Semi-Compressed CRYSTALS-Kyber

TL;DR

This paper reduces Kyber's communication overhead by 54% using optimal quantization and encoding techniques, enabling more efficient post-quantum cryptography with minimal security compromise.

Contribution

It introduces a novel compression scheme for Kyber combining Lloyd-Max quantization and advanced encoding, optimizing communication efficiency while maintaining security.

Findings

Achieved 54% reduction in communication overhead.

Demonstrated encoding scheme encapsulates 638 bits per ciphertext.

Derived explicit expressions for decryption failure rate and minimum overhead.

Abstract

In this paper, we investigate the communication overhead of the Kyber, which has recently been standardized by the National Institute of Standards and Technology (NIST). Given the same decryption failure rate (DFR) and security argument, we show it is feasible to reduce the communication overhead of the Kyber by 54%. The improvement is based on two technologies: ciphertext quantization and plaintext encoding. First, we prove that the Lloyd-Max quantization is optimal to minimize the decryption decoding noise. The original Kyber compression function is not optimal. Second, we propose an encoding scheme, which combines Pulse-Amplitude Modulation (PAM), Gray mapping, and a binary error correcting code. An explicit expression for the DFR is derived. The minimum possible communication overhead is also derived. Finally, we demonstrate that with the Lloyd-Max quantization, 8-PAM, Gray mapping, and a shortened binary BCH(768,638,13) code, the proposed scheme encapsulates 638 bits (e.g., 2.5 AES keys) in a single ciphertext.