Relation between XL algorithm and Gröbner Bases Algorithms
نویسندگان
چکیده
We clarify a relation between the XL algorithm and Gröbner bases algorithms. The XL algorithm was proposed to be a more efficient algorithm to solve a system of equations with a special assumption without trying to calculate a whole Gröbner basis. But in our result, it is shown that the XL algorithm is also a Gröbner bases algorithm which can be represented as a redundant version of a Gröbner bases algorithm F4 under the assumption in XL. keywords : Algebraic attacks, Gröbner bases algorithm, F4, XL algorithm
منابع مشابه
Relation between the XL Algorithm and Gröbner Basis Algorithms
We clarify a relation between the XL algorithm and known Gröbner 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 Gröbner 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 ...
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This paper compares the XL algorithm with known Gröbner basis algorithms. We show that to solve a system of algebraic equations via the XL algorithm is equivalent to calculate the reduced Gröbner basis of the ideal associated with the system. Moreover we show that the XL algorithm is also a Gröbner basis algorithm which can be represented as a redundant variant of a Gröbner basis algorithm F4. ...
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ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2004 شماره
صفحات -
تاریخ انتشار 2004