A combinatorial approach to avoiding weak keys in the BIKE cryptosystem

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2025-05-14 DOI:10.1007/s10623-025-01643-7

Gretchen L. Matthews, Emily McMillon

引用次数: 0

Abstract

Bit Flipping Key Encapsulation (BIKE) is a code-based cryptosystem that was considered in Round 4 of the NIST Post-Quantum Cryptography Standardization process. It is based on quasi-cyclic moderate-density parity-check (QC-MDPC) codes paired with an iterative decoder. While (low-density) parity-check codes have been shown to perform well in practice, their capabilities are governed by the code’s graphical representation and the choice of decoder rather than the traditional code parameters, making it difficult to determine the decoder failure rate (DFR). Moreover, decoding failures have been demonstrated to lead to attacks that recover the BIKE private key. In this paper, we demonstrate a strong correlation between weak keys and 4-cycles in their associated Tanner graphs. We give concrete ways to enumerate the number of 4-cycles in a BIKE key and use these results to present a filtering algorithm that will filter BIKE keys with large numbers of 4-cycles. These results also apply to more general parity check codes.

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避免BIKE密码系统中弱密钥的组合方法

比特翻转密钥封装（BIKE）是一种基于代码的密码系统，在NIST后量子加密标准化过程的第4轮中被考虑。它基于准循环中密度奇偶校验（QC-MDPC）码与迭代解码器配对。虽然（低密度）奇偶校验码在实践中表现良好，但它们的能力受代码的图形表示和解码器的选择而不是传统代码参数的控制，这使得难以确定解码器故障率（DFR）。此外，已经证明解码失败会导致恢复BIKE私钥的攻击。在本文中，我们证明了弱键与4环在它们的相关Tanner图中的强相关性。我们给出了具体的方法来枚举一个BIKE密钥中4个循环的个数，并利用这些结果提出了一种过滤具有大量4个循环的BIKE密钥的过滤算法。这些结果也适用于更一般的奇偶校验码。

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 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.