Internet-Draft xwing January 2024
Connolly, et al. Expires 25 July 2024 [Page]
Workgroup:
Crypto Forum
Internet-Draft:
draft-connolly-cfrg-xwing-kem-01
Published:
Intended Status:
Informational
Expires:
Authors:
D. Connolly
SandboxAQ
P. Schwabe
MPI-SP & Radboud University
B. E. Westerbaan
Cloudflare

X-Wing: general-purpose hybrid post-quantum KEM

Abstract

This memo defines X-Wing, a general-purpose post-quantum/traditional hybrid key encapsulation mechanism (PQ/T KEM) built on X25519 and ML-KEM-768.

About This Document

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

The latest revision of this draft can be found at https://dconnolly.github.io/draft-connolly-cfrg-xwing-kem/draft-connolly-cfrg-xwing-kem.html. Status information for this document may be found at https://datatracker.ietf.org/doc/draft-connolly-cfrg-xwing-kem/.

Discussion of this document takes place on the Crypto Forum Research Group mailing list (mailto:cfrg@ietf.org), which is archived at https://mailarchive.ietf.org/arch/search/?email_list=cfrg. Subscribe at https://www.ietf.org/mailman/listinfo/cfrg/.

Source for this draft and an issue tracker can be found at https://github.com/dconnolly/draft-connolly-cfrg-xwing-kem.

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 Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.

Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."

This Internet-Draft will expire on 25 July 2024.

Table of Contents

1. Introduction

1.1. Warning: ML-KEM-768 has not been standardised

X-Wing uses ML-KEM-768, which has not been standardised yet. Thus X-Wing is not finished, yet, and should not be used, yet.

1.2. Motivation

There are many choices that can be made when specifying a hybrid KEM: the constituent KEMs; their security levels; the combiner; and the hash within, to name but a few. Having too many similar options are a burden to the ecosystem.

The aim of X-Wing is to provide a concrete, simple choice for post-quantum hybrid KEM, that should be suitable for the vast majority of use cases.

1.3. Design goals

By making concrete choices, we can simplify and improve many aspects of X-Wing.

  • Simplicity of definition. Because all shared secrets and cipher texts are fixed length, we do not need to encode the length. Using SHA3-256, we do not need HMAC-based construction. For the concrete choice of ML-KEM-768, we do not need to mix in its ciphertext, see Section 6.

  • Security analysis. Because ML-KEM-768 already assumes QROM, we do not need to complicate the analysis of X-Wing by considering stronger models.

  • Performance. Not having to mix in the ML-KEM-768 ciphertext is a nice performance benefit. Furthermore, by using SHA3-256 in the combiner, which matches the hashing in ML-KEM-768, this hash can be computed in one go on platforms where two-way Keccak is available.

We aim for "128 bits" security (NIST PQC level 1). Although at the moment there is no peer-reviewed evidence that ML-KEM-512 does not reach this level, we would like to hedge against future cryptanalytic improvements, and feel ML-KEM-768 provides a comfortable margin.

We aim for X-Wing to be usable for most applications, including specifically HPKE [RFC9180].

1.4. Not an interactive key-agreement

Traditionally most protocols use a Diffie-Hellman (DH) style non-interactive key-agreement. In many cases, a DH key agreement can be replaced by the interactive key-agreement afforded by a KEM without change in the protocol flow. One notable example is TLS [HYBRID] [XYBERTLS]. However, not all uses of DH can be replaced in a straight-forward manner by a plain KEM.

1.5. Not an authenticated KEM

In particular, X-Wing is not, borrowing the language of [RFC9180], an authenticated KEM.

1.6. Comparisons

1.6.1. With HPKE X25519Kyber768Draft00

X-Wing is most similar to HPKE's X25519Kyber768Draft00 [XYBERHPKE]. The key differences are:

  • X-Wing uses the final version of ML-KEM-768.

  • X-Wing hashes the shared secrets, to be usable outside of HPKE.

  • X-Wing has a simpler combiner by flattening DHKEM(X25519) into the final hash.

  • X-Wing does not hash in the ML-KEM-768 ciphertext.

There is also a different KEM called X25519Kyber768Draft00 [XYBERTLS] which is used in TLS. This one should not be used outside of TLS, as it assumes the presence of the TLS transcript to ensure non malleability.

1.6.2. With generic combiner

The generic combiner of [I-D.ounsworth-cfrg-kem-combiners] can be instantiated with ML-KEM-768 and DHKEM(X25519). That achieves similar security, but:

  • X-Wing is more performant, not hashing in the ML-KEM-768 ciphertext, and flattening the DHKEM construction, with the same level of security.

  • X-Wing has a fixed 32 byte shared secret, instead of a variable shared secret.

  • X-Wing does not accept the optional counter and fixedInfo arguments.

2. Requirements Notation

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. Conventions and Definitions

This document is consistent with all terminology defined in [I-D.driscoll-pqt-hybrid-terminology].

The following terms are used throughout this document to describe the operations, roles, and behaviors of HPKE:

4. Cryptographic Dependencies

X-Wing relies on the following primitives:

Note that 9 is the standard basepoint for X25519, cf Section 6.1 of [RFC7748].

5. X-Wing Construction

5.1. Encoding and sizes

X-Wing encapsulation key, decapsulation key, ciphertexts and shared secrets are all fixed length byte strings.

Decapsulation key (private):

2464 bytes

Encapsulation key (public):

1216 bytes

Ciphertext:

1120 bytes

Shared secret:

32 bytes

5.2. Key generation

An X-Wing keypair (decapsulation key, encapsulation key) is generated as follows.

def GenerateKeyPair():
  (pk_M, sk_M) = ML-KEM-768.KeyGen()
  sk_X = random(32)
  pk_X = X25519(sk_X, X25519_BASE)
  return concat(sk_M, sk_X, pk_X), concat(pk_M, pk_X)

GenerateKeyPair() returns the 2464 byte secret encapsulation key sk and the 1216 byte decapsulation key pk.

5.2.1. Key derivation

For testing, it is convenient to have a deterministic version of key generation. An X-Wing implementation MAY provide the following derandomized variant of key generation.

def GenerateKeyPairDerand(seed):
  (pk_M, sk_M) = ML-KEM-768.KeyGenDerand(seed[0:64])
  sk_X = seed[64:96]
  pk_X = X25519(sk_X, X25519_BASE)
  return concat(sk_M, sk_X, pk_X), concat(pk_M, pk_X)

seed must be 96 bytes.

GenerateKeyPairDerand() returns the 2464 byte secret encapsulation key sk and the 1216 byte decapsulation key pk.

5.3. Combiner

Given 32 byte strings ss_M, ss_X, ct_X, pk_X, representing the ML-KEM-768 shared secret, X25519 shared secret, X25519 ciphertext (ephemeral public key) and X25519 public key respectively, the 32 byte combined shared secret is given by:

def Combiner(ss_M, ss_X, ct_X, pk_X):
  return SHA3-256(concat(
    XWingLabel,
    ss_M,
    ss_X,
    ct_X,
    pk_X
  ))

where XWingLabel is the following 6 byte ASCII string

XWingLabel = concat(
    "\./",
    "/^\",
)

5.4. Encapsulation

Given an X-Wing encapsulation key pk, encapsulation proceeds as follows.

def Encapsulate(pk):
  pk_M = pk[0:1184]
  pk_X = pk[1184:1216]
  ek_X = random(32)
  ct_X = X25519(ek_X, X25519_BASE)
  ss_X = X25519(ek_X, pk_X)
  (ss_M, ct_M) = ML-KEM-768.Encaps(pk_M)
  ss = Combiner(ss_M, ss_X, ct_X, pk_X)
  ct = concat(ct_M, ct_X)
  return (ss, ct)

pk is a 1216 byte X-Wing encapsulation key resulting from GeneratePublicKey()

Encapsulate() returns the 32 byte shared secret ss and the 1120 byte ciphertext ct.

5.4.1. Derandomized

For testing, it is convenient to have a deterministic version of encapsulation. An X-Wing implementation MAY provide the following derandomized function.

def EncapsulateDerand(pk, seed):
  pk_M = pk[0:1184]
  pk_X = pk[1184:1216]
  ek_X = seed[32:64]
  ct_X = X25519(ek_X, X25519_BASE)
  ss_X = X25519(ek_X, pk_X)
  (ss_M, ct_M) = ML-KEM-768.EncapsDerand(pk_M, seed[0:32])
  ss = Combiner(ss_M, ss_X, ct_X, pk_X)
  ct = concat(ct_M, ct_X)
  return (ss, ct)

pk is a 1216 byte X-Wing encapsulation key resulting from GeneratePublicKey() seed MUST be 64 bytes.

EncapsulateDerand() returns the 32 byte shared secret ss and the 1120 byte ciphertext ct.

5.5. Decapsulation

def Decapsulate(ct, sk):
  ct_M = ct[0:1088]
  ct_X = ct[1088:1120]
  sk_M = sk[0:2400]
  sk_X = sk[2400:2432]
  pk_X = sk[2432:2464]
  ss_M = ML-KEM-768.Decapsulate(ct_M, sk_M)
  ss_X = X25519(sk_X, ct_X)
  return Combiner(ss_M, ss_X, ct_X, pk_X)

ct is the 1120 byte ciphertext resulting from Encapsulate() sk is a 2464 byte X-Wing decapsulation key resulting from GenerateKeyPair()

Decapsulate() returns the 32 byte shared secret.

5.6. Use in HPKE

X-Wing satisfies the HPKE KEM interface as follows.

The SerializePublicKey, DeserializePublicKey, SerializePrivateKey and DeserializePrivateKey are the identity functions, as X-Wing keys are fixed-length byte strings, see Section 5.1.

DeriveKeyPair() is given by

def DeriveKeyPair(ikm):
  return GenerateKeyPairDerand(SHAKE128(ikm, 96))

where the HPKE private key and public key are the X-Wing decapsulation key and encapsulation key respectively.

The argument ikm to DeriveKeyPair() SHOULD be at least 32 octets in length. (This is contrary to [RFC9180] which stipulates it should be at least Nsk=2432 octets in length.)

Encap() is Encapsulate() from Section 5.4.

Decap() is Decapsulate() from Section 5.5.

X-Wing is not an authenticated KEM: it does not support AuthEncap() and AuthDecap(), see Section 1.5.

Nsecret, Nenc, Npk, and Nsk are defined in Section 7.

5.7. Use in TLS 1.3

For the client's share, the key_exchange value contains the X-Wing encapsulation key.

For the server's share, the key_exchange value contains the X-Wing ciphertext.

6. Security Considerations

Informally, X-Wing is secure if SHA3 is secure, and either X25519 is secure, or ML-KEM-768 is secure.

More precisely, if SHA3-256, SHA3-512, SHAKE-128, and SHAKE-256 may be modelled as a random oracle, then the IND-CCA security of X-Wing is bounded by the IND-CCA security of ML-KEM-768, and the gap-CDH security of Curve25519, see [PROOF].

The security of X-Wing relies crucially on the specifics of the Fujisaki-Okamoto transformation used in ML-KEM-768. In particular, the X-Wing combiner cannot be assumed to be secure, when used with different KEMs.

7. IANA Considerations

This document requests/registers a new entry to the "HPKE KEM Identifiers" registry.

Value:

TBD (please)

KEM:

X-Wing

Nsecret:

32

Nenc:

1120

Npk:

1216

Nsk:

2464

Auth:

no

Reference:

This document

Furthermore, this document requests/registers a new entry to the TLS Named Group (or Supported Group) registry, according to the procedures in Section 6 of [TLSIANA].

Value:

TBD (please)

Description:

X-Wing

DTLS-OK:

Y

Recommended:

Y

Reference:

This document

Comment:

PQ/T hybrid of X25519 and ML-KEM-768

8. TODO

9. References

9.1. Normative References

[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <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, , <https://www.rfc-editor.org/rfc/rfc8174>.

9.2. Informative References

[FIPS202]
National Institute of Standards and Technology, "FIPS 202: SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions", n.d., <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf>.
[HYBRID]
Stebila, D., Fluhrer, S., and S. Gueron, "Hybrid key exchange in TLS 1.3", Work in Progress, Internet-Draft, draft-stebila-tls-hybrid-design-03, , <https://datatracker.ietf.org/doc/html/draft-stebila-tls-hybrid-design-03>.
[I-D.driscoll-pqt-hybrid-terminology]
D, F., "Terminology for Post-Quantum Traditional Hybrid Schemes", Work in Progress, Internet-Draft, draft-driscoll-pqt-hybrid-terminology-02, , <https://datatracker.ietf.org/doc/html/draft-driscoll-pqt-hybrid-terminology-02>.
[I-D.ounsworth-cfrg-kem-combiners]
Ounsworth, M., Wussler, A., and S. Kousidis, "Combiner function for hybrid key encapsulation mechanisms (Hybrid KEMs)", Work in Progress, Internet-Draft, draft-ounsworth-cfrg-kem-combiners-04, , <https://datatracker.ietf.org/doc/html/draft-ounsworth-cfrg-kem-combiners-04>.
[MLKEM]
National Institute of Standards and Technology, "FIPS 203 (Initial Draft): Module-Lattice-Based Key-Encapsulation Mechanism Standard", n.d., <https://csrc.nist.gov/pubs/fips/203/ipd>.
[PROOF]
Barbosa, M., Connolly, D., Duarte, J., Kaiser, A., Schwabe, P., Varner, K., and B. E. Westerbraan, "X-Wing: The Hybrid KEM You’ve Been Looking For", n.d., <https://eprint.iacr.org/2024/039>.
[RFC7748]
Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, , <https://www.rfc-editor.org/rfc/rfc7748>.
[RFC9180]
Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180, , <https://www.rfc-editor.org/rfc/rfc9180>.
[TLSIANA]
Salowey, J. A. and S. Turner, "IANA Registry Updates for TLS and DTLS", Work in Progress, Internet-Draft, draft-ietf-tls-rfc8447bis-08, , <https://datatracker.ietf.org/doc/html/draft-ietf-tls-rfc8447bis-08>.
[XYBERHPKE]
Westerbaan, B. and C. A. Wood, "X25519Kyber768Draft00 hybrid post-quantum KEM for HPKE", Work in Progress, Internet-Draft, draft-westerbaan-cfrg-hpke-xyber768d00-02, , <https://datatracker.ietf.org/doc/html/draft-westerbaan-cfrg-hpke-xyber768d00-02>.
[XYBERTLS]
Westerbaan, B. and D. Stebila, "X25519Kyber768Draft00 hybrid post-quantum key agreement", Work in Progress, Internet-Draft, draft-tls-westerbaan-xyber768d00-03, , <https://datatracker.ietf.org/doc/html/draft-tls-westerbaan-xyber768d00-03>.

Appendix A. Test vectors # TODO: replace with test vectors that re-use ML-KEM, X25519 values

seed
  7f9c2ba4e88f827d616045507605853ed73b8093f6efbc88eb1a6eacfa66ef263cb1eea9
  88004b93103cfb0aeefd2a686e01fa4a58e8a3639ca8a1e3f9ae57e235b8cc873c23dc62
  b8d260169afa2f75ab916a58d974918835d25e6a435085b2
sk
  24c59d1c7603e7b74bc7aa1bc2cb3a214b3cfaebb63bd85b65408427c498ba394371bb27
  1f92a3b506b81d54a95a7c0ddfbaa1519553d6f3cd5a601b7db6b0e91a5149468f1f68ad
  26478bf3c6670e093ac4c49e7a90ba46595de94c50e04129a811a841b39534a87f0ae7b1
  116553e20c9a566b9b8ff7c7e728b8b201893403a4f252a55230874c256b897834cda349
  807b25cbd75a30867bfb80328200017f1cb70b56cc546b65d3dc9cdb45107cf10dba3496
  19043ac35c0b9546309a239039813ed5c40f353a5e8e42193564496112bda56cb38c081d
  f252ae9c2c7e441a062e92a7c8da7a240c9952d86b5f1bb6a53b38a5ac0a54a84b43f12d
  a1d0525655684a12090b60b28b0c628db092015547d1070af5d6192e639636615d03c654
  bb90008ca15b784119f6178a00d7bef4a54a274ac922e55c61a3a8840aa258639484a3bc
  e2e43b6c969b11275631daa129a61ea0e2939f0877e1a110c8a44b24c54fbb07a958db9f
  eeca1eb52b086c87bf43a9b02a5b2c4762117c3a99ae4c4e2eaa7a33b9a714737215c103
  17514f6c4299ef92acd64c4858e85ce737a801890022d7381f3540230c0c8ef50a848a28
  b09ba0bf8b50619c905751601d7629767449c9c0b2bae321f438a77f412a55e45ecab4b3
  9053c6561801c639be6495be8fa144ef6029af663407ca9181946de5f3aec7236343ab3b
  c5a38a09c01b412baf0afb23f9e9b8f2b40810f2ce4ffbcdbfd87972323e98065160bcba
  34b3afd6c25b664745fca99a9ea75cef019d768485ec23336d9b39e4d05d8d587b30633d
  4f69ade5753a39680235e44f27995da96798f3a85e184a9fad19320829629f4140417bb7
  dbf5851ab79258134146d088452774991a087a1c2beaea89f218087ba774ae253b494c27
  750b1de04b44d953c5e47ab10f65205ee212f9c30391e5299553954916873a0b41164543
  e801c0b099cb44f48995675823c10b40f4bbac9177a558ca0c30765c2aabfd6a4da54c84
  13e33902d63f064330f0464982429de2604cd03b4de84a9f821a5470423a40a964dcc418
  63363d77b02c3127304f942ee71c98c643a427533ef300104948b825277953aaabfd8555
  88f75a77d199a213ad348116e9e539f6d37068a551c710548b7a2c7ee95f9cd9b3483332
  673cc44bcb18a778a49455c768e0b340f81102ac6b76b064057151ef101ae143787f5485
  53558df8035a3ce00c9c43cda43142cca39034b09a7e6089867b4c64980a69ecab2e6818
  724c35cb909d5d45bc6a349c71b306567664adc0cc8ef698049b4b4b432dd0f69fac0758
  0f77c4f79b22bb90cb97b341880716853431694c9120f6724ad58d57127fced999ff6229
  a5d4c3c240129cc812acc73698f949d8e73661f2528262bfccfa5cdf5a2104649806e295
  ea161217083365aa26cee6ae2f1356e8e1c5cefcc85703447ef1160a1b4a0e8c017b1738
  02c66c88ab70d39a6c96c1569d5a86245a7eeb087d682219080768745b44bf244f65b567
  b2658dbae6962ba52b322118e214cfadd7cf3502582dc9cafba952a9637ad36007102597
  78d99d23f8235da90791604b4f0a4f7640680f59b633d93dfb84282ba54c674b115684a4
  1bc331b659a61a04883d0c5ebbc0772754a4c33b6a90e52e0678ce06a0453ba8a188b15a
  496bae6a24177b636d12fbb088f2cd9504ac200231473031a31a5c62e46288fb3edb858b
  21bc0ea59a212fd1c6dba09e920712d068a2be7abcf4f2a3533443ee1780dd419681a960
  cd90af5fcaab8c1552ef25572f157a2bbb934a18a5c57a761b54a45d774ac6bc593583a1
  bcfc4dcd0cca87ab9cff463dc5e80ebbb501d18c8b39e324dbd07ca06cbf75ba33297abc
  c7aabdd5b308401ba387f533f3927b51e91380f5a59b119e354835ab182db62c76d6d85f
  a63241743a52012aac281222bc0037e2c493b4777a99cb5929aba155a006bc9b461c365f
  a3583fac5414b403af9135079b33a10df8819cb462f067253f92b3c45a7fb1c1478d4091
  e39010ba44071019010daa15c0f43d14641a8fa3a94cfaa2a877ae8113bbf8221ee13223
  376494fb128b825952d5105ae4157dd6d70f71d5bd48f34d469976629bce6c12931c88ca
  0882965e27538f272b19796b251226075b131b38564f90159583cd9c4c3c098c8f06a267
  b262b8731b9e962976c41152a76c30b502d0425635357b43cd3a3ecef5bc9910bb89ca9e
  91ba75e8121d53c2329b5222df12560d242724523ff60b6ead310d99954d483b91383a72
  6a937f1b60b474b22ea5b81954580339d81c9f47bab44a3fe0c833a7dba1f5b33a5a2a45
  9812645c6537c2317163d71b7bd7a4a5459a28a1c28659aad9a1ca9a99a363062d453355
  108445a673438e77624e73757c1a84d031cf0fb24b1187aafbe6738e9abaf5b42b004b1f
  a0d96426d3c5324235dd871e7a89364d335ebb6718ad098154208b143b2b43eb9e5fd881
  6c5225d494b40809b2459903c6486a1db9ac3414945e1867b5869c2f88cf9edc0a216681
  804578d34923e5a353babba923db907725b384e74e66987292e007e05c6766f267f839b7
  617c55e28b0fa2121da2d037d6830af9d869e1fb52b0cb645fe221a79b2a46e41980d346
  71ccc58d8756054b2cca7b13715a05f3925355cca838ab8d2425255f61135727167ad6bc
  b0632ebf86384b950ad21088c292b4a4fcc0e59c42d3f77fac85cd9f5cb049b3a29505a9
  84c4c6ac98ca3d0a8f30d2b1bd9815b94b27051b40ffc3455a668b9e141428611b280c1b
  8f2b55f6eb04e10c68f1340ef1582115f10ee2b785b7ebb0ec3a0c61670cf48107b594cd
  6e238e0d68961b47983b87879771519d2b7c21681cd494b420f03d004bb06eeb54f9c080
  c2f2aff6759074d5b3a3b11c73f1af6dc874eeec254d5409fceaa90ff66d90b6930a540f
  d1d9be1844af1d861ff96a611a414a6c61a78fb2a78e74383ab05ebc73855a818a627242
  d523a3e2a35ab4285b4a2564f76772aaf8cdc9f87c65f1b4b5819905fb4f9ea59166fbbd
  b201c5eefc0df7418ca211b5b079a511b8b94429847b537fbed82d57632d63e815d8212d
  8a280d43328604a6c4d2c1887e7ab061f120a0168db2f4735369b193780f0aeb381ff265
  3f3b46e206afe77a7e814c7716a1b166727dd2a0b9a7d8aeace425da63977f8103457c9f
  438a2676c10e3a9c630b855873288ee560ca05c37cc7329e9e502cfac918b9420544445d
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ct
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seed
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sk
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pk
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eseed
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ct
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  f5647437
ss     1e037823ddbf1875756d86a3374b2d2347d5b7f3c84d229ecc5960523cdaa8b4

Appendix B. Acknowledgments

TODO acknowledge.

Appendix C. Change log

C.1. Since draft-connolly-cfrg-xwing-kem-00

  • A copy of the X25519 public key is now included in the X-Wing decapsulation (private) key, so that decapsulation does not require separate access to the X-Wing public key. See #2.

Authors' Addresses

Deirdre Connolly
SandboxAQ
Peter Schwabe
MPI-SP & Radboud University
Bas Westerbaan
Cloudflare