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a new efficient algorithm for computing all low degree annihilators of sparse polynomials with a high number of variables
作者: Xu Lin ; Lin Dongdai ; Li Xin
会议文集: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
会议名称: 6th International Conference on Information Security Practice and Experience
会议日期: MAY 12-13,
出版日期: 2010
会议地点: Seoul, SOUTH KOREA
关键词: algebraic attack ; annihilator ; algebraic immunity ; boolean polynomial ; computational algebra
出版者: INFORMATION SECURITY PRACTICE AND EXPERIENCE, PROCEEDINGS
出版地: HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY
ISSN: 0302-9743
ISBN: 978-3-642-12826-4
部门归属: Xu, Lin; Lin, Dongdai; Li, Xin Chinese Acad Sci, State Key Lab Informat Secur, Inst Software, Beijing 100080, Peoples R China.
主办者: Korea Internet & Security Agcy, Elect & Telecommun Res Inst, Korea Inst Informat Security & Cryptography, Korea Commun Commiss
英文摘要: Algebraic attacks have proved to be an effective threat to block and stream cipher systems. In the realm of algebraic attacks, there is one major concern that, for a given Boolean polynomial f, if f or f 1 has low degree annihilators. Existing methods for computing all annihilators within degree d of f in n variables, such as Gauss elimination and interpolation, have a complexity based on the parameter k(n,d) = Sigma(d)(i=0) ((n)(i)), which increases dramatically with n. As a result, these methods are impractical when dealing with sparse polynomials with a large n, which widely appear in modern cipher systems. In this paper, we present a new tool for computing annihilators, the characters w.r.t. a Boolean polynomial. We prove that the existence of annihilators of f and f 1 7-esp. relies on the zero characters and the critical characters zu.r.t. f. Then we present a new algorithm for computing annihilators whose complexity relies on lef,d, the number of zero or critical characters within degree d w.r.t.f. Since 16,d << k(n,d) when f is sparse, this algorithm is very efficient for sparse polynomials with a large n. In our experiments, all low degree annihilators of a random balanced sparse polynomial in 256 variables can be found in a few minutes.
内容类型: 会议论文
URI标识: http://ir.iscas.ac.cn/handle/311060/8616
Appears in Collections:信息安全国家重点实验室_会议论文

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Xu Lin,Lin Dongdai,Li Xin. a new efficient algorithm for computing all low degree annihilators of sparse polynomials with a high number of variables[C]. 见:6th International Conference on Information Security Practice and Experience. Seoul, SOUTH KOREA. MAY 12-13,.
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