Lattice codes for CRYSTALS-Kyber

IF 1.4 2区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Shuiyin Liu, Amin Sakzad
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Abstract

This paper describes a constant-time lattice encoder for the National Institute of Standards and Technology (NIST) recommended post-quantum encryption algorithm: Kyber. The first main contribution of this paper is to refine the analysis of Kyber decoding noise and prove that Kyber decoding noise can be bounded by a sphere. This result shows that the Kyber encoding problem is essentially a sphere packing in a hypercube. The original Kyber encoder uses the integer lattice for sphere packing purposes, which is far from optimal. Our second main contribution is to construct optimal lattice codes to ensure denser packing and a lower decryption failure rate (DFR). Given the same ciphertext size as the original Kyber, the proposed lattice encoder enjoys a larger decoding radius, and is able to encode much more information bits. This way we achieve a decrease of the communication cost by up to \(32.6\%\), and a reduction of the DFR by a factor of up to \(2^{85}\). Given the same plaintext size as the original Kyber, e.g., 256 bits, we propose a bit-interleaved coded modulation (BICM) approach, which combines a BCH code and the proposed lattice encoder. The proposed BICM scheme significantly reduces the DFR of Kyber, thus enabling further compression of the ciphertext. Compared with the original Kyber encoder, the communication cost is reduced by \(24.49\%\), while the DFR is decreased by a factor of \(2^{39}\). The proposed encoding scheme is a constant-time algorithm, thus resistant against the timing side-channel attacks.

晶格代码为CRYSTALS-Kyber
本文介绍了一种恒时点阵编码器为美国国家标准与技术研究院(NIST)推荐的后量子加密算法:Kyber。本文的第一个主要贡献是改进了Kyber译码噪声的分析,并证明了Kyber译码噪声可以被一个球有界。这个结果表明Kyber编码问题本质上是一个在超立方体中的球体填充问题。最初的Kyber编码器使用整数晶格进行球体填充,这远非最优。我们的第二个主要贡献是构造最优的格码,以确保更密集的包装和更低的解密失败率(DFR)。给定与原始Kyber相同的密文大小,所提出的点阵编码器具有更大的解码半径,并且能够编码更多的信息位。通过这种方式,我们将通信成本降低了\(32.6\%\),并将DFR降低了\(2^{85}\)。给定与原始Kyber相同的明文大小,例如256位,我们提出了一种比特交错编码调制(BICM)方法,该方法结合了BCH编码和所提出的点阵编码器。提出的BICM方案显著降低了Kyber的DFR,从而能够进一步压缩密文。与原Kyber编码器相比,通信成本降低了\(24.49\%\), DFR降低了\(2^{39}\)。所提出的编码方案是一种恒定时间算法,因此可以抵抗定时旁信道攻击。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Designs, Codes and Cryptography
Designs, Codes and Cryptography 工程技术-计算机:理论方法
CiteScore
2.80
自引率
12.50%
发文量
157
审稿时长
16.5 months
期刊介绍: Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.
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