ML-KEM Security Considerations

Introduction A Cryptographically Relevent Quantum Computer (CRQC) is a large and reliable Quantum Computer that can break protocols which rely on the traditional RSA, DH, or ECDH methods of securely exchanging keys. Even though it is not believed that, at the time of this writing, there exists a CRQC, there still remains the possibility that an adversary may record the protocol exchange, and then later (when they have access to a CRQC) go ahead and read the traffic. Because of this threat, NIST has published FIPS 203 , which standardizes a method for allowing two systems to securely exchange keying material and which is not vulnerable to a CRQC. This method is based on module lattices, and is called ML-KEM. ML-KEM is a Key Encapsulation Mechanism (KEM), which can be used to generate a shared secret key between two parties. A KEM is a public key mechanism where one side (Alice) can generate a public/private key pair, and send the public key to the other side (Bob). Bob then can use it to generate both a ciphertext and a shared secret key. Bob then sends the ciphertext to Alice, who uses her private key to generate the shared secret key. The idea is that someone in the middle, listening into the exchanged public keys and ciphertexts will not be able to recovered the shared secret key that Alice and Bob learns. Hence, Alice and Bob can use their shared secret key to establish secure symmetric communication. One common misunderstanding of the term KEM is the expectation that Bob freely chooses the shared secret, and encrypts that when sending to Alice. What actually happens in ML-KEM is that randomness from both sides are used to contribute to the shared secret. That is, ML-KEM internally generates the shared secret in a way that Bob cannot select the value. Now, Bob can generate a number of ciphertext/shared secret pairs, and select the shared secret that he prefers, but he cannot freely choose it or make secrets shared with two parties be equal. A KEM (such as ML-KEM) sounds like it may be a drop-in replacement for Diffie-Hellman (and in some scenarios, it can be). However this is not always the case. In Diffie-Hellman, the parties exchange two public keys, whereas in a KEM, the ciphertext is necessarily a function of Alice's public key, and thus can only be useful only with that specific public key. Additionally, a KEM differs from Diffie-Hellman which is asynchronous and non-interactive. In particular, for an 'ephemeral-ephemeral' key establishment, an encapsulator cannot pre-emptively initiate a key establishment, but requires an encapulation key. Nor can participants compute parts of the key establishment in parallel as is the case with Diffie-Hellman. As long as the application can handle larger public keys and ciphertexts, a KEM is a drop-in replacement for 'ephemeral-ephemeral' key exchange in protocols like TLS and SSH as well as 'static-ephemeral' key exchange in protocols like ECIES/HPKE , that is, in cases where Alice has a long term public key, and Bob can use that long term public key to establish communication. A KEM is not a drop-in replacement in applications such as the Diffie-Hellman ratchet in Signal , implicit 'ephemeral-static' DH authentication in Noise , Wireguard , and EDHOC , and 'static-static' configurations in CMS and Group OSCORE , where both sides have long-term public keys. ML-KEM can also be used to perform public key encryption, that is, where a sender encrypts a message with a public key, and only the holder of the private key can decrypt the message. To use ML-KEM for this task, it is recommended that you it within the Hybrid Public Key Encryption framework to perform the operations. You can use draft-connolly-cfrg-hpke-mlkem, which is three ML-KEM perameter sets that has been proposed for HPKE.

Using ML-KEM To use ML-KEM, there are three steps involved:

ML-KEM Key Generation The first step for Alice is to generate a public and private keypair. In FIPS 203, the key generation function is ML-KEM.KeyGen() (see section 7.1 of ). It internally calls the random number generator for a seed and produces both a public key (known as an encapsulation key in FIPS 203) and a private key (known as a decapsulation key). The seed can be securely stored, but must be treated with the same safeguards as the private key. The seed format allows fast reconstruction of the expanded key pair format, and elides the need for format checks of the expanded key formats. Other intermediate data must be securely deleted. The public key can be freely published (and Bob will need it for his part of the process); this step may be performed simply by transmitting the key to Bob. However, the private key (in either format) must be kept secret. It is essential that the public key is generated correctly when the initial key generation is performed. Lattice public keys consist of a lattice and a secret hidden by an error term; if additional error can be introduced into the public key generation stage, then the success of decapsulation can reveal enough of the secret that successive queries determine the private key. Notably, this means a public key can be 'poisoned' such that a future adversary can recover the private key even though it will appear correct in normal usage.

ML-KEM Encapsulation The second step is for Bob to generate a ciphertext and a shared secret key. To perform this step, Bob would first run the Encapsulation Key Check on Alice's public key as outlined at the beginning of section 7.2 of . If that test passes, then Bob would perform what FIPS 203 terms as ML-KEM.Encaps() (see section 7.2 of ). This step takes the validated public key, internally calls the random number generator for a seed, and produces both a ciphertext and a 32-byte shared secret key. Intermediate data other than the ciphertext and shared secret key (and the "matrix data" internal to ML-KEM, which can be deduced from the public key) must be securely deleted. The ciphertext can be transmitted back to Alice; if the exchange is successful, the 32-byte shared secret key will be the key shared with Alice. It may be that some libraries combine the validation and the encapsulation step; implementations should determine whether the library they are using does. For static public keys, the Encapsulation Key Check only needs to be performed once.

ML-KEM Decapsulation The third and final step is for Alice to take the ciphertext and generate the shared secret key. To perform this step, Alice would first run the Decapsulation Key Check on Bob's ciphertext as outlined at the beginning of section 7.3 of . If that test passes, then Alice would perform what FIPS 203 terms as ML-KEM.Decaps() (see section 7.3 of ). This step takes the ciphertext from Bob and the private key that was previously generated by Alice, and produces a 32-byte shared secret key. It also repeats the encapsulation process to ensure that the ciphertext was created strictly according to the specification, with invalid ciphertexts generating an unrelated 32 byte value that gives no information. Although not necessary for the correctness of the key establishment, this step should not be skipped as a maliciously generated ciphertext could induce decapsulation failures that can allow an attacker to deduce the private key with a sufficient number of exchanges. Intermediate data other than the shared secret key (and the "matrix data" internal to ML-KEM, which can be deduced from the public key) must be securely deleted. If the exchange is successful, the 32-byte key generated on both sides will be the same. The shared secret key is always 32 bytes for all parameter sets. It may be that some libraries combine the validation and the encapsulation step; implementations should determine whether the library they are using does. For static public keys, the Encapsulation Key Check only needs to be performed once.

ML-KEM Parameter Sets FIPS 203 specifies three parameter sets; ML-KEM-512, ML-KEM-768 and ML-KEM-1024. It is assumed that Alice and Bob both know which parameter set they use (either by negotiation or by having one selection fixed in the protocol). shows the sizes of the cryptographic material of ML-KEM for each parameter set, as well as their relative cryptographic strength: pk = public key, sk = private key, expanded form, ct = ciphertext, ss = shared key, all lengths in bytes

	pk size	sk size	ct size	ss size	as strong as
ML-KEM-512	800	1632	768	32	AES-128
ML-KEM-768	1184	2400	1088	32	AES-192
ML-KEM-1024	1568	3168	1568	32	AES-256

shows an example of ML-KEM performance of each parameter set on one specific platform: Single-core performance in operation per second on AMD Ryzen 7 7700

	key generation	encapsulation	decapsulation
ML-KEM-512	244000	153000	202000
ML-KEM-768	142000	103000	134000
ML-KEM-1024	109000	77000	99000

Data sourced from As can be seen from and , ML-KEM has significantly larger public keys and ciphertexts than ECDH but very good performance.

KEM Security Considerations This section pertains to KEM (Key Encapsulation Mechanisms) in general, including ML-KEM. A KEM requires high-quality source of entropy during both the keypair generation and ciphertext generation steps. If an adversary can recover the random bits used in either of these processes, they can recover the shared secret. If an adversary can recover the random bits used during key generation, they can also recover the secret key. Alice needs to keep her private key secret. It is recommended that she zeroize her private key when she will have no further need of it, that is, when she knows she never needs to decapsulate any further ciphertexts with it. A KEM (including ML-KEM) provides no authentication of either communicating party. If an adversary could replace either the public key or the ciphertext with its own, it would generate a shared key with Alice or Bob. Hence, it is important that the protocol that uses a KEM lets Bob be able to verify that the public key he obtains came from Alice and lets Alice verify that the ciphertext came from Bob (that is, an entity that Alice is willing to communicate with). Such verification can be performed by cryptographic methods such as digital signatures or a MAC to verify integrity of the protocol exchange.

ML-KEM Security Considerations This section pertains specifically to ML-KEM, and may not be true of KEMs in general. The fundamental security property of ML-KEM is that someone listening to the exchanges (and thus obtains both the public key and the ciphertext) cannot reconstruct the shared secret key, and this is true even if the adversary has access to a CRQC. ML-KEM is IND-CCA2 secure; that is, it remains secure even if an adversary is able to submit arbitrary ciphertexts used a fixed public key and observe the resulting shared key. Submitting invalid ciphertexts to ML-KEM.Decaps() does not help the attacker obtain information about the decryption key of the PKE-Decrypt function inside the ML-KEM.Decaps(). Substituting the public key Alice sends Bob by another public key chosen by the attacker will not help the attacker get any information about Alice's private key, it would just make Alice and Bob not have a same shared secret key. However, if it is possible to substitute the copy of the public key for both Alice and Bob, an attacker can introduce a malicious public key where the same private key can be used for decapsulation, but the probability of decryption failure is marginally higher. As decryption failures can leak information about the secret decapulation key, it is important that Alice keeps a secure copy of the public key as part of her secret key. For practical purposes, IND-CCA2 means that ML-KEM is secure to use with static public keys. ML-KEM requires that a source of random bits with security strength greater than or equal to the security strength of the ML-KEM parameter set be used when generating the keypair and ciphertext during ML-KEM.KeyGen() and ML-KEM.Encaps() respectively. The cryptographic library that implements ML-KEM may access this source of randomness internally. A fresh string of bytes must be used for every sampling of random bytes in key generation and encapsulation. The random bytes should come from an approved RBG. Alice must keep her private key secret (both private and secure from modification). A copy of the public key and its hash are included in the private key and must be protected from modification. If the ciphertext that Alice receives from Bob is tampered with (either by small modification or by replacing it with an entirely different ciphertext), the shared secret key that Alice derives will be uncorrelated with the shared secret key that Bob obtains. An attacker will not be able to determine any information about the correct shared secret key or Alice's private key, even if the attacker obtains Alice's modified shared secret key which is the output of the ML-KEM.Decaps() function taking the modified ciphertext as input. It is secure to reuse a public key multiple times. That is, instead of Alice generating a fresh public and private keypair for each exchange, Alice may generate a public key once, and then publish that public key, and use it for multiple incoming ciphertexts, generating multiple shared secret keys. While this is safe, it is recommended that if the protocol already has Alice send Bob her unauthenticated public key, she should generate a fresh keypair each time (and zeroize the private key immediately after ML-KEM.Decaps()) to obtain Perfect Forward Secrecy. Generally key generation of ML-KEM is very fast (see ). Hence, if Alice generates a fresh ML-KEM key each time, then even if Alice's system is subverted (either by a hacker or a legal warrant), the previous communications remain secure (because Alice no longer has the information needed to recover the shared secret keys). Alice and Bob must perform the Key Check steps (the Encapsulation Key Check on the public key for Bob, the Decapsulation Key Check on the ciphertext for Alice). The cryptographic libraries that Alice and Bob use may automatically perform such checks; they should each verify that is the case. The shared secret key for all three parameter sets, ML-KEM-512, ML-KEM-768 and ML-KEM-1024 is 32 bytes which are indistinguishable from 32-byte pseudorandom byte-strings of 128, 192 and 256 bits of strengths respectively. As such, the 32-byte string is suitable for both directly as a symmetric key (for use by a symmetric cipher such as AES or a MAC), and also as input into a Key Derivation Function. This is in contrast to a Diffie-Hellman (or ECDH) operation, where the output is distinguishable from random. With ML-KEM, there is a tiny probability of decapsulation failure. That is, even if Alice and Bob perform their roles honestly and the public key and ciphertext are transmitted correctly, there is a tiny probability that Alice and Bob will not derive the same shared key. However, even though that is a theoretical possibility, practically speaking this will never happen. For all three parameter sets, the probability is so low that most likely an actual decapsulation failure will never be seen for any ML-KEM exchange anywhere (not only for your protocol, but over all protocols that uses ML-KEM). If the adversary has control over the ML-KEM private key, it has been shown that adversary can cause a ‘misbinding’ between the shared key and either the ciphertext or the public key. That is, by generating an impossible private key (a key that cannot occur with the standard ML-KEM key generation process), the adversary could be able to create public keys for which different ciphertexts or public keys may result in the same shared secret (these security notions are called MAL-BIND-K-CT and MAL-BIND-K-PK in the cryptographical literature ). This is not a threat to normal uses of ML-KEM as a key exchange or a public key encryption method. If ML-KEM is used as an authentication method where the shared key is used for authentication (and adversary control of the private key is possible), it may be advisable if the protocol also authenticate the public key and ciphertext as well.

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