



PQUIP                                                          L. Prabel
Internet-Draft                                                    S. Sun
Intended status: Standards Track                                 G. Zeng
Expires: 23 April 2026                                           G. Wang
                                                                  Huawei
                                                         20 October 2025


                    Post-Quantum Algorithms guidance
                   draft-prabel-pquip-pqc-guidance-01

Abstract

   This document provides general information (such as parameter sizes,
   security assumptions, and targeted security models) on a range of
   widely studied post-quantum cryptographic algorithms, including Key
   Encapsulation Mechanisms (KEMs) and digital signature schemes.

   The cryptographic schemes described in this document are among those
   recommended by major security agencies and/or standardization bodies,
   and are believed to be secure against Cryptographically Relevant
   Quantum Computer (CRQC).

   The goal of this document is to offer a high-level overview of these
   schemes and their distinguishing features, to help implementers,
   protocol designers, standards developers, and policymakers in
   understanding and selecting appropriate post-quantum cryptographic
   primitives for use in protocols and systems.

   By aggregating and presenting this information in a unified format,
   this document aims to facilitate informed decision-making and
   interoperability during the migration to post-quantum cryptography,
   and to encourage consistent practices when evaluating and deploying
   Post-Quantum Cryptography (PQC) schemes in cryptographic protocols.

About This Document

   This note is to be removed before publishing as an RFC.

   Status information for this document may be found at
   https://datatracker.ietf.org/doc/draft-prabel-pquip-pqc-guidance/.

   Discussion of this document takes place on the Post-Quantum Use In
   Protocols Working Group mailing list (mailto:pqc@ietf.org), which is
   archived at https://mailarchive.ietf.org/arch/browse/pqc/.  Subscribe
   at https://www.ietf.org/mailman/listinfo/pqc/.





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   Source for this draft and an issue tracker can be found at
   https://github.com/USER/REPO.

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   This Internet-Draft will expire on 23 April 2026.

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   document authors.  All rights reserved.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Conventions and Definitions . . . . . . . . . . . . . . . . .   3
   3.  Parameter Sizes . . . . . . . . . . . . . . . . . . . . . . .   4
     3.1.  Key Encapsulation Mechanism (KEM) Schemes . . . . . . . .   4
       3.1.1.  ML-KEM  . . . . . . . . . . . . . . . . . . . . . . .   5
       3.1.2.  FrodoKEM  . . . . . . . . . . . . . . . . . . . . . .   5
       3.1.3.  Classic McEliece  . . . . . . . . . . . . . . . . . .   6
       3.1.4.  HQC . . . . . . . . . . . . . . . . . . . . . . . . .   8
       3.1.5.  NTRU  . . . . . . . . . . . . . . . . . . . . . . . .   8
     3.2.  Signature Schemes . . . . . . . . . . . . . . . . . . . .   9
       3.2.1.  ML-DSA  . . . . . . . . . . . . . . . . . . . . . . .   9
       3.2.2.  FN-DSA  . . . . . . . . . . . . . . . . . . . . . . .  10



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       3.2.3.  SLH-DSA . . . . . . . . . . . . . . . . . . . . . . .  10
       3.2.4.  LMS . . . . . . . . . . . . . . . . . . . . . . . . .  11
       3.2.5.  XMSS / XMSS^MT  . . . . . . . . . . . . . . . . . . .  19
   4.  Security Properties . . . . . . . . . . . . . . . . . . . . .  21
     4.1.  Quantum-Vulnerable Asymmetric Cryptography  . . . . . . .  21
     4.2.  Quantum-Safe Asymmetric Cryptography  . . . . . . . . . .  22
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  23
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  23
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .  23
     6.2.  Informative References  . . . . . . . . . . . . . . . . .  23
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  25

1.  Introduction

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.

   This document follows the terminology for post-quantum hybrid schemes
   defined in [I-D.draft-ietf-pquip-pqt-hybrid-terminology-04].

   This section recalls some of this terminology, but also adds other
   definitions used throughout the whole document:

   _Traditional Asymmetric Cryptographic Algorithm_: An asymmetric
   cryptographic algorithm based on integer factorisation, finite field
   discrete logarithms, elliptic curve discrete logarithms, or related
   mathematical problems.  They can also be called classical or
   conventional algorithms.

   _Post-Quantum Asymmetric Cryptographic Algorithm_: An asymmetric
   cryptographic algorithm that is intended to be secure against attacks
   using quantum computers as well as classical computers.  They can
   also be called quantum-resistant or quantum-safe algorithms.

   As with all cryptography, it always remains the case that attacks,
   either quantum or classical, may be found against post-quantum
   algorithms.  Therefore it should not be assumed that just because an
   algorithm is designed to provide post-quantum security it will not be
   compromised.  Should an attack be found against a post-quantum
   algorithm, it is commonly still referred to as a post-quantum
   algorithm as they were designed to protect against an adversary with
   access to a CRQC and the labels are referring to the designed or
   desired properties.



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   _IND-CCA2_: Indistinguishability under Adaptive Chosen-Ciphertext
   Attack.  It is the standard security notion for KEM schemes.

   _EUF-CMA_: Existential Unforgeability under Chosen-Message Attack.
   It is the standard security notion for digital signature schemes.

   _SUF-CMA_: Strong Existential Unforgeability under Chosen-Message
   Attack.  It is a stronger security notion than EUF-CMA.

3.  Parameter Sizes

   This section is divided into two different subsections, one focused
   on Key Encapsulation Mechanism, and the other on signature schemes.

   The "claimed security level" in each table refers to the NIST Post-
   Quantum Cryptography Evaluation Criteria.  We summarize this
   classification in Table 1 below.  Additional details are available at
   [IR.8547].

       +===================+===========================+==========+
       | Security Category | Attack Type               | Example  |
       +===================+===========================+==========+
       | 1                 | Key search on a block     | AES-128  |
       |                   | cipher with a 128-bit key |          |
       +-------------------+---------------------------+----------+
       | 2                 | Collision search on a     | SHA-256  |
       |                   | 256-bit hash function     |          |
       +-------------------+---------------------------+----------+
       | 3                 | Key search on a block     | AES-192  |
       |                   | cipher with a 192-bit key |          |
       +-------------------+---------------------------+----------+
       | 4                 | Collision search on a     | SHA3-384 |
       |                   | 384-bit hash function     |          |
       +-------------------+---------------------------+----------+
       | 5                 | Key search on a block     | AES-256  |
       |                   | cipher with a 256-bit key |          |
       +-------------------+---------------------------+----------+

          Table 1: NIST Post-Quantum Cryptography Classification

3.1.  Key Encapsulation Mechanism (KEM) Schemes

   A Key Encapsulation Mechanism (KEM) is a cryptographic primitive that
   can be used as a building block within a broader key establishment
   protocol.  Therefore, while KEMs are often employed to achieve the
   same end goal as a traditional key exchange, they do not, by
   themselves, define the interactive procedures, message flows, or
   authentication steps that a full key exchange protocol requires.



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   This distinction is particularly relevant for implementers and
   developers to avoid confusion:

   *  A KEM provides the mechanism for securely deriving and
      encapsulating a shared secret.

   *  A Key Exchange Protocol defines the interaction between parties
      that uses one or more KEMs (and possibly other primitives) to
      securely establish a secret key in context.

3.1.1.  ML-KEM

   ML-KEM, formerly known as CRYSTALS-Kyber, is a structured lattice-
   based KEM, the first PQC KEM standardized by NIST.  The security of
   ML-KEM is based on the computational hardness of the Module Learning
   with Errors problem.

   NIST recommends Security Level 3 by default, and European security
   agencies recommend a minimum of the same security level.

   The NIST specification of ML-KEM is available at [MLKEM.SPEC].

    +=============+========+=========+============+========+==========+
    | Scheme      | Public | Private | Ciphertext | Shared | Claimed  |
    |             | Key    | Key     |            | Secret | Security |
    |             |        |         |            |        | Level    |
    +=============+========+=========+============+========+==========+
    | ML-KEM-512  | 800    | 1632    | 768        | 32     | 1        |
    +-------------+--------+---------+------------+--------+----------+
    | ML-KEM-768  | 1184   | 2400    | 1088       | 32     | 3        |
    +-------------+--------+---------+------------+--------+----------+
    | ML-KEM-1024 | 1568   | 2168    | 1568       | 32     | 5        |
    +-------------+--------+---------+------------+--------+----------+

                 Table 2: ML-KEM Parameter Sizes (in bytes)

   [MLKEM.SPEC] also allows to use a 64-bytes seed to represent the
   private key.

3.1.2.  FrodoKEM

   FrodoKEM is a lattice-based KEM whose security is based on the plain
   Learning with Errors (LWE) hardness assumption, unlike ML-KEM which
   is based on structured lattices.  This makes FrodoKEM a more
   conservative KEM scheme.

   It is considered for standardization by ISO, and it is recommended by
   European security agencies.



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   Each security level allows the choice between AES and SHAKE as the
   underlying symmetric primitive.  The AES variant is beneficial on
   devices with AES hardware acceleration, while the SHAKE variant
   generally provides better performance if hardware acceleration is not
   available.

   The FrodoKEM specification is available at [FRODOKEM.SPEC].

    +=====================+======+=======+============+======+========+
    | Scheme              |Public|Private| Ciphertext |Shared|Claimed |
    |                     |Key   |Key    |            |Secret|Security|
    |                     |      |       |            |      |Level   |
    +=====================+======+=======+============+======+========+
    | FrodoKEM-640-AES    |9616  |19888  | 9720       |16    |1       |
    +---------------------+------+-------+------------+------+--------+
    | FrodoKEM-640-SHAKE  |9616  |19888  | 9720       |16    |1       |
    +---------------------+------+-------+------------+------+--------+
    | FrodoKEM-976-AES    |15632 |31296  | 15744      |24    |3       |
    +---------------------+------+-------+------------+------+--------+
    | FrodoKEM-976-SHAKE  |15632 |31296  | 15744      |24    |3       |
    +---------------------+------+-------+------------+------+--------+
    | FrodoKEM-1344-AES   |21520 |43088  | 21632      |32    |5       |
    +---------------------+------+-------+------------+------+--------+
    | FrodoKEM-1344-SHAKE |21520 |43088  | 21632      |32    |5       |
    +---------------------+------+-------+------------+------+--------+

                Table 3: FrodoKEM Parameter Sizes (in bytes)

3.1.3.  Classic McEliece

   Classic McEliece is a conservative, code-based KEM, based on the
   original McEliece cryptosystem from 1978.

   It requires larger key sizes compared to the other KEMs discussed
   here, but relatively small ciphertext sizes.

   Each security level includes an 'f' variant that is more complex
   internally than the 'non-f' variant but enables faster key
   generation.

   It has withstood extensive cryptanalysis over several decades, and
   several European security agencies have expressed confidence in its
   security.  It is considered for standardization by ISO.

   The Classic McEliece specification is available at
   [CLASSICMCELIECE.SPEC].





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    +===========+=========+=========+============+========+==========+
    | Scheme    | Public  | Private | Ciphertext | Shared | Claimed  |
    |           | Key     | Key     |            | Secret | Security |
    |           |         |         |            |        | Level    |
    +===========+=========+=========+============+========+==========+
    | Classic-M | 261120  | 6492    | 96         | 32     | 1        |
    | cEliece-  |         |         |            |        |          |
    | 348864    |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-  | 261120  | 6492    | 96         | 32     | 1        |
    | McEliece- |         |         |            |        |          |
    | 348864f   |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-M | 524160  | 13608   | 156        | 32     | 3        |
    | cEliece-  |         |         |            |        |          |
    | 460896    |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-  | 524160  | 13608   | 156        | 32     | 3        |
    | McEliece- |         |         |            |        |          |
    | 460896f   |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-M | 1044992 | 13932   | 208        | 32     | 5        |
    | cEliece-  |         |         |            |        |          |
    | 6688128   |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-  | 1044992 | 13932   | 208        | 32     | 5        |
    | McEliece- |         |         |            |        |          |
    | 6688128f  |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-M | 1047319 | 13948   | 194        | 32     | 5        |
    | cEliece-  |         |         |            |        |          |
    | 6960119   |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-  | 1047319 | 13948   | 194        | 32     | 5        |
    | McEliece- |         |         |            |        |          |
    | 6960119f  |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-M | 1357824 | 14120   | 208        | 32     | 5        |
    | cEliece-  |         |         |            |        |          |
    | 8192128   |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+
    | Classic-  | 1357824 | 14120   | 208        | 32     | 5        |
    | McEliece- |         |         |            |        |          |
    | 8192128f  |         |         |            |        |          |
    +-----------+---------+---------+------------+--------+----------+

           Table 4: Classic-McEliece Parameter Sizes (in bytes)




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3.1.4.  HQC

   HQC is a code-based KEM relying on the decisional Quasi-Cyclic
   Syndrome Decoding (QCSD) hardness assumption.

   HQC offers small public key and ciphertext sizes, although these are
   larger than those of ML-KEM.

   It will be standardized by NIST.

   The HQC specification is available at [HQC.SPEC].

   +=========+========+=========+============+========+================+
   | Scheme  | Public | Private | Ciphertext | Shared | Claimed        |
   |         | Key    | Key     |            | Secret | Security       |
   |         |        |         |            |        | Level          |
   +=========+========+=========+============+========+================+
   | HQC-128 | 2249   | 2305    | 4433       | 64     | 1              |
   +---------+--------+---------+------------+--------+----------------+
   | HQC-192 | 4522   | 4586    | 8978       | 64     | 3              |
   +---------+--------+---------+------------+--------+----------------+
   | HQC-256 | 7245   | 7317    | 14421      | 64     | 5              |
   +---------+--------+---------+------------+--------+----------------+

                  Table 5: HQC Parameter Sizes (in bytes)

3.1.5.  NTRU

   NTRU is a structured lattice-based KEM.  It has a long, well-
   established history and has been widely analyzed.

   It is considered for standardization by ISO.

   The NTRU specification is available at [NTRU.SPEC].

















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   +================+======+=========+============+========+==========+
   | Scheme         |Public| Private | Ciphertext | Shared | Claimed  |
   |                |Key   | Key     |            | Secret | Security |
   |                |      |         |            |        | Level    |
   +================+======+=========+============+========+==========+
   | ntruhps2048509 |699   | 935     | 699        | 32     | 1        |
   +----------------+------+---------+------------+--------+----------+
   | ntruhps2048677 |930   | 1235    | 930        | 32     | 3        |
   +----------------+------+---------+------------+--------+----------+
   | ntruhps4096821 |1230  | 1592    | 1230       | 32     | 5        |
   +----------------+------+---------+------------+--------+----------+
   | ntruhrss701    |1138  | 1452    | 1138       | 32     | 3        |
   +----------------+------+---------+------------+--------+----------+
   | ntruhrss1373   |2401  | 2983    | 2401       | 32     | 5        |
   +----------------+------+---------+------------+--------+----------+

                 Table 6: NTRU Parameter Sizes (in bytes)

3.2.  Signature Schemes

   Digital signatures are cryptographic primitives used to provide
   authenticity, integrity, and non-repudiation of messages or data.

   In the context of post-quantum cryptography, signature schemes are
   designed to remain secure against adversaries with quantum computing
   capabilities.  They can be used in various scenarios, including
   authentication of protocol messages, code signing, and certificates,
   and are often combined with key establishment mechanisms in secure
   communication protocols.

3.2.1.  ML-DSA

   ML-DSA, formerly known as CRYSTALS-Dilithium, is a structured
   lattice-based signature scheme, now standardized by NIST.  The
   security of ML-DSA is based on the computational hardness of the
   Module Learning with Errors problem as well as the SelfTargetMSIS
   problem, a variant of the Module Short Integer Solution problem.

   European security agencies recommend at least Security Level 3.

   The NIST specification of ML-DSA is available at [MLDSA.SPEC].










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   +===========+============+=============+===========+================+
   | Scheme    | Public Key | Private     | Signature | Claimed        |
   |           |            | Key         |           | Security Level |
   +===========+============+=============+===========+================+
   | ML-DSA-44 | 1312       | 2560        | 2420      | 2              |
   +-----------+------------+-------------+-----------+----------------+
   | ML-DSA-65 | 1952       | 4032        | 3309      | 3              |
   +-----------+------------+-------------+-----------+----------------+
   | ML-DSA-87 | 2592       | 4896        | 4627      | 5              |
   +-----------+------------+-------------+-----------+----------------+

                 Table 7: ML-DSA Parameter Sizes (in bytes)

   [MLDSA.SPEC] also allows to use a 32-bytes seed to represent the
   private key.

3.2.2.  FN-DSA

   FN-DSA, formerly known as Falcon, is a lattice-based signature scheme
   that was selected by NIST for standardization.

   It relies on floating-point arithmetic, which is considered
   challenging to implement securely, especially with respect to side-
   channel attacks.

   The Falcon specification is available at [FNDSA.SPEC].

     +====================+========+=========+===========+==========+
     | Scheme             | Public | Private | Signature | Claimed  |
     |                    | Key    | Key     |           | Security |
     |                    |        |         |           | Level    |
     +====================+========+=========+===========+==========+
     | Falcon-512         | 897    | 1281    | 752       | 1        |
     +--------------------+--------+---------+-----------+----------+
     | Falcon-1024        | 1793   | 2305    | 1462      | 5        |
     +--------------------+--------+---------+-----------+----------+
     | Falcon-padded-512  | 897    | 1281    | 666       | 1        |
     +--------------------+--------+---------+-----------+----------+
     | Falcon-padded-1024 | 1793   | 2305    | 1280      | 5        |
     +--------------------+--------+---------+-----------+----------+

                Table 8: FN-DSA Parameter Sizes (in bytes)

3.2.3.  SLH-DSA

   SLH-DSA, formerly known as SPHINCS+, is a stateless hash-based
   signature scheme now standardized by NIST.




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   Each security level offers two possible hash function families (SHA-2
   or SHAKE) and for both, two specific variants.  The 's' variant has
   smaller signature sizes, while the 'f' variant has faster signature
   generation.

   The NIST specification of SLH-DSA is available at [SLHDSA.SPEC].

     +====================+========+=========+===========+==========+
     | Scheme             | Public | Private | Signature | Claimed  |
     |                    | Key    | Key     |           | Security |
     |                    |        |         |           | Level    |
     +====================+========+=========+===========+==========+
     | SLH-DSA-SHA2-128s  | 32     | 64      | 7856      | 1        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHAKE-128s | 32     | 64      | 7856      | 1        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHA2-128f  | 32     | 64      | 17088     | 1        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHAKE-128f | 32     | 64      | 17088     | 1        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHA2-192s  | 48     | 96      | 16224     | 3        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHAKE-192s | 48     | 96      | 16224     | 3        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHA2-192f  | 48     | 96      | 35664     | 3        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHAKE-192f | 48     | 96      | 35664     | 3        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHA2-256s  | 64     | 128     | 29762     | 5        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHAKE-256s | 64     | 128     | 29762     | 5        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHA2-256f  | 64     | 128     | 49856     | 5        |
     +--------------------+--------+---------+-----------+----------+
     | SLH-DSA-SHAKE-256f | 64     | 128     | 49856     | 5        |
     +--------------------+--------+---------+-----------+----------+

               Table 9: SLH-DSA Parameter Sizes (in bytes)

3.2.4.  LMS

   Leighton-Micali Signatures (LMS) is a stateful hash-based signature
   scheme that uses LM-OTS for one-time signatures, and is based on
   Merkle hash trees.







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   It requires careful state management.
   [I-D.draft-ietf-pquip-hbs-state] provides guidance and security
   considerations on state management for stateful hash-based signature
   schemes.

   The NIST specification of LMS is available at [LMS.SPEC].

3.2.4.1.  LMS with SHA-256

   The signatures' sizes for the LMS_SHA256_M32_H{5, 10, 15, 20, 25}
   signature scheme depend on the choice of the underlying LMOTS scheme
   and in particular on the value of the Winternitz parameter W.
   Therefore, the signatures' sizes of LMS_SHA256_M32_H{5, 10, 15, 20,
   25} are given in a 4-element array where values correspond to the
   value of W = 8, 4, 2, 1 in that order.




































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   +=====================+========+============+===========+==========+
   | Scheme              | Public | Private    | Signature | Claimed  |
   |                     | Key    | Key        |           | Security |
   |                     |        |            |           | Level    |
   +=====================+========+============+===========+==========+
   | LMOTS_SHA256_N32_W1 | 56     | 8504       | 8516      | x        |
   +---------------------+--------+------------+-----------+----------+
   | LMOTS_SHA256_N32_W2 | 56     | 4280       | 4292      | x        |
   +---------------------+--------+------------+-----------+----------+
   | LMOTS_SHA256_N32_W4 | 56     | 2168       | 2180      | x        |
   +---------------------+--------+------------+-----------+----------+
   | LMOTS_SHA256_N32_W8 | 56     | 1112       | 1124      | x        |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M32_H5   | 56     | 1796       | [1296,    | 5        |
   |                     |        |            | 2352,     |          |
   |                     |        |            | 4464,     |          |
   |                     |        |            | 8688]     |          |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M32_H10  | 56     | 57348      | [1456,    | 5        |
   |                     |        |            | 2512,     |          |
   |                     |        |            | 4624,     |          |
   |                     |        |            | 8848]     |          |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M32_H15  | 56     | 1835012    | [1616,    | 5        |
   |                     |        |            | 2672,     |          |
   |                     |        |            | 4784,     |          |
   |                     |        |            | 9008]     |          |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M32_H20  | 56     | 58720260   | [1776,    | 5        |
   |                     |        |            | 2832,     |          |
   |                     |        |            | 4944,     |          |
   |                     |        |            | 9168]     |          |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M32_H25  | 56     | 1879048196 | [1936,    | 5        |
   |                     |        |            | 2992,     |          |
   |                     |        |            | 5104,     |          |
   |                     |        |            | 9328]     |          |
   +---------------------+--------+------------+-----------+----------+

           Table 10: LMS with SHA256 Parameter Sizes (in bytes)











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3.2.4.2.  LMS with SHA-256/192

   The signatures' sizes for the LMS_SHA256/192_M24_H{5, 10, 15, 20, 25}
   signature scheme depend on the choice of the underlying LMOTS scheme
   and in particular on the value of the Winternitz parameter W.
   Therefore, the signatures' sizes of LMS_SHA256/192_M24_H{5, 10, 15,
   20, 25} are given in a 4-element array where values correspond to the
   value of W = 8, 4, 2, 1 in that order.











































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   +=====================+========+============+===========+==========+
   | Scheme              | Public | Private    | Signature | Claimed  |
   |                     | Key    | Key        |           | Security |
   |                     |        |            |           | Level    |
   +=====================+========+============+===========+==========+
   | LMOTS_SHA256_N24_W1 | 56     | 4824       | 4828      | x        |
   +---------------------+--------+------------+-----------+----------+
   | LMOTS_SHA256_N24_W2 | 56     | 2448       | 2452      | x        |
   +---------------------+--------+------------+-----------+----------+
   | LMOTS_SHA256_N24_W4 | 56     | 1248       | 1251      | x        |
   +---------------------+--------+------------+-----------+----------+
   | LMOTS_SHA256_N24_W8 | 56     | 648        | 652       | x        |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M24_H5   | 56     | 1796       | [784,     | 5        |
   |                     |        |            | 1384,     |          |
   |                     |        |            | 2584,     |          |
   |                     |        |            | 4960]     |          |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M24_H10  | 56     | 57348      | [904,     | 5        |
   |                     |        |            | 1504,     |          |
   |                     |        |            | 2704,     |          |
   |                     |        |            | 5080]     |          |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M24_H15  | 56     | 1835012    | [1024,    | 5        |
   |                     |        |            | 1624,     |          |
   |                     |        |            | 2824,     |          |
   |                     |        |            | 5200]     |          |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M24_H20  | 56     | 58720260   | [1144,    | 5        |
   |                     |        |            | 1744,     |          |
   |                     |        |            | 2944,     |          |
   |                     |        |            | 5320]     |          |
   +---------------------+--------+------------+-----------+----------+
   | LMS_SHA256_M24_H25  | 56     | 1879048196 | [1264,    | 5        |
   |                     |        |            | 1864,     |          |
   |                     |        |            | 3064,     |          |
   |                     |        |            | 5440]     |          |
   +---------------------+--------+------------+-----------+----------+

         Table 11: LMS with SHA256/192 Parameter Sizes (in bytes)











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3.2.4.3.  LMS with SHAKE256/256

   The signatures' sizes for the LMS_SHA256_M32_H{5, 10, 15, 20, 25}
   signature scheme depend on the choice of the underlying LMOTS scheme
   and in particular on the value of the Winternitz parameter W.
   Therefore, the signatures' sizes of LMS_SHA256_M32_H{5, 10, 15, 20,
   25} are given in a 4-element array where values correspond to the
   value of W = 8, 4, 2, 1 in that order.











































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   +====================+========+============+=============+==========+
   | Scheme             | Public | Private    | Signature   | Claimed  |
   |                    | Key    | Key        |             | Security |
   |                    |        |            |             | Level    |
   +====================+========+============+=============+==========+
   | LMOTS_SHAKE_N32_W1 | 56     | 8504       | 8516        | x        |
   +--------------------+--------+------------+-------------+----------+
   | LMOTS_SHAKE_N32_W2 | 56     | 4280       | 4292        | x        |
   +--------------------+--------+------------+-------------+----------+
   | LMOTS_SHAKE_N32_W4 | 56     | 2168       | 2180        | x        |
   +--------------------+--------+------------+-------------+----------+
   | LMOTS_SHAKE_N32_W8 | 56     | 1112       | 1124        | x        |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M32_H5   | 56     | 1796       | [1296,      | 5        |
   |                    |        |            | 2352,       |          |
   |                    |        |            | 4464,       |          |
   |                    |        |            | 8688]       |          |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M32_H10  | 56     | 57348      | [1456,      | 5        |
   |                    |        |            | 2512,       |          |
   |                    |        |            | 4624,       |          |
   |                    |        |            | 8848]       |          |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M32_H15  | 56     | 1835012    | [1616,      | 5        |
   |                    |        |            | 2672,       |          |
   |                    |        |            | 4784,       |          |
   |                    |        |            | 9008]       |          |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M32_H20  | 56     | 58720260   | [1776,      | 5        |
   |                    |        |            | 2832,       |          |
   |                    |        |            | 4944,       |          |
   |                    |        |            | 9168]       |          |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M32_H25  | 56     | 1879048196 | [1936,      | 5        |
   |                    |        |            | 2992,       |          |
   |                    |        |            | 5104,       |          |
   |                    |        |            | 9328]       |          |
   +--------------------+--------+------------+-------------+----------+

         Table 12: LMS with SHAKE256/256 Parameter Sizes (in bytes)











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3.2.4.4.  LMS with SHAKE256/192

   The signatures' sizes for the LMS_SHA256/192_M24_H{5, 10, 15, 20, 25}
   signature scheme depend on the choice of the underlying LMOTS scheme
   and in particular on the value of the Winternitz parameter W.
   Therefore, the signatures' sizes of LMS_SHA256/192_M24_H{5, 10, 15,
   20, 25} are given in a 4-element array where values correspond to the
   value of W = 8, 4, 2, 1 in that order.











































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   +====================+========+============+=============+==========+
   | Scheme             | Public | Private    | Signature   | Claimed  |
   |                    | Key    | Key        |             | Security |
   |                    |        |            |             | Level    |
   +====================+========+============+=============+==========+
   | LMOTS_SHAKE_N24_W1 | 56     | 4824       | 4828        | x        |
   +--------------------+--------+------------+-------------+----------+
   | LMOTS_SHAKE_N24_W2 | 56     | 2448       | 2452        | x        |
   +--------------------+--------+------------+-------------+----------+
   | LMOTS_SHAKE_N24_W4 | 56     | 1248       | 1252        | x        |
   +--------------------+--------+------------+-------------+----------+
   | LMOTS_SHAKE_N24_W8 | 56     | 648        | 652         | x        |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M24_H5   | 56     | 1796       | [784,       | 5        |
   |                    |        |            | 1384,       |          |
   |                    |        |            | 2584,       |          |
   |                    |        |            | 4960]       |          |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M24_H10  | 56     | 57348      | [904,       | 5        |
   |                    |        |            | 1504,       |          |
   |                    |        |            | 2704,       |          |
   |                    |        |            | 5080]       |          |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M24_H15  | 56     | 1835012    | [1024,      | 5        |
   |                    |        |            | 1624,       |          |
   |                    |        |            | 2824,       |          |
   |                    |        |            | 5200]       |          |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M24_H20  | 56     | 58720260   | [1144,      | 5        |
   |                    |        |            | 1744,       |          |
   |                    |        |            | 2944,       |          |
   |                    |        |            | 5320]       |          |
   +--------------------+--------+------------+-------------+----------+
   | LMS_SHAKE_M24_H25  | 56     | 1879048196 | [1264,      | 5        |
   |                    |        |            | 1864,       |          |
   |                    |        |            | 3064,       |          |
   |                    |        |            | 5440]       |          |
   +--------------------+--------+------------+-------------+----------+

         Table 13: LMS with SHAKE256/192 Parameter Sizes (in bytes)

3.2.5.  XMSS / XMSS^MT

   The eXtended Merkle Signature Scheme (XMSS) is a stateful hash-based
   signature scheme that uses WOTS+ for one-time signatures, and is
   based on Merkle hash trees.  XMSS^MT is a variant that has multiple
   hash trees.




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   It requires careful state management.
   [I-D.draft-ietf-pquip-hbs-state] provides guidance and security
   considerations on state management for stateful hash-based signature
   schemes.

   The NIST specification of XMSS is available at [XMSS.SPEC].

    +===========================+======+=======+===========+==========+
    | Scheme                    |Public|Private| Signature | Claimed  |
    |                           |Key   |Key    |           | Security |
    |                           |      |       |           | Level    |
    +===========================+======+=======+===========+==========+
    | XMSS-SHA2_10_256          |64    |1793   | 2500      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHA2_16_256          |64    |2093   | 2692      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHA2_20_256          |64    |2573   | 2820      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHA2_20/2_256      |64    |5998   | 4963      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHA2_20/4_256      |64    |10938  | 9251      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHA2_40/2_256      |64    |9600   | 5605      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHA2_40/4_256      |64    |15252  | 9893      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHA2_40/8_256      |64    |24516  | 18469     | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHA2_60/3_256      |64    |16629  | 8392      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHA2_60/6_256      |64    |24507  | 14824     | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHA2_60/12_256     |64    |38095  | 27688     | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHA2_10_192          |48    |1053   | 1492      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHA2_16_192          |48    |1605   | 1636      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHA2_20_192          |48    |1973   | 1732      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHAKE256_10_256      |64    |1373   | 2500      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHAKE256_16_256      |64    |2093   | 2692      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHAKE256_20_256      |64    |2573   | 2820      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHAKE256_20/2_256  |64    |5998   | 4963      | 5        |
    +---------------------------+------+-------+-----------+----------+



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    | XMSSMT-SHAKE256_20/4_256  |64    |10938  | 9251      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHAKE256_40/2_256  |64    |9600   | 5605      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHAKE256_40/4_256  |64    |15252  | 9893      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHAKE256_40/8_256  |64    |24516  | 18469     | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHAKE256_60/3_256  |64    |24516  | 8392      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHAKE256_60/6_256  |64    |24507  | 14824     | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSSMT-SHAKE256_60/12_256 |64    |38095  | 27688     | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHAKE256_10_192      |48    |1053   | 1492      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHAKE256_16_192      |48    |1605   | 1636      | 5        |
    +---------------------------+------+-------+-----------+----------+
    | XMSS-SHAKE256_20_192      |48    |1973   | 1732      | 5        |
    +---------------------------+------+-------+-----------+----------+

                 Table 14: XMSS Parameter Sizes (in bytes)

4.  Security Properties

4.1.  Quantum-Vulnerable Asymmetric Cryptography

   Table 15 gives a list of asymmetric cryptographic schemes that are
   vulnerable to quantum computers and are planned to be deprecated and/
   or disallowed in the future by various organizations or security
   agencies.  In particular, NIST provides deprecation and disallowance
   timelines in [IR.8547].

   The EU PQC Workstream also published its roadmap for the transition
   to post-quantum cryptography in [EU.Roadmap].  It distinguishes
   between low, medium and high quantum risk levels, and recommends
   completing the PQC transition for high-risk use cases before 2031,
   for medium-risk use cases before 2036, and for low-risk use cases
   before 2036, as much as feasible.












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        +========+===========================+===================+
        | Scheme | Hardness assumption       | Disallowed (NIST) |
        +========+===========================+===================+
        | ECDSA  | Discrete Logarithm        | after 2035        |
        +--------+---------------------------+-------------------+
        | EdDSA  | Discrete Logarithm        | after 2035        |
        +--------+---------------------------+-------------------+
        | RSA    | Factorisation             | after 2035        |
        +--------+---------------------------+-------------------+
        | (EC)DH | Decisional Diffie Hellman | after 2035        |
        +--------+---------------------------+-------------------+

          Table 15: Quantum-Vulnerable Asymmetric Cryptographic
                                 Schemes

4.2.  Quantum-Safe Asymmetric Cryptography

   Table 16 gives a brief summary of the security properties of various
   KEM algorithms.

      +==========+======+===================+===========+==========+
      | Scheme   | SDO  | Hardness          | Security  | Comments |
      |          |      | assumption        | Model     |          |
      +==========+======+===================+===========+==========+
      | ML-KEM   | NIST | Module LWE        | IND-CCA-2 | xxx      |
      +----------+------+-------------------+-----------+----------+
      | FrodoKEM | ISO  | Unstructured LWE  | IND-CCA2  | xxx      |
      +----------+------+-------------------+-----------+----------+
      | HQC      | NIST | Decisional Quasi- | IND-CCA2  | xxx      |
      |          |      | Cyclic Syndrome   |           |          |
      |          |      | Decoding Problem  |           |          |
      +----------+------+-------------------+-----------+----------+
      | Classic  | ISO  | Syndrome Decoding | IND-CCA2  | xxx      |
      | McEliece |      | Problem, Goppa    |           |          |
      |          |      | code recovery     |           |          |
      +----------+------+-------------------+-----------+----------+
      | NTRU     | ISO  | NTRU              | IND-CCA2  | xxx      |
      +----------+------+-------------------+-----------+----------+

                   Table 16: Properties of KEM schemes

   FrodoKEM is believed to have conservative security compared to
   schemes based on structured lattices like ML-KEM or NTRU.

   Table 17 gives a summary of the security properties of different
   signature algorithms.





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    +=========+======+=================+==========+==================+
    | Scheme  | SDO  | Hardness        | Security | Comments         |
    |         |      | assumption      | Model    |                  |
    +=========+======+=================+==========+==================+
    | ML-DSA  | NIST | Module LWE,     | SUF-CMA  | xxx              |
    |         |      | SelfTargetMSIS  |          |                  |
    +---------+------+-----------------+----------+------------------+
    | FN-DSA  | NIST | SIS over NTRU   | EUF-CMA  | Uses floating    |
    |         |      | lattices        |          | point arithmetic |
    +---------+------+-----------------+----------+------------------+
    | SLH-DSA | NIST | Second-preimage | SUF-CMA  | xxx              |
    |         |      | resistance      | (*)      |                  |
    +---------+------+-----------------+----------+------------------+
    | LMS     | NIST | Collision       | SUF-CMA  | Need state       |
    |         |      | resistance      | (*)      | management       |
    +---------+------+-----------------+----------+------------------+
    | XMSS    | NIST | Collision       | SUF-CMA  | Need state       |
    |         |      | resistance      | (*)      | management       |
    +---------+------+-----------------+----------+------------------+

                Table 17: Properties of signatures schemes

   (*) There is no known attack on the SUF-CMA security of those
   schemes, which are widely believed to be SUF-CMA secure.  However, no
   formal proof exists yet.

   Hash-based signature schemes such as SLH-DSA, LMS, and XMSS are
   believed to offer more conservative security compared to lattice-
   based schemes like ML-DSA or FN-DSA.

5.  IANA Considerations

   This document has no IANA action.

6.  References

6.1.  Normative References

   [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/rfc/rfc2119>.

   [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/rfc/rfc8174>.

6.2.  Informative References



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   [CLASSICMCELIECE.SPEC]
              "Classic McEliece: conservative code-based cryptography",
              October 2022,
              <https://classic.mceliece.org/mceliece-spec-20221023.pdf>.

   [EU.Roadmap]
              EU PQC Workstream, "A Coordinated Implementation Roadmap
              for the Transition to Post-Quantum Cryptography", June
              2025, <https://digital-strategy.ec.europa.eu/en/library/
              coordinated-implementation-roadmap-transition-post-
              quantum-cryptography>.

   [FNDSA.SPEC]
              "Falcon: Fast-Fourier Lattice-based Compact Signatures
              over NTRU", October 2020,
              <https://falcon-sign.info/falcon.pdf>.

   [FRODOKEM.SPEC]
              "FrodoKEM: Learning With Errors Key Encapsulation",
              December 2024, <https://frodokem.org/files/
              FrodoKEM_standard_proposal_20241205.pdf>.

   [HQC.SPEC] "Hamming Quasi-Cyclic (HQC)", February 2025, <https://pqc-
              hqc.org/doc/hqc-specification_2025-02-19.pdf>.

   [I-D.draft-ietf-pquip-hbs-state]
              Wiggers, T., Bashiri, K., Kölbl, S., Goodman, J., and S.
              Kousidis, "Hash-based Signatures: State and Backup
              Management", Work in Progress, Internet-Draft, draft-ietf-
              pquip-hbs-state-00, 17 June 2025,
              <https://datatracker.ietf.org/doc/html/draft-ietf-pquip-
              hbs-state-00>.

   [I-D.draft-ietf-pquip-pqt-hybrid-terminology-04]
              D, F., P, M., and B. Hale, "Terminology for Post-Quantum
              Traditional Hybrid Schemes", Work in Progress, Internet-
              Draft, draft-ietf-pquip-pqt-hybrid-terminology-04, 10
              September 2024, <https://datatracker.ietf.org/doc/html/
              draft-ietf-pquip-pqt-hybrid-terminology-04>.

   [IR.8547]  National Institute of Standards and Technology (NIST),
              "Transition to Post-Quantum Cryptography Standards",
              November 2024, <https://nvlpubs.nist.gov/nistpubs/ir/2024/
              NIST.IR.8547.ipd.pdf>.







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   [LMS.SPEC] "Stateless Hash-Based Digital Signature Standard", August
              2024,
              <https://nvlpubs.nist.gov/nistpubs/SpecialPublications/
              NIST.SP.800-208.pdf>.

   [MLDSA.SPEC]
              "Module-Lattice-Based Digital Signature Standard", August
              2024, <https://nvlpubs.nist.gov/nistpubs/fips/
              nist.fips.204.pdf>.

   [MLKEM.SPEC]
              National Institute of Standards and Technology (NIST),
              "Module-Lattice-Based Digital Signature Standard", August
              2024, <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.204.pdf>.

   [NTRU.SPEC]
              "NTRU Key Encapsulation", March 2025,
              <https://www.ietf.org/id/draft-fluhrer-cfrg-ntru-02.html>.

   [SLHDSA.SPEC]
              "Stateless Hash-Based Digital Signature Standard", August
              2024, <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.205.pdf>.

   [XMSS.SPEC]
              "Recommendation for Stateful Hash-Based Signature
              Schemes", October 2020,
              <https://nvlpubs.nist.gov/nistpubs/SpecialPublications/
              NIST.SP.800-208.pdf>.

Authors' Addresses

   Lucas Prabel
   Huawei
   Email: lucas.prabel@huawei.com


   Shuzhou Sun
   Huawei
   Email: sunshuzhou@huawei.com


   Guang Zeng
   Huawei
   Email: zengguang13@huawei.com





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Internet-Draft              PQC Algo Guidance               October 2025


   Guilin Wang
   Huawei
   Email: wang.guilin@huawei.com
















































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