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IRTF Crypto Forum post quantum kem PQ hpke hybrid encryption This document defines Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) KEM options for Hybrid Public-Key Encryption (HPKE). ML-KEM is believed to be secure even against adversaries who possess a cryptographically-relevant quantum computer. About This Document The latest revision of this draft can be found at . Status information for this document may be found at . Discussion of this document takes place on the Crypto Forum Research Group mailing list (), which is archived at . Subscribe at . Source for this draft and an issue tracker can be found at .

Introduction

Motivation ML-KEM is a Key-Encapsulation Mechanism (KEM) which is believed to be secure against both classical and quantum cryptographic attacks. For parties that must move to exclusively post-quantum algorithms, this document defines pure post-quantum algorithms for the Hybrid Public-Key Encryption (HPKE) protocol . ML-KEM as a post-quantum IND-CCA2-secure KEM fits nicely into HPKE's design. Supporting multiple security levels for ML-KEM allows a spectrum of use cases including settings where the (United States) National Institute of Standards (NIST) security category 5 is required.

Not an authenticated KEM ML-KEM is a plain KEM that does not support the static-static key exchange that allows HPKE based on Diffie-Hellman (DH) based KEMs and their (optional) authenticated modes.

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 when, and only when, they appear in all capitals, as shown here. The following terms are used throughout this document to describe the operations, roles, and behaviors of HPKE:

• concat(x0, ..., xN): returns the concatenation of byte strings. concat(0x01, 0x0203, 0x040506) = 0x010203040506.
• random(n): return a pseudorandom byte string of length n bytes produced by a cryptographically-secure random number generator, specifically MUST be a FIPS-approved random bit generator (RBG) as described in section 3.3 of .

GenerateKeyPair, DeriveKeyPair, SerializePublicKey, DeserializePublicKey, Encap, Decap, AuthEncap, AuthDecap, Nsecret, Nenc, Npk, and Nsk are defined in Section 4 of . When used in the Security Consideration section, PK refers to public key and CT refers to ciphertext as modeled in . TODO: explain or reference IND-CCA, IND-CCA2, MAL-BIND-K-PK, MAL-BIND-K-CT, and LEAK-BIND-K-PK.

Usage supports two different key formats - this document only supports the 64-byte seed (d, z). This format supports stronger binding properties for ML-KEM than the expanded format. The 64-byte seed format protects against re-encapsulation attacks. This format provides properties closer to the generic DHKEM binding properties defined in Section 4.1 of . The encapsulation and decapsulation keys are computed, serialized, and deserialized as described in where the decapsulation keys MUST be in the 64-byte (d, z) format. The 'expanded' format where the decapsulation key is expanded into a variable size based on the parameter set but includes the hash of the encapsulation key is not used.

Key generation ML-KEM satisfies the HPKE KEM function GenerateKeyPair(), the randomized algorithm to generate a key pair, via Algorithm 19 ML-KEM.KeyGen() in . To be explicit, we use only the seed format (d, z) generated by lines 1 and 2 of Algorithm 19 ML-KEM.KeyGen() of and stored securely as described in section 7.1 of .

Key derivation ML-KEM satisfies the HPKE KEM function DeriveKeyPair(ikm), the deterministic algorithm to derive a key pair from the byte string ikm, where ikm SHOULD have at least Nsk bytes, via Algorithm 16 ML-KEM.KeyGen_internal(d, z) in . The input ikm is the 64-byte decapsulation key (d, z), described as the seed in section 7.1 in . The 64 bytes of ikm MUST be generated according to section 7.1, Algorithm 19, of , that is by freshly sourcing 32 random bytes for d and then freshly sourcing another 32 random bytes for z from a FIPS-approved RBG. The RBG MUST have a security strength of at least 128 bits for ML-KEM-512, at least 192 bits for ML-KEM-768, and at least 256 bits for ML-KEM-1024.

Public key serialization The HPKE KEM function SerializePublicKey() is the identity function, since the ML-KEM already uses fixed-length byte strings for public encapsulation keys per parameter set.

Public key deserialization The HPKE KEM function DeserializePublicKey() is the identity function, since the ML-KEM already uses fixed-length byte strings for public encapsulation keys per parameter set.

Encapsulation ML-KEM satisfies the HPKE KEM function Encap(pkR) via Algorithm 20, ML-KEM.Encaps(ek), of , where an ML-KEM encapsulation key check failure causes an HPKE EncapError.

Decapsulation ML-KEM satisfies the HPKE KEM function Decap(enc, skR) via Algorithm 21, ML-KEM.Decaps(dk, c), of , where an ML-KEM ciphertext check failure or decapsulation key check failure or hash check failure cause an HPKE DecapError. To be explicit, we derive the expanded decapsulation key from the 64-byte seed format and invoke ML-KEM.Decaps(dk) with it:

AuthEncap and AuthDecap HPKE-ML-KEM is not an authenticated KEM and does not support AuthEncap() nor AuthDecap(), see .

Security Considerations HPKE's IND-CCA2 security relies upon the IND-CCA and IND-CCA2 security of the underlying KEM and AEAD schemes, respectively. ML-KEM is believed to be IND-CCA secure via multiple analyses. The HPKE key schedule is independent of the encapsulated KEM shared secret ciphertext and public key of the ciphersuite KEM, and dependent on the shared secret produced by the KEM. If HPKE had committed to the encapsulated shared secret ciphertext and public key, we wouldn't have to worry about the binding properties of the ciphersuite KEM's X-BIND-K-CT and X-BIND-K-PK properties. These computational binding properties for KEMs were formalized in . describes DHKEM as MAL-BIND-K-PK and MAL-BIND-K-CT secure as a result of the inclusion of the serialized DH public keys (the KEM's PK and CT) in the DHKEM Key Derivation Function (KDF). MAL-BIND-K-PK and MAL-BIND-K-CT security ensures that the shared secret K 'binds' (is uniquely determined by) the encapsulation key and/or the ciphertext, even when the adversary is able to create or modify the key pairs or has access to honestly-generated leaked key material. ML-KEM as specified in with the seed key format provides MAL-BIND-K-CT security and LEAK-BIND-K-PK security . LEAK-BIND-K-PK security is resiliant where the involved key pairs are output by the honest key generation algorithm of the KEM and then leaked to the adversary. MAL-BIND-K-CT security strongly binds the shared secret and the ciphertext even when an adversary can manipulate key material like the decapsulation key. ML-KEM using the seed key format (providing MAL-BIND-K-CT and LEAK-BIND-K-PK) nearly matches the binding properties of DHKEM (the default HPKE KEM construction). The ML-KEM ciphertext is strongly bound by the shared secret. The encapsulation key is more weakly bound, and protocols integrating HPKE using ML-KEM even with the seed key format should evaluate whether they need to strongly bind to the PK elsewhere (outside of ML-KEM or HPKE) to be resilient against a MAL adversary, or to achieve other tight binding to the encapsulation key PK to achieve properties like implicit authentication or session independence.

IANA Considerations This document requests/registers two new entries to the "HPKE KEM Identifiers" registry.

Value:

0x0040 (please)

KEM:

ML-KEM-512

Nsecret:

32

Nenc:

768

Npk:

800

Nsk:

64

Auth:

no

Reference:

This document

Value:

0x0041 (please)

KEM:

ML-KEM-768

Nsecret:

32

Nenc:

1088

Npk:

1184

Nsk:

64

Auth:

no

Reference:

This document

Value:

0x0042 (please)

KEM:

ML-KEM-1024

Nsecret:

32

Nenc:

1568

Npk:

1568

Nsk:

64

Auth:

no

Reference:

This document

References Normative References This document describes a scheme for hybrid public key encryption (HPKE). This scheme provides a variant of public key encryption of arbitrary-sized plaintexts for a recipient public key. It also includes three authenticated variants, including one that authenticates possession of a pre-shared key and two optional ones that authenticate possession of a key encapsulation mechanism (KEM) private key. HPKE works for any combination of an asymmetric KEM, key derivation function (KDF), and authenticated encryption with additional data (AEAD) encryption function. Some authenticated variants may not be supported by all KEMs. We provide instantiations of the scheme using widely used and efficient primitives, such as Elliptic Curve Diffie-Hellman (ECDH) key agreement, HMAC-based key derivation function (HKDF), and SHA2. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. National Institute of Standards and Technology In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. Informative References CISPA Helmholtz Center for Information Security CISPA Helmholtz Center for Information Security CISPA Helmholtz Center for Information Security

Acknowledgments The authors would like to thank Cas Cremers for their input.

Change log

• RFC Editor's Note: Please remove this section prior to publication of a final version of this document.

TODO

Since draft-connolly-cfrg-hpke-mlkem-00 TODO

Test Vectors This section contains test vectors formatted similary to that which are found in , with two changes. First, we only provide vectors for the non-authenticated modes of operation. Secondly, as ML-KEM 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, so ier[0:32] is the seed that is fed to H in the first step of ML-KEM encapsulation in .

ML-KEM-512 TODO

ML-KEM-768 TODO

ML-KEM-1024 TODO