求解多元二次方程欠定义系统算法的改进

IF 0.4 Q4 MATHEMATICS, APPLIED
Yasufumi Hashimoto
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引用次数: 1

摘要

一般来说,求解有限域上的多元二次方程组是一个难题。然而,当变量数量足够大于方程数量时,已经有几种有效求解二次方程系统的算法(例如,Kipnis等人,Eurocrypt 1999, Thomae-Wolf, PKC 2012, Cheng等人,PQCrypto 2014和fuue等人,PQCrypto 2021)。在本文中,我们提出了一种新的算法,当变量的数量小于先前给出的算法所需的数量时,该算法是可用的。我们还分析了MAYO的安全性,这是UOV的一种变体,在SAC 2021中提出,并提交给NIST的后量子加密的其他数字签名方案标准化项目。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An improvement of algorithms to solve under-defined systems of multivariate quadratic equations
The problem of solving a system of multivariate quadratic equations over a finite field is known to be hard in general. However, there have been several algorithms of solving the system of quadratic equations efficiently when the number of variables is sufficiently larger than the number of equations (e.g., Kipnis et al., Eurocrypt 1999, Thomae-Wolf, PKC 2012, Cheng et al., PQCrypto 2014 and Furue et al., PQCrypto 2021). In the present paper, we propose a new algorithm which is available if the number of variables is smaller than that required in the previously given algorithms. We also analyze the security of MAYO, a variant of UOV, proposed in SAC 2021 and submitted to NIST’s standardization project of additional digital signature schemes for Post-Quantum Cryptography.
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来源期刊
JSIAM Letters
JSIAM Letters MATHEMATICS, APPLIED-
自引率
25.00%
发文量
27
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