Cryptographic Suite for Algebraic Lattices



Kyber is an IND-CCA2-secure key encapsulation mechanism (KEM), whose security is based on the hardness of solving the learning-with-errors (LWE) problem over module lattices. Kyber is one of the finalists in the NIST post-quantum cryptography project. The submission lists three different parameter sets aiming at different security levels. Specifically, Kyber-512 aims at security roughly equivalent to AES-128, Kyber-768 aims at security roughly equivalent to AES-192, and Kyber-1024 aims at security roughly equivalent to AES-256.

For users who are interested in using Kyber, we recommend the following:

  • Use Kyber in a so-called hybrid mode in combination with established "pre-quantum" security; for example in combination with elliptic-curve Diffie-Hellman.
  • We recommend using the Kyber-768 parameter set, which—according to a very conservative analysis—achieves more than 128 bits of security against all known classical and quantum attacks.

Scientific Background

The design of Kyber has its roots in the seminal LWE-based encryption scheme of Regev. Since Regev's original work, the practical efficiency of LWE encryption schemes has been improved by observing that the secret in LWE can come from the same distribution as the noise and also noticing that "LWE-like" schemes can be built by using a square (rather than a rectangular) matrix as the public key. Another improvement was applying an idea originally used in the NTRU cryptosystem to define the Ring-LWE and Module-LWE problems that used polynomial rings rather than integers. The CCA-secure KEM Kyber is built on top of a CPA-secure cryptosystem that is based on the hardness of Module-LWE.

Users of Kyber

Kyber is already being integrated into libraries and systems by industry. For example,

Performance Overview

The tables below gives an indication of the performance of Kyber. All benchmarks were obtained on one core of an Intel Core-i7 4770K (Haswell) CPU. We report benchmarks of two different implementations: a C reference implementation and an optimized implementation using AVX2 vector instructions. For benchmarks on an ARM Cortex-M4 microcontroller, see the benchmarks reported by the pqm4 project.

Sizes (in bytes) Haswell cycles (ref) Haswell cycles (avx2)
sk: 1632 gen: 122684 gen: 33856
pk: 800 enc: 154524 enc: 45200
ct: 768 dec: 187960 dec: 34572
Sizes (in bytes) Haswell cycles (ref) Haswell cycles (avx2)
sk: 2400 gen: 199408 gen: 52732
pk: 1184 enc: 235260 enc: 67624
ct: 1088 dec: 274900 dec: 53156
Sizes (in bytes) Haswell cycles (ref) Haswell cycles (avx2)
sk: 3168 gen: 307148 gen: 73544
pk: 1568 enc: 346648 enc: 97324
ct: 1568 dec: 396584 dec: 79128

As an update for round 2 of the NIST project we also proposed a variant of Kyber that is meant to showcase the performance of Kyber when hardware support for the symmetric primitives is available. This variant, called Kyber-90s, uses AES-256 in counter mode and SHA2 instead of SHAKE.

Haswell cycles (ref) Haswell cycles (avx2)
gen: 213156 gen: 21880
enc: 213156 enc: 28592
dec: 277612 dec: 20980
Haswell cycles (ref) Haswell cycles (avx2)
gen: 389760 gen: 30460
enc: 432764 enc: 40140
dec: 473984 dec: 30108
Haswell cycles (ref) Haswell cycles (avx2)
gen: 636380 gen: 43212
enc: 672644 enc: 56556
dec: 724144 dec: 44328