The "Cryptographic Suite for Algebraic Lattices" (CRYSTALS) encompasses two cryptographic primitives: Kyber , an IND-CCA2-secure key-encapsulation mechanism (KEM); and Dilithium , a strongly EUF-CMA-secure digital signature algorithm. Both algorithms are based on hard problems over module lattices, are designed to withstand attacks by large quantum computers, and have been submitted to the NIST post-quantum cryptography project .
Module lattices can be thought of as lattices that lie between the ones used in the definitions of the LWE problem , and those used for the Ring-LWE problem. If the ring underlying the module has a sufficiently high degree (like 256), then these lattices inherit all the efficiency of the ones used in the Ring-LWE problem, and additionally have the following advantages, when used in our cryptographic algorithms:
The design and implementation of Kyber and Dilithium have been supported by
Peter Schwabe