|標題：On asymptotic security estimates in XL and groebner bases related algebraic cryptanalysis|
|作品名稱||On asymptotic security estimates in XL and groebner bases related algebraic cryptanalysis|
|作品名稱（其他語言）||XL (延伸線性化) 與 Groebner 基底類代數攻擊的漸近行為|
|著者||Yang, Bo-yin; Chen, Jiun-ming|
|出版者||Berlin Heidelberg : Springer-Verlag GmbH|
|著錄名稱、卷期、頁數||Lecture Notes in Computer Science 3269, pp.401-413|
|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.