A technique to reduce memory usage of M4GB algorithm

Takuma Ito; Koutaro Kobayashi; Takashi Kurokawa; Naoyuki Shinohara; Shigenori Uchiyama

doi:10.14495/jsiaml.15.125

Takuma Ito , Koutaro Kobayashi, Takashi Kurokawa, Naoyuki Shinohara, Shigenori Uchiyama

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Keywords: multivariate polynomials, multivariate public key cryptosystems, Gröbner bases, MQ problems

JOURNAL FREE ACCESS

2023 Volume 15 Pages 125-128

DOI https://doi.org/10.14495/jsiaml.15.125

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Abstract

The problem of finding solutions to a system of multivariate quadratic (MQ) algebraic equations, called the MQ problem, is important research for the security evaluation of multivariate public key cryptosystems. Algorithms for computing Gröbner bases are often used as tools for solving the MQ problem. M4GB algorithm is known as an efficient algorithm to compute Gröbner bases. M4GB stores many polynomials to efficiently compute Gröbner bases, which tends to increase space complexity, i.e., memory usage. In this article, we propose a technique to reduce memory usage of M4GB algorithm.

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