CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM

TLDR

Rapid advances in quantum computing and NIST’s push for new post‑quantum standards have spurred interest in schemes like Kyber, a successor to NEWHOPE. The paper introduces Kyber, a post‑quantum key‑encapsulation mechanism based on module‑lattice hardness. The authors build a CPA‑secure public‑key encryption, transform it via Fujisaki‑Okamoto to a CCA‑secure KEM, and derive CCA‑secure encryption, key‑exchange, and authenticated‑key‑exchange schemes, with security based on Module‑LWE and parameters targeting over 128‑bit post‑quantum security. Kyber achieves roughly half the key and ciphertext sizes of NEWHOPE, provides CCA security, is based on a more general lattice problem, and its optimized implementation runs in essentially the same time as NEWHOPE.

Abstract

Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digitalsignature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of postquantum security.