



LAMPS                                                         V. Smyslov
Internet-Draft                                                ELVIS-PLUS
Intended status: Standards Track                        20 February 2026
Expires: 24 August 2026


  Internet X.509 Public Key Infrastructure - Algorithm Identifiers for
                                FrodoKEM
              draft-smyslov-lamps-frodokem-certificates-01

Abstract

   FrodoKEM is an unstructured lattice-based Key Encapsulation Mechanism
   (KEM).  Compared to ML-KEM, FrodoKEM is considered as having more
   conservative design.  This document specifies the conventions for
   using FrodoKEM in X.509 Public Key Infrastructure.  The conventions
   for the subject public keys and private keys are also specified.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on 24 August 2026.

Copyright Notice

   Copyright (c) 2026 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
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   Please review these documents carefully, as they describe your rights
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   extracted from this document must include Revised BSD License text as
   described in Section 4.e of the Trust Legal Provisions and are
   provided without warranty as described in the Revised BSD License.



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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Applicability Statement . . . . . . . . . . . . . . . . .   2
   2.  Conventions and Definitions . . . . . . . . . . . . . . . . .   2
   3.  Algorithm Identifiers . . . . . . . . . . . . . . . . . . . .   3
   4.  Subject Public Key Fields . . . . . . . . . . . . . . . . . .   4
   5.  Key Usage Bits  . . . . . . . . . . . . . . . . . . . . . . .   6
   6.  Private Key Format  . . . . . . . . . . . . . . . . . . . . .   6
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .   7
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   8
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   8
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .   8
     9.2.  Informative References  . . . . . . . . . . . . . . . . .   9
   Appendix A.  ASN.1 Module . . . . . . . . . . . . . . . . . . . .   9
   Appendix B.  Parameter Set Security and Sizes . . . . . . . . . .  14
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  15
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  15

1.  Introduction

   FrodoKEM [I-D.longa-cfrg-frodokem] is an unstructured lattice-based
   Key Encapsulation Mechanism (KEM).  At the time of writing this
   document, FrodoKEM is being standardized in ISO (International
   Organization for Standardization) as a quantum-resistant key-
   encapsulation mechanism.

   This document specifies the use of FrodoFEM in Public Key
   Infrastructure X.509 (PKIX) certificates [RFC5280] at two security
   levels: FrodoKEM-976 and FrodoKEM-1344, using object identifiers
   assigned by ISO.  The private key format is also specified.

1.1.  Applicability Statement

   FrodoKEM certificates are used in protocols where the public key is
   used to generate and encapsulate a shared secret used to derive a
   symmetric key used to encrypt a payload, like in CMS.  To be used in
   TLS, FrodoKEM certificates could only be used as end-entity identity
   certificates and would require significant updates to the protocol;
   see, for example, [I-D.celi-wiggers-tls-authkem].

2.  Conventions and Definitions

   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.



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3.  Algorithm Identifiers

   The AlgorithmIdentifier type is defined in [RFC5912] as follows:

    AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::=
      SEQUENCE {
        algorithm   ALGORITHM-TYPE.&id({AlgorithmSet}),
        parameters  ALGORITHM-TYPE.
                      &Params({AlgorithmSet}{@algorithm}) OPTIONAL
      }

      |  NOTE: The above syntax is from [RFC5912] and is compatible with
      |  the 2021 ASN.1 syntax [X680].  See [RFC5280] for the 1988 ASN.1
      |  syntax.

   The fields in AlgorithmIdentifier have the following meanings:

   *  algorithm identifies the cryptographic algorithm with an object
      identifier.

   *  parameters, which are optional, are the associated parameters for
      the algorithm identifier in the algorithm field.

   The AlgorithmIdentifier for a FrodoKEM public key MUST use one of the
   object identifiers (OID) from ISO listed below, based on the security
   level.  The parameters field of the AlgorithmIdentifier for the
   FrodoKEM public key MUST be absent.

     frodokem OBJECT IDENTIFIER ::= { iso(1) standard(0)
     encryption-algorithms(18033) part2(2)
     key-encapsulation-mechanism(2) 7 }

     id-kem-frodokem976-shake OBJECT IDENTIFIER ::= { frodokem 1 }

     id-kem-frodokem1344-shake OBJECT IDENTIFIER ::= { frodokem 2 }

     id-kem-efrodokem976-shake OBJECT IDENTIFIER ::= { frodokem 3 }

     id-kem-efrodokem1344-shake OBJECT IDENTIFIER ::= { frodokem 4 }

     id-kem-frodokem976-aes OBJECT IDENTIFIER ::= { frodokem 5 }

     id-kem-frodokem1344-aes OBJECT IDENTIFIER ::= { frodokem 6 }

     id-kem-efrodokem976-aes OBJECT IDENTIFIER ::= { frodokem 7 }

     id-kem-efrodokem1344-aes OBJECT IDENTIFIER ::= { frodokem 8 }




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4.  Subject Public Key Fields

   In the X.509 certificate, the subjectPublicKeyInfo field has the
   SubjectPublicKeyInfo type, which has the following ASN.1 syntax:

     SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE {
         algorithm        AlgorithmIdentifier {PUBLIC-KEY, {IOSet}},
         subjectPublicKey BIT STRING
     }

   The fields in SubjectPublicKeyInfo have the following meaning:

   *  algorithm is the algorithm identifier and parameters for the
      public key (see above).

   *  subjectPublicKey contains the byte stream of the public key.

   For each FrodoKEM security level, see Table 1, we define a PUBLIC-KEY
   ASN.1 type as follows.

   pk-frodokem976-shake PUBLIC-KEY ::= {
     IDENTIFIER id-kem-frodokem976-shake
     -- KEY no ASN.1 wrapping; 15632 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-rodokem976-shake -- defined in Section 6
     }

   pk-frodokem1344-shake PUBLIC-KEY ::= {
     IDENTIFIER id-kem-frodokem1344-shake
     -- KEY no ASN.1 wrapping; 21520 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-frodokem1344-shake -- defined in Section 6
     }

   pk-efrodokem976-shake PUBLIC-KEY ::= {
     IDENTIFIER id-kem-efrodokem976-shake
     -- KEY no ASN.1 wrapping; 15632 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-efrodokem976-shake -- defined in Section 6
     }

   pk-efrodokem1344-shake PUBLIC-KEY ::= {
     IDENTIFIER id-kem-efrodokem1344-shake
     -- KEY no ASN.1 wrapping; 21520 octets --
     PARAMS ARE absent



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     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-efrodokem1344-shake -- defined in Section 6
     }

   pk-frodokem976-aes PUBLIC-KEY ::= {
     IDENTIFIER id-kem-frodokem976-aes
     -- KEY no ASN.1 wrapping; 15632 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-frodokem976-aes -- defined in Section 6
     }

   pk-frodokem1344-aes PUBLIC-KEY ::= {
     IDENTIFIER id-kem-frodokem1344-aes
     -- KEY no ASN.1 wrapping; 21520 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-frodokem1344-aes -- defined in Section 6
     }

   pk-efrodokem976-aes PUBLIC-KEY ::= {
     IDENTIFIER id-kem-efrodokem976-aes
     -- KEY no ASN.1 wrapping; 15632 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-efrodokem976-aes -- defined in Section 6
     }

   pk-efrodokem1344-aes PUBLIC-KEY ::= {
     IDENTIFIER id-kem-efrodokem1344-aes
     -- KEY no ASN.1 wrapping; 21520 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-efrodokem1344-aes -- defined in Section 6
     }

   PublicKey-FrodoKEM976-SHAKE ::= OCTET STRING (SIZE (15632))

   PublicKey-FrodoKEM1344-SHAKE ::= OCTET STRING (SIZE (21520))

   PublicKey-eFrodoKEM976-SHAKE ::= OCTET STRING (SIZE (15632))

   PublicKey-eFrodoKEM1344-SHAKE ::= OCTET STRING (SIZE (21520))

   PublicKey-FrodoKEM976-AES ::= OCTET STRING (SIZE (15632))

   PublicKey-FrodoKEM1344-AES ::= OCTET STRING (SIZE (21520))




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   PublicKey-eFrodoKEM976-AES ::= OCTET STRING (SIZE (15632))

   PublicKey-eFrodoKEM1344-AES ::= OCTET STRING (SIZE (21520))

   When a FrodoKEM public key appears outside of a SubjectPublicKeyInfo
   type in an environment that uses ASN.1 encoding, it can be encoded as
   an OCTET STRING by using the PublicKey-FrodoKEM976-SHAKE, PublicKey-
   FrodoKEM1344-SHAKE, PublicKey-eFrodoKEM976-SHAKE, PublicKey-
   eFrodoKEM1344-SHAKE, PublicKey-FrodoKEM976-AES, PublicKey-
   FrodoKEM1344-AES, PublicKey-eFrodoKEM976-AES, and PublicKey-
   eFrodoKEM1344-AES types corresponding to the correct key size.

   [RFC5958] describes the Asymmetric Key Package's OneAsymmetricKey
   type for encoding asymmetric keypairs.  When a FrodoKEM private key
   or keypair is encoded as a OneAsymmetricKey, it follows the
   description in Section 6.

5.  Key Usage Bits

   The intended application for the key is indicated in the keyUsage
   certificate extension; see Section 4.2.1.3 of [RFC5280].  If the
   keyUsage extension is present in certificates, then keyEncipherement
   MUST be the only key usage set for certificates that indicate id-kem-
   frodokem976-shake, id-kem-frodokem1344-shake, id-kem-
   efrodokem976-shake, id-kem-efrodokem1344-shake, id-kem-
   frodokem976-aes, id-kem-frodokem1344-aes, id-kem-efrodokem976-aes,
   id-kem-efrodokem1344-aes in SubjectPublicKeyInfo.

6.  Private Key Format

   "Asymmetric Key Packages" [RFC5958] describes how to encode a private
   key in a structure that both identifies which algorithm the private
   key is for and allows for the public key and additional attributes
   about the key to be included as well.  For illustration, the ASN.1
   structure OneAsymmetricKey is replicated below.
















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     OneAsymmetricKey ::= SEQUENCE {
       version                  Version,
       privateKeyAlgorithm      SEQUENCE {
       algorithm                PUBLIC-KEY.&id({PublicKeySet}),
       parameters               PUBLIC-KEY.&Params({PublicKeySet}
                                  {@privateKeyAlgorithm.algorithm})
                                     OPTIONAL}
       privateKey               OCTET STRING (CONTAINING
                                  PUBLIC-KEY.&PrivateKey({PublicKeySet}
                                    {@privateKeyAlgorithm.algorithm})),
       attributes           [0] Attributes OPTIONAL,
       ...,
       [[2: publicKey       [1] BIT STRING (CONTAINING
                                  PUBLIC-KEY.&Params({PublicKeySet}
                                    {@privateKeyAlgorithm.algorithm})
                                    OPTIONAL ]],
       ...
     }

     ...

     PrivateKey ::= OCTET STRING
                        -- Content varies based on type of key. The
                        -- algorithm identifier dictates the format of
                        -- the key.

   For FrodoKEM private keys, the privateKey field in OneAsymmetricKey
   contains the OCTET STRING representation of the FrodoKEM private key.

   The privateKeyAlgorithm field uses the AlgorithmIdentifier structure
   with the appropriate OID as defined in Section 3.

   The publicKey field contains the byte stream of the public key.  If
   present, the publicKey field will hold the encoded public key as
   defined in Section 4.

7.  Security Considerations

   The Security Considerations section of [RFC5280] applies to this
   specification as well.

   Protection of the private-key information, i.e., the seed, is vital
   to public-key cryptography.  Disclosure of the private-key material
   to another entity can lead to masquerades.

   The generation of private keys relies on random numbers.  The use of
   inadequate pseudo-random number generators (PRNGs) to generate these
   values can result in little or no security.  An attacker may find it



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   much easier to reproduce the PRNG environment that produced the keys,
   searching the resulting small set of possibilities, rather than brute
   force searching the whole key space.  The generation of quality
   random numbers is difficult.

   For more detailed FrodoKEM specific security considerations refer to
   [I-D.longa-cfrg-frodokem].

8.  IANA Considerations

   For the ASN.1 Module in Appendix A, IANA is requested to assign an
   object identifier (OID) for the module identifier (TBD) with a
   Description of "id-mod-frodokem-kem-2026".  The OID for the module
   should be allocated in the "SMI Security for PKIX Module Identifier"
   registry (1.3.6.1.5.5.7.0).

9.  References

9.1.  Normative References

   [I-D.longa-cfrg-frodokem]
              Longa, P., Bos, J. W., Ehlen, S., and D. Stebila,
              "FrodoKEM: key encapsulation from learning with errors",
              Work in Progress, Internet-Draft, draft-longa-cfrg-
              frodokem-01, 16 September 2025,
              <https://datatracker.ietf.org/doc/html/draft-longa-cfrg-
              frodokem-01>.

   [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>.

   [RFC5280]  Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
              Housley, R., and W. Polk, "Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,
              <https://www.rfc-editor.org/info/rfc5280>.

   [RFC5912]  Hoffman, P. and J. Schaad, "New ASN.1 Modules for the
              Public Key Infrastructure Using X.509 (PKIX)", RFC 5912,
              DOI 10.17487/RFC5912, June 2010,
              <https://www.rfc-editor.org/info/rfc5912>.

   [RFC5958]  Turner, S., "Asymmetric Key Packages", RFC 5958,
              DOI 10.17487/RFC5958, August 2010,
              <https://www.rfc-editor.org/info/rfc5958>.




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   [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>.

   [RFC9629]  Housley, R., Gray, J., and T. Okubo, "Using Key
              Encapsulation Mechanism (KEM) Algorithms in the
              Cryptographic Message Syntax (CMS)", RFC 9629,
              DOI 10.17487/RFC9629, August 2024,
              <https://www.rfc-editor.org/info/rfc9629>.

   [X680]     ITU-T, "Information technology - Abstract Syntax Notation
              One (ASN.1): Specification of basic notation", ITU-T
              Recommendation X.680, ISO/IEC 8824-1:2021, February 2021,
              <https://www.itu.int/rec/T-REC-X.680>.

9.2.  Informative References

   [I-D.celi-wiggers-tls-authkem]
              Wiggers, T., Celi, S., Schwabe, P., Stebila, D., and N.
              Sullivan, "KEM-based Authentication for TLS 1.3", Work in
              Progress, Internet-Draft, draft-celi-wiggers-tls-authkem-
              06, 4 November 2025,
              <https://datatracker.ietf.org/doc/html/draft-celi-wiggers-
              tls-authkem-06>.

Appendix A.  ASN.1 Module

   This appendix includes the ASN.1 module [X680] for FrodoKEM.  Note
   that as per [RFC5280], certificates use the Distinguished Encoding
   Rules; see [X690].  This module imports objects from [RFC5912] and
   [RFC9629].

   <CODE BEGINS>
   X509-FRODOKEM-2026
   { iso(1) identified-organization(3) dod(6)
     internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
     id-mod-frodokem-kem-2026(TBD) }

   DEFINITIONS IMPLICIT TAGS ::= BEGIN

   EXPORTS ALL;

   IMPORTS

    PUBLIC-KEY
      FROM AlgorithmInformation-2009  -- [RFC 5912]
        { iso(1) identified-organization(3) dod(6) internet(1)
          security(5) mechanisms(5) pkix(7) id-mod(0)



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          id-mod-algorithmInformation-02(58) }

    KEM-ALGORITHM
      FROM KEMAlgorithmInformation-2023  -- [RFC 9629]
        { iso(1) identified-organization(3) dod(6) internet(1)
          security(5) mechanisms(5) pkix(7) id-mod(0)
          id-mod-kemAlgorithmInformation-2023(109) };

   --
   -- FrodoKEM Identifiers
   --

   frodokem OBJECT IDENTIFIER ::= { iso(1) standard(0)
   encryption-algorithms(18033) part2(2)
   key-encapsulation-mechanism(2) 7 }

   id-kem-frodokem976-shake OBJECT IDENTIFIER ::= { frodokem 1 }

   id-kem-frodokem1344-shake OBJECT IDENTIFIER ::= { frodokem 2 }

   id-kem-efrodokem976-shake OBJECT IDENTIFIER ::= { frodokem 3 }

   id-kem-efrodokem1344-shake OBJECT IDENTIFIER ::= { frodokem 4 }

   id-kem-frodokem976-aes OBJECT IDENTIFIER ::= { frodokem 5 }

   id-kem-frodokem1344-aes OBJECT IDENTIFIER ::= { frodokem 6 }

   id-kem-efrodokem976-aes OBJECT IDENTIFIER ::= { frodokem 7 }

   id-kem-efrodokem1344-aes OBJECT IDENTIFIER ::= { frodokem 8 }

   --
   -- Public Key Algorithms
   --

   PublicKeys PUBLIC-KEY ::= {
     -- This expands PublicKeys from [RFC 5912]
     pk-frodokem976-shake |
     pk-frodokem1344-shake |
     pk-efrodokem976-shake |
     pk-efrodokem1344-shake |
     pk-frodokem976-aes |
     pk-frodokem1344-aes |
     pk-efrodokem976-aes |
     pk-efrodokem1344-aes,
     ...
     }



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   --
   -- FrodoKEM Public Keys
   --

   pk-frodokem976-shake PUBLIC-KEY ::= {
     IDENTIFIER id-kem-frodokem976-shake
     -- KEY no ASN.1 wrapping; 15632 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-frodokem976-shake
     }

   pk-frodokem1344-shake PUBLIC-KEY ::= {
     IDENTIFIER id-kem-frodokem1344-shake
     -- KEY no ASN.1 wrapping; 21520 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-frodokem1344-shake
     }

   pk-efrodokem976-shake PUBLIC-KEY ::= {
     IDENTIFIER id-kem-efrodokem976-shake
     -- KEY no ASN.1 wrapping; 15632 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-efrodokem976-shake
     }

   pk-efrodokem1344-shake PUBLIC-KEY ::= {
     IDENTIFIER id-kem-efrodokem1344-shake
     -- KEY no ASN.1 wrapping; 21520 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-efrodokem1344-shake
     }

   pk-frodokem976-aes PUBLIC-KEY ::= {
     IDENTIFIER id-kem-frodokem976-aes
     -- KEY no ASN.1 wrapping; 15632 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-frodokem976-aes
     }

   pk-frodokem1344-aes PUBLIC-KEY ::= {
     IDENTIFIER id-kem-frodokem1344-aes
     -- KEY no ASN.1 wrapping; 21520 octets --
     PARAMS ARE absent



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     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-frodokem1344-aes
     }

   pk-efrodokem976-aes PUBLIC-KEY ::= {
     IDENTIFIER id-kem-efrodokem976-aes
     -- KEY no ASN.1 wrapping; 15632 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-efrodokem976-aes
     }

   pk-efrodokem1344-aes PUBLIC-KEY ::= {
     IDENTIFIER id-kem-efrodokem1344-aes
     -- KEY no ASN.1 wrapping; 21520 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY PrivateKey-efrodokem1344-aes
     }


   PublicKey-FrodoKEM976-SHAKE ::= OCTET STRING (SIZE (15632))

   PublicKey-FrodoKEM1344-SHAKE ::= OCTET STRING (SIZE (21520))

   PublicKey-eFrodoKEM976-SHAKE ::= OCTET STRING (SIZE (15632))

   PublicKey-eFrodoKEM1344-SHAKE ::= OCTET STRING (SIZE (21520))

   PublicKey-FrodoKEM976-AES ::= OCTET STRING (SIZE (15632))

   PublicKey-FrodoKEM1344-AES ::= OCTET STRING (SIZE (21520))

   PublicKey-eFrodoKEM976-AES ::= OCTET STRING (SIZE (15632))

   PublicKey-eFrodoKEM1344-AES ::= OCTET STRING (SIZE (21520))


   --
   -- FrodoKEM Private Keys
   --

   PrivateKey-frodokem976-shake ::= OCTET STRING (SIZE (31296))

   PrivateKey-frodokem1344-shake ::= OCTET STRING (SIZE (43088))

   PrivateKey-efrodokem976-shake ::= OCTET STRING (SIZE (31296))




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   PrivateKey-efrodokem1344-shake ::= OCTET STRING (SIZE (43088))

   PrivateKey-frodokem976-aes ::= OCTET STRING (SIZE (31296))

   PrivateKey-frodokem1344-aes ::= OCTET STRING (SIZE (43088))

   PrivateKey-efrodokem976-aes ::= OCTET STRING (SIZE (31296))

   PrivateKey-efrodokem1344-aes ::= OCTET STRING (SIZE (43088))

   --
   -- KEM-ALGORITHMs for FrodoKEM
   --

   kema-frodokem976-shake KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-frodokem976-shake
      PUBLIC-KEYS { pk-frodokem976-shake }
      UKM ARE optional
      SMIME-CAPS { IDENTIFIED BY id-kem-frodokem976-shake }}

   kema-frodokem1344-shake KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-frodokem1344-shake
      PUBLIC-KEYS { pk-frodokem1344-shake }
      UKM ARE optional
      SMIME-CAPS { IDENTIFIED BY id-kem-frodokem1344-shake }}

   kema-efrodokem976-shake KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-efrodokem976-shake
      PUBLIC-KEYS { pk-efrodokem976-shake }
      UKM ARE optional
      SMIME-CAPS { IDENTIFIED BY id-kem-efrodokem976-shake }}

   kema-efrodokem1344-shake KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-efrodokem1344-shake
      PUBLIC-KEYS { pk-efrodokem1344-shake }
      UKM ARE optional
      SMIME-CAPS { IDENTIFIED BY id-kem-efrodokem1344-shake }}

   kema-frodokem976-aes KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-frodokem976-aes
      PUBLIC-KEYS { pk-frodokem976-aes }
      UKM ARE optional
      SMIME-CAPS { IDENTIFIED BY id-kem-frodokem976-aes }}

   kema-frodokem1344-aes KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-frodokem1344-aes
      PUBLIC-KEYS { pk-frodokem1344-aes }
      UKM ARE optional



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      SMIME-CAPS { IDENTIFIED BY id-kem-frodokem1344-aes }}

   kema-efrodokem976-aes KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-efrodokem976-aes
      PUBLIC-KEYS { pk-efrodokem976-aes }
      UKM ARE optional
      SMIME-CAPS { IDENTIFIED BY id-kem-efrodokem976-aes }}

   kema-efrodokem1344-aes KEM-ALGORITHM ::= {
      IDENTIFIER id-kem-efrodokem1344-aes
      PUBLIC-KEYS { pk-efrodokem1344-aes }
      UKM ARE optional
      SMIME-CAPS { IDENTIFIED BY id-kem-efrodokem1344-aes }}

   END
   <CODE ENDS>

Appendix B.  Parameter Set Security and Sizes

   Instead of defining the strength of a quantum algorithm in a
   traditional manner using the imprecise notion of bits of security,
   NIST has defined security levels by picking a reference scheme, which
   NIST expects to offer notable levels of resistance to both quantum
   and classical attack.  To wit, a KEM algorithm that achieves NIST PQC
   security must require computational resources to break IND-CCA
   security comparable or greater than that required for key search on
   AES-128, AES-192, and AES-256 for Levels 1, 3, and 5, respectively.
   Levels 2 and 4 use collision search for SHA-256 and SHA-384 as
   reference.

   +=======+================+========+========+============+===========+
   | Level | Parameter Set  | Public | Secret | Ciphertext | Shared    |
   |       |                | Key pk | Key sk | ct         | Secret    |
   |       |                |        |        |            | ss        |
   +=======+================+========+========+============+===========+
   | 3     | FrodoKEM-976   | 15,632 | 31,296 | 15,792     | 24        |
   +=======+================+========+========+============+===========+
   | 3     | eFrodoKEM-976  | 15,632 | 31,296 | 15,744     | 24        |
   +=======+================+========+========+============+===========+
   | 5     | FrodoKEM-1344  | 21,520 | 43,088 | 21,696     | 32        |
   +=======+================+========+========+============+===========+
   | 5     | eFrodoKEM-1344 | 21,520 | 43,088 | 21,632     | 32        |
   +=======+================+========+========+============+===========+

      Table 1: Mapping between NIST Security Level, FrodoKEM parameter
                          set, and sizes in bytes





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Acknowledgments

   Most of the text was impudently stolen from draft-ietf-lamps-kyber-
   certificates.  Author is very grateful to Russ Housley for his help
   in defining and verifying the ASN.1 Module for FrodoKEM.

Author's Address

   Valery Smyslov
   ELVIS-PLUS
   Russian Federation
   Email: svan@elvis.ru







































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