CRYSTALS (Cryptographic Suite for Algebraic Lattices) supports two quantum robust mechanisms: Kyber for key-encapsulation mechanism (KEM) and key exchange; and Dilithium for a digital signature algorithm. CRYSTALS-Kyber uses LWE (Learning with Errors) with lattice methods. A new lattice attack was discovered within the period of the assessment [1], but it is hoped that an updated version of Kyber can be produced for the final assessment. NIST have some worried about its side-channel robustness, but is a strong contender for KEM. Overall a KEM allows a symmetric key to be passed using public key methods. In this case, Alice will generate her key pair of a public key (\(pk\)) and a private key (\(sk\)). She then passes her public key to Bob, and then Bob creates a cipher text (\(ct\)) with Alice's public key. He passes the ciphertext to Alice, and who decrypts with her private key. This will reveal the key that Bob wants Alice to use. Kyber512 has a security level of AES-128, Kyber738 maps to AES-192, and Keyber1024 to AES-256. [Kyber KEM] [SABER KEM] [NTRU KEM] [McEliece KEM]
Related: [Kyber KEM][Kyber KEX][Dilithium Dig Sig Speed][Factoring signature (ECC)][Factoring signature (Logs)][Falcon Digital Signature][Rainbow Digital Signature][Dilithium Digital Signature][SPHINCS+]