A polynomial-time algorithm for solving a class of underdetermined multivariate quadratic equations over fields of odd characteristics

Chen Mou Cheng, Yasufumi Hashimoto, Hiroyuki Miura, Tsuyoshi Takagi

研究成果: Contribution to journalArticle査読

2 被引用数 (Scopus)

抄録

Following up a series of works by Kipnis-Patarin-Goubin, Courtois-Goubin-Meier-Tacier, and Thomae-Wolf, in PQCrypto 2013 Miura, Hashimoto, and Takagi proposed an efficient algorithm for solving a class of underdetermined multivariate quadratic equations. Their algorithm does not use any generic Gröbner-basis solving techniques and asymptotically requires the least degree of underdeterminedness among all similar algorithms in the current literature. Building on top of their work, in this paper we focus on solving polynomially underdetermined multivariate quadratic equations over fields of odd characteristics. We show that we can further improve the applicable range of the Miura- Hashimoto-Takagi algorithm essentially for free. Furthermore, we show how to allow a certain degree of trade-off between applicable range and running time. Last but not least, we show that the running time of the improved algorithm is actually polynomial in number of equations and variables. To the best of our knowledge, this is the first result showing that this class of polynomially underdetermined multivariate quadratic equations over fields of odd characteristics can be solved in polynomial time.

本文言語英語
ページ(範囲)40-58
ページ数19
ジャーナルLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
8772
DOI
出版ステータス出版済み - 2014

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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