Internet-Draft | xwing | January 2024 |
Connolly, et al. | Expires 13 July 2024 | [Page] |
- Workgroup:
- Crypto Forum
- Internet-Draft:
- draft-connolly-cfrg-xwing-kem-00
- Published:
- Intended Status:
- Informational
- Expires:
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 13 July 2024.¶
Copyright Notice
Copyright (c) 2024 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/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document.¶
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:¶
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:¶
-
ML-KEM-768 post-quantum key-encapsulation mechanism (KEM) [MLKEM]:¶
-
ML-KEM-768.KeyGen()
: Randomized algorithm to generate an ML-KEM-768 key pair(pk_M, sk_M)
of an encapsulation keypk_M
and decapsulation keysk_M
. Note thatML-KEM-768.KeyGen()
returns the keys in reverse order ofGenerateKeyPair()
defined below.¶ -
ML-KEM-768.Encaps(pk_M)
: Randomized algorithm to generate(ss_M, ct_M)
, an ephemeral 32 byte shared keyss_M
, and a fixed-length encapsulation (ciphertext) of that keyct_M
for encapsulation keypk_M
.¶ -
ML-KEM-768.Decap(ct_M, sk_M)
: Deterministic algorithm using the decapsulation keysk_M
to recover the shared key fromct_M
.¶
To generate deterministic test vectors, we also use¶
-
ML-KEM-768.KeyGenDerand(seed)
: Same asML-KEM-768.KeyGen()
, but derandomized as follows.seed
is 64 bytes.seed[0:32]
is used forz
(line 1 algorithm 15), andseed[32:64]
is used ford
(line 1 algorithm 12).¶ -
ML-KEM-768.EncapsDerand(pk_M, seed)
: Same asML-KEM-768.Encaps()
but derandomized as follows.seed
is 32 bytes and used form
(line 1 algorithm 16).¶
-
-
X25519 elliptic curve Diffie-Hellman key-exchange defined in Section 5 of [RFC7748]:¶
-
X25519(k,u)
: takes 32 byte strings k and u representing a Curve25519 scalar and curvepoint respectively, and returns the 32 byte string representing their scalar multiplication.¶ -
X25519_BASE
: the 32 byte string representing the standard base point of Curve25519. In hex it is given by09000000000000000000000000000000000000000000
.¶
-
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.¶
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), concat(pk_M, pk_X)¶
GenerateKeyPair()
returns the 2432 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), concat(pk_M, pk_X)¶
seed
must be 96 bytes.¶
GenerateKeyPairDerand()
returns the 2432 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, pk): ct_M = ct[0:1088] ct_X = ct[1088:1120] sk_M = sk[0:2400] sk_X = sk[2400:2432] pk_M = pk[0:1184] pk_X = pk[1184:1216] 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 2432 byte X-Wing decapsulation key resulting from GenerateKeyPair()
pk
is a 1216 byte X-Wing encapsulation 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.¶
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:
-
2432¶
- 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].¶
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-07, , <https://datatracker.ietf.org/doc/html/draft-ietf-tls-rfc8447bis-07>.
- [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 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Acknowledgments
TODO acknowledge.¶