Simple matrix cryptosystem is not broken by Liu's attack

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-05-10 DOI:10.1016/j.ffa.2025.102643

Lih-Chung Wang, Yen-Liang Kuan, Po-En Tseng, Chun-Yen Chou

引用次数: 0

Abstract

At PQCrypto2013, Tao et al. proposed a new multivariate public key cryptosystem for encryption called Simple Matrix (or ABC) encryption scheme. In 2018, Liu et al. proposed a key recovery attack on ABC scheme with claimed complexity of

O (s^{4 w})

, where s is the size of the

s \times s

square matrices in the scheme,

w = 3

in the usual Gaussian elimination algorithm and

w = 2.3776

in improved scheme. In this paper, we show that Liu's attack only works for the case

s = 2

of ABC scheme which means that Liu's attack doesn't break ABC scheme.

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简单矩阵密码系统没有被刘的攻击所破解

在PQCrypto2013上，Tao等人提出了一种新的用于加密的多元公钥密码系统，称为简单矩阵（Simple Matrix，简称ABC）加密方案。2018年，Liu等人提出了一种针对ABC方案的密钥恢复攻击，声称复杂度为O(s4w)，其中s为方案中s×s方阵的大小，在通常的高斯消去算法中w=3，在改进方案中w=2.3776。在本文中，我们证明了Liu的攻击只对ABC方案的s=2的情况有效，这意味着Liu的攻击不会破坏ABC方案。

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

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.