ML-KEM Post-Quantum Key Agreement for TLS 1.3

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Table of Contents

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.¶

3. Key encapsulation mechanisms

This document models key agreement as key encapsulation mechanisms (KEMs), which consist of three algorithms:¶

• KeyGen() -> (pk, sk): A probabilistic key generation algorithm, which generates a public encapsulation key pk and a secret decapsulation key sk.¶

• Encaps(pk) -> (ct, shared_secret): A probabilistic encapsulation algorithm, which takes as input a public encapsulation key pk and outputs a ciphertext ct and shared secret shared_secret.¶

• Decaps(sk, ct) -> shared_secret: A decapsulation algorithm, which takes as input a secret decapsulation key sk and ciphertext ct and outputs a shared secret shared_secret.¶

ML-KEM-768 and ML-KEM-1024 conform to this API:¶

• ML-KEM-768 has encapsulation keys of size 1184 bytes, decapsulation keys of 2400 bytes, ciphertext size of 1088 bytes, and shared secrets of size 32 bytes¶

• ML-KEM-1024 has encapsulation keys of size 1568 bytes, decapsulation keys of 3168 bytes, ciphertext size of 1568 bytes, and shared secrets of size 32 bytes¶

4. Construction

We define the KEMs as NamedGroups and sent in the supported_groups extension.¶

    enum {

         ...,

          /* ML-KEM Key Agreement Methods */
          mlkem768(0x0768),
          mlkem1024(0x1024)

         ...,

    } NamedGroup;

    struct {
        NamedGroup group;
        opaque key_exchange<1..2^16-1>;
    } KeyShareEntry;

    struct {
        KeyShareEntry client_shares<0..2^16-1>;
    } KeyShareClientHello;

    struct {
        KeyShareEntry server_share;
    } KeyShareServerHello;

                                    0
                                    |
                                    v
                      PSK ->  HKDF-Extract = Early Secret
                                    |
                                    +-----> Derive-Secret(...)
                                    +-----> Derive-Secret(...)
                                    +-----> Derive-Secret(...)
                                    |
                                    v
                              Derive-Secret(., "derived", "")
                                    |
                                    v
             shared_secret -> HKDF-Extract = Handshake Secret
             ^^^^^^^^^^^^^          |
                                    +-----> Derive-Secret(...)
                                    +-----> Derive-Secret(...)
                                    |
                                    v
                              Derive-Secret(., "derived", "")
                                    |
                                    v
                         0 -> HKDF-Extract = Master Secret
                                    |
                                    +-----> Derive-Secret(...)
                                    +-----> Derive-Secret(...)
                                    +-----> Derive-Secret(...)
                                    +-----> Derive-Secret(...)

5. Discussion

Larger encapsulation keys and/or ciphertexts The HybridKeyExchange struct in Section 4.2 limits public keys and ciphertexts to 2^16-1 bytes; this is bounded by the same (2^16-1)-byte limit on the key_exchange field in the KeyShareEntry struct. All defined parameter sets for ML-KEM have encapsulation keys and ciphertexts that fall within the TLS constraints.¶

Failures Some post-quantum key exchange algorithms, including ML-KEM, have non-zero probability of failure, meaning two honest parties may derive different shared secrets. This would cause a handshake failure. ML-KEM has a cryptographically small failure rate; implementers should be aware of the potential of handshake failure. Clients can retry if a failure is encountered.¶

6. Security Considerations

IND-CCA The main security property for KEMs is indistinguishability under adaptive chosen ciphertext attack (IND-CCA2), which means that shared secret values should be indistinguishable from random strings even given the ability to have other arbitrary ciphertexts decapsulated. IND-CCA2 corresponds to security against an active attacker, and the public key / secret key pair can be treated as a long-term key or reused. A common design pattern for obtaining security under key reuse is to apply the Fujisaki-Okamoto (FO) transform [FO] or a variant thereof [HHK].¶

Key exchange in TLS 1.3 is phrased in terms of Diffie-Hellman key exchange in a group. DH key exchange can be modeled as a KEM, with KeyGen corresponding to selecting an exponent x as the secret key and computing the public key g^x; encapsulation corresponding to selecting an exponent y, computing the ciphertext g^y and the shared secret g^(xy), and decapsulation as computing the shared secret g^(xy). See [HPKE] for more details of such Diffie-Hellman-based key encapsulation mechanisms. Diffie-Hellman key exchange, when viewed as a KEM, does not formally satisfy IND-CCA2 security, but is still safe to use for ephemeral key exchange in TLS 1.3, see e.g. [DOWLING].¶

TLS 1.3 does not require that ephemeral public keys be used only in a single key exchange session; some implementations may reuse them, at the cost of limited forward secrecy. As a result, any KEM used in the manner described in this document MUST explicitly be designed to be secure in the event that the public key is reused. Finite-field and elliptic-curve Diffie-Hellman key exchange methods used in TLS 1.3 satisfy this criteria. For generic KEMs, this means satisfying IND-CCA2 security or having a transform like the Fujisaki-Okamoto transform [FO] [HHK] applied. While it is recommended that implementations avoid reuse of KEM public keys, implementations that do reuse KEM public keys MUST ensure that the number of reuses of a KEM public key abides by any bounds in the specification of the KEM or subsequent security analyses. Implementations MUST NOT reuse randomness in the generation of KEM ciphertexts.¶

Binding properties TLS 1.3's key schedule commits to the the ML-KEM encapsulation key and the encapsulated shared secret ciphertext as the key_exchange field as part of the key_share extension are populated with those values are included as part of the handshake messages, providing resilience against re-encapsulation attacks against KEMs used for key agreement.¶

ML-KEM is MAL-BIND-K-PK-secure but only LEAK-BIND-K-CT and LEAK-BIND-K,PK-CT-secure, but because of the inclusion of the ML-KEM ciphertext in the TLS 1.3 key schedule there is no concern of malicious tampering (MAL) adversaries, not just honestly-generated but leaked key pairs (LEAK adversaries). The same is true of other KEMs with weaker binding properties, even if they were to have more constraints for secure use in contexts outside of TLS 1.3 handshake key agreement.These computational binding properties for KEMs were formalized in [CDM23].¶

7. IANA Considerations

This document requests/registers two new entries to the TLS Supported Groups registry, according to the procedures in Section 6 of [tlsiana].¶

Value:

0x0768 (please)¶

Description:

MLKEM768¶

DTLS-OK:

Y¶

Recommended:

N¶

Reference:

This document¶

Comment:

FIPS 203 version of ML-KEM-768¶

Value:

0x1024 (please)¶

Description:

MLKEM1024¶

DTLS-OK:

Y¶

Recommended:

N¶

Reference:

This document¶

Comment:

FIPS 203 version of ML-KEM-1024¶

Acknowledgments

Thanks to Douglas Stebila for consultation on the draft-ietf-tls-hybrid-design design.¶

Author's Address