BF 0A F4 20 90
   00060:   C2 3A E1 BF CC B4 37 B3




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   OMAC-ACPKM-Master mode with AES-256
   ***********************************
   k = 256
   n = 128
   c for the CTR-ACPKM mode = 64
   N = 256
   T* = 768

   Initial key K:
   00000:   88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
   00010:   FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF

   Plaintext M:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
   00010:   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
   00020:   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
   00030:   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
   00040:   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22

   K^1 | K^1_1 | K^2 | K^2_1 | K^3 | K^3_1:
   00000:   9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
   00010:   39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
   00020:   77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
   00030:   AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
   00040:   9D CC 66 42 0D FF 45 5B 21 F3 93 F0 D4 D6 6E 67
   00050:   BB 1B 06 0B 87 66 6D 08 7A 9D A7 49 55 C3 5B 48
   00060:   F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
   00070:   2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
   00080:   78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07

   Section_1

   K^1:
   00000:   9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
   00010:   39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60

   K^1_1:
   00000:   77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0

   Plaintext block M_1:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88

   Input block M_1 (xor) C_0:
   00000:   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88

   Output block C_1:
   00000:   0B A5 89 BF 55 C1 15 42 53 08 89 76 A0 FE 24 3E




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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   Plaintext block M_2:
   00000:   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A

   Input block M_2 (xor) C_1:
   00000:   0B B4 AB 8C 11 94 73 35 DB 91 23 CD 6C 10 DB 34

   Output block C_2:
   00000:   1C 53 DD A3 6D DC E1 17 ED 1F 14 09 D8 6A F3 2C

   Section_2

   K^2:
   00000:   AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
   00010:   9D CC 66 42 0D FF 45 5B 21 F3 93 F0 D4 D6 6E 67

   K^2_1:
   00000:   BB 1B 06 0B 87 66 6D 08 7A 9D A7 49 55 C3 5B 48

   Plaintext block M_3:
   00000:   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00

   Input block M_3 (xor) C_2:
   00000:   0D 71 EE E7 38 BA 96 9F 74 B5 AF C5 36 95 F9 2C

   Output block C_3:
   00000:   4E D4 BC A6 CE 6D 6D 16 F8 63 85 13 E0 48 59 75

   Plaintext block M_4:
   00000:   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11

   Input block M_4 (xor) C_3:
   00000:   6C E7 F8 F3 A8 1A E5 8F 52 D8 49 FD 1F 42 59 64

   Output block C_4:
   00000:   B6 83 E3 96 FD 30 CD 46 79 C1 8B 24 03 82 1D 81

   Section_3

   K^3:
   00000:   F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
   00010:   2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12

   K^3_1:
   00000:   78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07

   MSB1(K1) == 0 -> K2 = K1 << 1





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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


   K1:
   00000:   78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07

   K2:
   00000:   F0 43 8F 8E D9 7A F2 C6 AD 59 F1 1C D2 D4 00 0E

   Plaintext M_5:
   00000:   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22

   Using K1, padding is not required

   Input block M_5 (xor) C_4:
   00000:   FD E6 71 37 E6 05 2D 8F 94 A1 9D 55 60 E8 0C A4

   Output block C_5:
   00000:   B3 AD B8 92 18 32 05 4C 09 21 E7 B8 08 CF A0 B8

   Message authentication code T:
   00000:   B3 AD B8 92 18 32 05 4C 09 21 E7 B8 08 CF A0 B8
































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RFC 8645         Re-keying Mechanisms for Symmetric Keys     August 2019


Acknowledgments

   We thank Mihir Bellare, Scott Fluhrer, Dorothy Cooley, Yoav Nir, Jim
   Schaad, Paul Hoffman, Dmitry Belyavsky, Yaron Sheffer, Alexey
   Melnikov, and Spencer Dawkins for their useful comments.

Contributors

   Russ Housley
   Vigil Security, LLC
   housley@vigilsec.com

   Evgeny Alekseev
   CryptoPro
   alekseev@cryptopro.ru

   Ekaterina Smyshlyaeva
   CryptoPro
   ess@cryptopro.ru

   Shay Gueron
   University of Haifa, Israel
   Intel Corporation, Israel Development Center, Israel
   shay.gueron@gmail.com

   Daniel Fox Franke
   Akamai Technologies
   dfoxfranke@gmail.com

   Lilia Ahmetzyanova
   CryptoPro
   lah@cryptopro.ru

Author's Address

   Stanislav Smyshlyaev (editor)
   CryptoPro
   18, Suschevskiy val
   Moscow  127018
   Russian Federation

   Phone: +7 (495) 995-48-20
   Email: svs@cryptopro.ru








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