Relation between the XL Algorithm and Grobner Basis Algorithms(Symmetric Key Cryptography, <Special Section>Cryptography and Information Security)

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概要

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• We clarify a relation between the XL algorithm and known Grobner basis algorithms. The XL algorithm was proposed to be a more efficient algorithm to solve a system of algebraic equations under a special condition, without calculating a whole Grobner basis. But in our result, it is shown that to solve a system of algebraic equations with a special condition under which the XL algorithm works is equivalent to calculate the reduced Grobner basis of the ideal associated with the system. Moreover we show that the XL algorithm is a Grobner basis algorithm which can be represented as a redundant variant of a known Grobner basis algorithm F_4.

• 社団法人電子情報通信学会の論文
• 2006-01-01

著者

• 川添 充

  大阪府立大学総合教育研究機構

• KAWAZOE Mitsuru

  Faculty of Liberal Arts and Sciences, Osaka Prefecture University

• IMAI Hideki

  Institute of Industrial Science, The University of Tokyo

• Kawazoe Mitsuru

  Faculty Of Liberal Arts And Sciences Osaka Prefecture University

• Imai Hideki

  Institute Of Industrial Science The University Of Tokyo

• Sugita Makoto

  It Security Center Information-technology Promotion Agency

• 川添 充

  大阪府立大総合教育研究機構

• Imai Hideki

  Institute Of Industrial Science Interfaculty Initiative For Information Studies University Of Tokyo

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