| a new efficient algorithm for computing all low degree annihilators of sparse polynomials with a high number of variables | |
| Xu Lin; Lin Dongdai; Li Xin | |
| 2010 | |
| 会议名称 | 6th International Conference on Information Security Practice and Experience |
| 会议录名称 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| 页码 | 123-137 |
| 会议日期 | MAY 12-13, |
| 会议地点 | Seoul, SOUTH KOREA |
| 出版地 | HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY |
| 出版者 | INFORMATION SECURITY PRACTICE AND EXPERIENCE, PROCEEDINGS |
| 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. |
| 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. |
| 关键词 | Algebraic Attack Annihilator Algebraic Immunity Boolean Polynomial Computational Algebra |
| 主办者 | Korea Internet & Security Agcy, Elect & Telecommun Res Inst, Korea Inst Informat Security & Cryptography, Korea Commun Commiss |
| 内容类型 | 会议论文 |
| URI标识 | http://ir.iscas.ac.cn/handle/311060/8616 |
| 专题 | 信息安全国家重点实验室 |
| 推荐引用方式 GB/T 7714 | 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]. HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY:INFORMATION SECURITY PRACTICE AND EXPERIENCE, PROCEEDINGS,2010:123-137. |
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