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    题名: On asymptotic security estimates in XL and groebner bases related algebraic cryptanalysis
    其它题名: XL (延伸線性化) 與 Groebner 基底類代數攻擊的漸近行為
    作者: Yang, Bo-yin;Chen, Jiun-ming
    贡献者: 淡江大學數學學系
    关键词: XL;Gröbner Bases;multivariate quadratics;algebraic cryptanalysis;asymptotic security estimates
    日期: 2004-10
    上传时间: 2010-01-28 07:24:13 (UTC+8)
    出版者: Berlin Heidelberg : Springer-Verlag GmbH
    摘要: “Algebraic Cryptanalysis” against a cryptosystem often comprises finding enough relations that are generally or probabilistically valid, then solving the resultant system. The security of many schemes (most important being AES) thus depends on the difficulty of solving multivariate polynomial equations. Generically, this is NP-hard.
    The related methods of XL (eXtended Linearization), Gröbner Bases, and their variants (of which a large number has been proposed) form a unified approach to solving equations and thus affect our assessment and understanding of many cryptosystems.
    Building on prior theory, we analyze these XL variants and derive asymptotic formulas giving better security estimates under XL-related algebraic attacks; through this examination we have hopefully improved our understanding of such variants. In particular, guessing a portion of variables is a good idea for both XL and Gröbner Bases methods.
    關聯: Lecture Notes in Computer Science 3269, pp.401-413
    DOI: 10.1007/978-3-540-30191-2_31
    显示于类别:[數學學系暨研究所] 期刊論文

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