All in the XL family : theory and practice

doi:10.1007/11496618_7

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 期刊論文 > Item 987654321/41373

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题名:	All in the XL family : theory and practice
其它题名:	XL (延伸線性化) 類方法的理論和實際的探討
作者:	Yang, Bo-yin
贡献者:	淡江大學數學學系
关键词:	algebraic analysis;finite field;Gröbner Bases;multivariate quadratics;multivariate cryptography;XL
日期:	2005-04
上传时间:	2010-01-28 07:24:44 (UTC+8)
出版者:	Berlin Heidelberg : Springer-Verlag GmbH
摘要:	The XL (eXtended Linearization) equation-solving algorithm belongs to the same extended family as the advanced Gröbner Bases methods F4/F5. XL and its relatives may be used as direct attacks against multivariate Public-Key Cryptosystems and as final stages for many “algebraic cryptanalysis” used today. We analyze the applicability and performance of XL and its relatives, particularly for generic systems of equations over medium-sized finite fields. In examining the extended family of Gröbner Bases and XL from theoretical, empirical and practical viewpoints, we add to the general understanding of equation-solving. Moreover, we give rigorous conditions for the successful termination of XL, Gröbner Bases methods and relatives. Thus we have a better grasp of how such algebraic attacks should be applied. We also compute revised security estimates for multivariate cryptosystems. For example, the schemes SFLASHv2 and HFE Challenge 2 are shown to be unbroken by XL variants.
關聯:	Lecture Notes in Computer Science 3506,　p.67-86
DOI:	10.1007/11496618_7
显示于类别:	[數學學系暨研究所] 期刊論文

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