淡江大學機構典藏:Item 987654321/41370
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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/41370


    Title: On asymptotic security estimates in XL and groebner bases related algebraic cryptanalysis
    Other Titles: XL (延伸線性化) 與 Groebner 基底類代數攻擊的漸近行為
    Authors: Yang, Bo-yin;Chen, Jiun-ming
    Contributors: 淡江大學數學學系
    Keywords: XL;Gröbner Bases;multivariate quadratics;algebraic cryptanalysis;asymptotic security estimates
    Date: 2004-10
    Issue Date: 2010-01-28 07:24:13 (UTC+8)
    Publisher: Berlin Heidelberg : Springer-Verlag GmbH
    Abstract: “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.
    Relation: Lecture Notes in Computer Science 3269,　p.401-413
    DOI: 10.1007/978-3-540-30191-2_31
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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