Extended algorithm for solving underdefined multivariate quadratic equations

Hiroyuki Miura, Yasufumi Hashimoto, Tsuyoshi Takagi

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

9 被引用数 (Scopus)

抄録

It is well known that solving randomly chosen Multivariate Quadratic equations over a finite field (MQ-Problem) is NP-hard, and the security of Multivariate Public Key Cryptosystems (MPKCs) is based on the MQ-Problem. However, this problem can be solved efficiently when the number of unknowns n is sufficiently greater than that of equations m (This is called "Underdefined"). Indeed, the algorithm by Kipnis et al. (Eurocrypt'99) can solve the MQ-Problem over a finite field of even characteristic in a polynomial-time of n when n ≥ m(m + 1). Therefore, it is important to estimate the hardness of the MQ-Problem to evaluate the security of Multivariate Public Key Cryptosystems. We propose an algorithm in this paper that can solve the MQ-Problem in a polynomial-time of n when n ≥ m(m + 3)/2, which has a wider applicable range than that by Kipnis et al. We will also compare our proposed algorithm with other known algorithms. Moreover, we implemented this algorithm with Magma and solved the MQ-Problem of m = 28 and n = 504, and it takes 78.7 seconds on a common PC.

本文言語英語
ホスト出版物のタイトルPost-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Proceedings
ページ118-135
ページ数18
DOI
出版ステータス出版済み - 2013
イベント5th International Workshop on Post-Quantum Cryptography, PQCrypto 2013 - Limoges, フランス
継続期間: 6月 4 20136月 7 2013

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7932 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他5th International Workshop on Post-Quantum Cryptography, PQCrypto 2013
国/地域フランス
CityLimoges
Period6/4/136/7/13

!!!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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