| Internet-Draft | hpke-xyber768d00 | April 2023 |
| Westerbaan & Wood | Expires 24 October 2023 | [Page] |
This memo defines X25519Kyber768Draft00, a hybrid post-quantum KEM, for HPKE (RFC9180). This KEM does not support the authenticated modes of HPKE.¶
This note is to be removed before publishing as an RFC.¶
The latest revision of this draft can be found at https://bwesterb.github.io/draft-westerbaan-cfrg-hpke-xyber768d00/draft-westerbaan-cfrg-hpke-xyber768d00.html. Status information for this document may be found at https://datatracker.ietf.org/doc/draft-westerbaan-cfrg-hpke-xyber768d00/.¶
Discussion of this document takes place on the Crypto Forum Research Group mailing list (mailto:[email protected]), 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/bwesterb/draft-westerbaan-cfrg-hpke-xyber768d00.¶
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 24 October 2023.¶
Copyright (c) 2023 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.¶
The final draft for Kyber is expected in 2024. There is a desire to deploy post-quantum cryptography earlier than that. To promote interoperability of early implementations, this document specifies a preliminary hybrid post-quantum key agreement.¶
Kyber is a plain KEM that does not support the static-ephemeral key exchange that allows HPKE based on Diffie-Hellman based KEMs its (optional) authenticated modes.¶
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.¶
In short, X25519Kyber768Draft00 is the parallel combination of DHKEM(X25519, HKDF-SHA256) [RFC9180] [RFC7748] and Kyber768Draft00 [KYBER]: wire encodings of public key, private key, cipher texts and shared secrets are simple concatenations.¶
A KEM private key is a tuple of an DHKEM(X25519, HKDF-SHA256) private key and Kyber768Draft00 private key, where each is an octet string of length 32 and 2400 bytes, respectively. Similarly, a KEM public key is a tuple of an DHKEM(X25519, HKDF-SHA256) public key and Kyber768Draft00 public key.¶
Kyber768Draft00 is Kyber768 as submitted to the third round of the NIST PQC process [KyberV302], where it is also known as v3.02.¶
Note that this hybrid KEM is different from the one defined in [TLS-XYBER] based on [HYBRID] for TLS, as raw X25519 shared secrets can be used, thanks to the message transcript.¶
We use HKDF-SHA256 as the HPKE HKDF. We denote the DHKEM(X25519, HKDF-SHA256) KEM as DHKEM throughout the document.¶
SerializePublicKey and DeserializePublicKey encode and decode X25519Kyber768Draft00 public keys to and from their wire format representation. Their implementation is described below.¶
Note that DHKEM public keys MUST be validated before they can be used as stipulated in Section 7.1.1 of [RFC9180].¶
def SerializePublicKey(pkX):
(pkA, pkB) = pkX
return concat(
DHKEM.SerializePublicKey(pkA),
pkB
)
def DeserializePublicKey(pkXm):
return (
DHKEM.DeserializePublicKey(pkXm[0:32]),
pkXm[32:1216]
)
¶
DHKEM.SerializePublicKey() and DHKEM.DeserializePublicKey() are SerializePublicKey() and respectively DeserializePublicKey() as defined for DHKEM in Section 7.1.1 of [RFC9180].¶
SerializePrivateKey and DeserializePrivateKey encode and decode X25519Kyber768Draft00 private keys to and from their wire format representation. Their implementation is described below.¶
def SerializePrivateKey(skX):
(skA, skB) = skX
return concat(
DHKEM.SerializePrivateKey(skA),
skB
)
def DeserializePrivateKey(skXm):
return (
DHKEM.DeserializePrivateKey(skXm[0:32]),
skXm[32:2432]
)
¶
DHKEM.SerializePrivateKey() and DHKEM.DeserializePrivateKey() are SerializePrivateKey() and respectively DeserializePrivateKey() as defined for DHKEM in Section 7.1.2 of [RFC9180].¶
DeriveKeyPair deterministically derives a X25519Kyber768Draft00 private and public key pair from a fixed-length seed. In particular, a single seed is stretched and passed to the relevant key derivation functions for DHKEM and Kyber768Draft00.¶
def DeriveKeyPair(ikm):
dkp_prk = LabeledExtract("", "dkp_prk", ikm)
seed = LabeledExpand(dkp_prk, "sk", 32 + 64)
seed1 = seed[0:32]
seed2 = seed[32:96]
sk1, pk1 = DHKEM.DeriveKeyPair(seed1)
sk2, pk2 = Kyber768Draft00.DeriveKeyPair(seed2)
return (concat(sk1, sk2), concat(pk1, pk2))
¶
DHKEM.DeriveKeyPair() is DeriveKeyPair() defined for DHKEM in Section 7.1.3 of [RFC9180]. Kyber768Draft00.DeriveKeyPair() is the key generation as defined in Section 11.1 of [KYBER].¶
The suite_id used implicitly in LabeledExtract() and LabeledExpand() on lines 2 and 3, is derived from the KEM identifier of the hybrid (0x0030).¶
The suite_id used implicitly in LabeledExpand() and LabeledExtract() within DHKEM.DeriveKeyPair() is the KEM identifier of DHKEM (0x0020).¶
ikm 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 and Decap are the primary KEM functions. Their implementation is described below.¶
def Encap(pkR):
(pkA, pkB) = pkR
(ss1, enc1) = DHKEM.Encap(pkA)
(ss2, enc2) = Kyber768Draft00.Encap(pkB)
return (
concat(ss1, ss2),
concat(enc1, enc2)
)
def Decap(enc, skR):
(skA, skB) = skR
enc1 = enc[0:32]
enc2 = enc[32:1120]
ss1 = DHKEM.Decap(enc1, skA)
ss2 = Kyber768Draft00.Decap(enc2, skB)
return concat(ss1, ss2)
¶
The suite_id used implicitly in the LabeledExtract() and LabeledExpand() within DHKEM.Encap() and DHKEM.Decap() is the one derived from the KEM id of DHKEM (0x0020).¶
X25519Kyber768Draft00 is not an authenticeted KEM and does not support AuthEncap() or AuthDecap(), see Section 1.2.¶
We aim for IND-CCA2 robustness: that means that if either constituent KEM is not IND-CCA2 secure, but the other is, the combined hybrid remains IND-CCA2 secure.¶
In general [GHP18] [COMBINERS] this requires a combiner that mixes in the cipher texts, such as, assuming fixed-length cipher texts and shared secrets:¶
HKDF(concat(ss1, ss2, enc1, enc2)).¶
In the present case, DHKEM(X25519, -) and Kyber768Draft00 already mix in the respective cipher texts into their shared secrets. Thus we can forgo mixing in the cipher texts a second time.¶
Furthermore, in HPKE, the shared secret is never used directly, but passed through HKDF (via KeySchedule), and thus we can forgo the call to HKDF as well.¶
This document requests/registers a new entry to the "HPKE KEM Identifiers" registry.¶
The authors would like to thank P. Kampanakis, I. Liusvaara, T. Wiggers, and S. Farrell for their input.¶
RFC Editor's Note: Please remove this section prior to publication of a final version of this document.¶
This section contains test vectors formatted similary to that which are found in [RFC9180], with two changes. First, we only provide vectors for the non-authenticated modes of operation. Secondly, as Kyber encapsulation does not involve an ephemeral keypair, we omit the ikmE, skEm, pkEm entries and provide an ier entry instead. The value of ier is the randomness used to encapsulate. To wit: the ephemeral X25519 keypair used in DHKEM.Encap() is DHKEM.DeriveKeyPair(ier[0:32]) and ier[32:64] is the seed that is fed to H in the first step of Kyber encapsulation [KYBER].¶
mode: 0 kem_id: 48 kdf_id: 1 aead_id: 1 info: 486561722068656172 ikmR: 3cb1eea988004b93103cfb0aeefd2a686e01fa4a58e8a3639ca8a1e3f9ae57e2 pkRm: a3aa882fee0de0059cec0569c8e1b4872fb6cb4d82361b72ee1148dc7ddc0c 2b210747403222b16597f4881d694c12366c53fde2b3d346b7ee87b16dd42f44ec59 4cea6ba78b256092cbbc16baaf6ccc46f2386da22de9d142f593739eb9c245018e0c 61975514ac42639d3c5b0299b772acd59d55520a5d660f135075e33a673fd5b9e2d5 6803889fc62b0362f8cbe9990cb36b4cdef17586c8cc58d72d84fb9398f1c1efb0a6 282508083c23965a9851acb89afc723e7a6c60bc4007a41ad1950c4590a2f8d2bb3b 832f5db1707ad8bad1c4c426aaa7da97b34a921283415851f19b0f01ca3924754dba 6596f9329454b1e3d9b5f357a66c59bf5fc4a045908b5eb107d3302f0cb9be0af958 4846c1475b92d3c16051935dc7411acaa64c80c836b0643fd72b38cb0a33feb11f48 13b66f705268b3838b8974e28c12b4f9bbc8623c936b32a015262d4a33172b7f3a69 b6c2fab5a3c18ffdab2927e77598d1556d51a8559550c251796290b617ac9804167b d9a76e9d8bba64059d165acfe2483e9ed0cbc11cb71dd148776aa1cb862ce2b1026e 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ef09255530c7ec817999c95e20aa23f8f6782aa820d34c89c2299ff0ec9a9021b6f7 dbbd19503fa6f170d8770e12875d558bbb2ca66fd1136e0e5729ef30346109cd289a 1ce0c531a493581ed64533e1749fc818b85ab664255bbfe4a641f6bdf43ac1695c28 ab2b58b3bab5bed5893439455b669b63d65ceff75b8c5857f4ba5cf767cf57aa8e28 691cc6dc67fca434e3b1560c6c53ce37c2a2f14764c1cf1e5697cd8757a544b05b76 6f4400cef7ecc46ec29a1d679d7fe385c4366579db06d1d840c9911fab8b6b5df203 5cb95410f79b861411b4eb5a4119208f8872674639617452f6b6394c94c6d6f5b833 690dd98406b5e7c0827b1a3617a03ba90c3d185a954252f1ba5b157a3f61749548e2 81fc543dec205e757932bcc717b99b7df7123500f3bcc660c080093b3fbac56ff51b 9c3b037f76e3f43c0e46b5588cf617f4de85044390a9947daacba87cd5 skRm: cf61f1a7b05c83f9c2a4b27dc0e9bdbf4e52ba1bbd906cb3776ac12268a9f4 d0c348342d192f0458ab53d19c1dc135d11b48978c878bca6d7d1bc91428259e43aa dc9700b76aa9aa66a65db91a77d72513e40697226557b53400bb6752fb4e11a5ba2f e12644698a48c9948ec121cc9c9ce7384c65f798012c9df8f5ac0cd371d7d19d9a24 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38f2be5f994d60c79e8a92121fb0488eef9690d550ef9fa40b1774221aac8c8c1dcf 97faa07c28e840feb9daf0bf3bed277a6e10a33490c0bee7e5fa318638f5b80a2272 700e591ffc14985d0ed19876725c2bec9356b45ca96d295e30bce86effc626a2bd78 39af05ae373801af510cfb378ce42088607909c91ceb4a90e4d7b2b6288b9cdfa262 570ffda8692b58f0b05a7c7899a717a3a97b6e64489f56323b000793f807ca75ca99 1 shared_secret: 1368d71518fadbe42fb75fbd356e016b0aaad6b4d3d91ce7f2070 73e4fb08c537217aba238aea92a7f855820518a8342b3a31f82ebbcdb479f33ad82b dcdc953 key_schedule_context: 009f749a195d1c8b3eaa8d5c3f571dc7231aafbbc0405e 4b484738352667c484867584e32e844cdf74d17b4ee224cc521bbc8bed221f21f34f 8ccc9842772686cb secret: 95f863934be4d0ef683770c7bd385839d19e525b467a332f47ae715c54183e1d key: 6bb5532badb078ce8f326daa6cfaef84 base_nonce: ff2b9a604a84754614e9e772 exporter_secret: fb6ca36cfb7881cf11dbcb8fde201f698f80d0b941b642bc0a6a3101c97b7fad¶
sequence number: 0 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d30 nonce: ff2b9a604a84754614e9e772 ct: a78ab8f057becc31cb3a5cff2fe2b18983b93ce74c6e7c45e0a57c4acc1976ee f755c08547564ceede3e5169f959ea6ad498 sequence number: 1 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d31 nonce: ff2b9a604a84754614e9e773 ct: c7e392bb20d256f0020ba0888996c4b0e2518b486ad5873263834e7f30fc43e6 f712ee8e42846179db284a56baba6252d38f sequence number: 2 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d32 nonce: ff2b9a604a84754614e9e770 ct: 86eeadf1593871435b643b7dde3d5a18b4dcb8d706c21abb69ae057af2a788a6 72198d46facadd396fa9fa6e1072c43a4f74 sequence number: 4 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d34 nonce: ff2b9a604a84754614e9e776 ct: 4aef2a67f307cb23dbe6d9ea2875add1e4bb0db6519836a2f1adca1d75a33bef 6df198b63f916385107677eef4e542e2c337 sequence number: 255 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d323535 nonce: ff2b9a604a84754614e9e78d ct: 94ab72b1e767b26e3cd2b2a862bdc52cdcb4140fc7b0133e4ca4f6c65b190527 1c971d2b5092204825683191f2ecdd0ec4e1 sequence number: 256 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d323536 nonce: ff2b9a604a84754614e9e672 ct: ca0612fa2d3b4ff5c6daafddbc9a359efd44ca3ffe2385d63ba1b4fb5b75b89d e55355dc4132399d3e7ae2676c4fb52418df¶
exporter_context: L: 32 exported_value: 0d15e6f37d0791a924c5b8a5c766db83d95703ddae889e6240c73926168ae6a8 exporter_context: 00 L: 32 exported_value: 6f7bc144a46519b718c93a86a4ce74dad186816c88791eeee4f39fd0a2dbcef2 exporter_context: 54657374436f6e74657874 L: 32 exported_value: 3a0064f88b02de081e9d5f4398093e016b00b01816db91f0686d50330a9886b2¶
mode: 1 kem_id: 48 kdf_id: 1 aead_id: 1 info: 486561722068656172 ikmR: 3cb1eea988004b93103cfb0aeefd2a686e01fa4a58e8a3639ca8a1e3f9ae57e2 pkRm: a3aa882fee0de0059cec0569c8e1b4872fb6cb4d82361b72ee1148dc7ddc0c 2b210747403222b16597f4881d694c12366c53fde2b3d346b7ee87b16dd42f44ec59 4cea6ba78b256092cbbc16baaf6ccc46f2386da22de9d142f593739eb9c245018e0c 61975514ac42639d3c5b0299b772acd59d55520a5d660f135075e33a673fd5b9e2d5 6803889fc62b0362f8cbe9990cb36b4cdef17586c8cc58d72d84fb9398f1c1efb0a6 282508083c23965a9851acb89afc723e7a6c60bc4007a41ad1950c4590a2f8d2bb3b 832f5db1707ad8bad1c4c426aaa7da97b34a921283415851f19b0f01ca3924754dba 6596f9329454b1e3d9b5f357a66c59bf5fc4a045908b5eb107d3302f0cb9be0af958 4846c1475b92d3c16051935dc7411acaa64c80c836b0643fd72b38cb0a33feb11f48 13b66f705268b3838b8974e28c12b4f9bbc8623c936b32a015262d4a33172b7f3a69 b6c2fab5a3c18ffdab2927e77598d1556d51a8559550c251796290b617ac9804167b d9a76e9d8bba64059d165acfe2483e9ed0cbc11cb71dd148776aa1cb862ce2b1026e 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7f9c2ba4e88f827d616045507605853ed73b8093f6efbc88eb1a6eacfa66ef26 psk_id: 6265666f7265206576657279626f647920666f72206576657279626f6479 20666f722065766572797468696e67 enc: 1d06980e46fd3842db6b87226231eedd2cc9684ee98a1d9d902bd9300e2c4d4 1b64fba47a50fe32dd0df3b0a75801c11022cd98a6ff5a83a8472ade82bdd6f1e8a6 5a94a88523ada0d8275165f707f1067a6a576e54525d9141e95223f5713456bda7ec 5eb558adfc6b7f0d80de46222579a3274e45ab43fad14f7e9855a872d2716e8dc78d 4c12027bef3184904476c8961552fd031361358f2d9deae8ad98194047a142229476 12972574c57514266e9e67a3b6dd89972cc8a0882be7474f4923549dfcd944dcbe58 b088079aa8b70c8f291cb4e45066bad4a832ccd8f40e51861f7a25b6a2358842f1bb e8108a6a6f0ae93153a2e7f9f53e180a90532531a632367b81bf08ed97effcf0140d d0e92cc438f6be7e6f3d97a9f7787f7e3981f971617f0bfb618caa7db1e453f33a38 6c3863b16d462229c41f4946b49e4e49c27e0f35d77e21304b6ad238a55a51e9e370 dd39e713d626044fb970bb7c2af7d7b9cb9004394741a0ea2de592816359006f24ab dfc2aa890720b00b2f7b8bb240120f22bdb84f9fc5c8fdc7ca7047ae633868c184c4 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4fa071c39942b43a0caf561278cfc1b47781fa9ef559f86b2dad703141b78b7ddb35 c9c9ff4c1134580da26367dbf3db7eaf039dfbae238959c4cf55d40d78a2c5597ba0 38f2be5f994d60c79e8a92121fb0488eef9690d550ef9fa40b1774221aac8c8c1dcf 97faa07c28e840feb9daf0bf3bed277a6e10a33490c0bee7e5fa318638f5b80a2272 700e591ffc14985d0ed19876725c2bec9356b45ca96d295e30bce86effc626a2bd78 39af05ae373801af510cfb378ce42088607909c91ceb4a90e4d7b2b6288b9cdfa262 570ffda8692b58f0b05a7c7899a717a3a97b6e64489f56323b000793f807ca75ca99 1 shared_secret: 1368d71518fadbe42fb75fbd356e016b0aaad6b4d3d91ce7f2070 73e4fb08c537217aba238aea92a7f855820518a8342b3a31f82ebbcdb479f33ad82b dcdc953 key_schedule_context: 011c0e82b54d88402f8c14c546eb2c5d2ddf5c0ad00953 b8c7917e143a660122927584e32e844cdf74d17b4ee224cc521bbc8bed221f21f34f 8ccc9842772686cb secret: 2398d859cca13a8e024a4303015d07b426f886cfb160104808d46afa3ed65c5d key: 2abc7960081169220e5316e8b4ca25c8 base_nonce: 9f4404e9a8a83dcdad85aaa4 exporter_secret: 37c64a38386a73522e517063be8e5dbac2dda13748e7e0204ef4781d37db91b2¶
sequence number: 0 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d30 nonce: 9f4404e9a8a83dcdad85aaa4 ct: 59ae4c0fe132882496ee546c59db8887d0ffa1e81c024f9f306e336c8b515aef c100de05caad51b224b8446424371610e94f sequence number: 1 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d31 nonce: 9f4404e9a8a83dcdad85aaa5 ct: 12ae854754ecf26efccd9a3d9006ccea7e58394314ac63537f71fa373475c9b5 def50550bd386a62a9f93dbb482aad08b83d sequence number: 2 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d32 nonce: 9f4404e9a8a83dcdad85aaa6 ct: 44dfad98e654637c47ea943787622c39cff096515d95124947b93962d570fb09 8a725a681c00bd95329ae7c87e7476a14c23 sequence number: 4 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d34 nonce: 9f4404e9a8a83dcdad85aaa0 ct: b4daec06cb05cad7987257b000662e329879885981431d8758167449912f4862 73621502cb6b8917259d43c0741c2221157f sequence number: 255 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d323535 nonce: 9f4404e9a8a83dcdad85aa5b ct: a45db83de0836912b692a3ceb870d4ada3c59813031e52b7efd511bdb3766d70 94c556ca067adefea6c1690c226a12ddd7d0 sequence number: 256 pt: 546f2074686520756e6976657273616c206465706c6f796d656e74206f6620505143 aad: 436f756e742d323536 nonce: 9f4404e9a8a83dcdad85aba4 ct: aa047d5fa79b00a1d70f8044136c3717eeb86913e50092784b750020a51f410d b12e47de6a7bae1596e6d21347a82cdc5ecd¶
exporter_context: L: 32 exported_value: 887a3f1c8097a127f3178ada5c83ba8c3c335b45b4b4be18a7885b669f7ba1e5 exporter_context: 00 L: 32 exported_value: faf29bee28fb70c380b1495afec1f0f3ab26552b3c9b1ae4beddfd005f388562 exporter_context: 54657374436f6e74657874 L: 32 exported_value: 4e8ef9bdec7cec015c62d863681245dd630ed8c9debccc5bbea1d97e1c651261¶