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| 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 | |
| Conference Name | 6th International Conference on Information Security Practice and Experience |
| Source | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Pages | 123-137 |
| Conference Date | MAY 12-13, |
| Conference Place | Seoul, SOUTH KOREA |
| Publish Place | HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY |
| Publisher | INFORMATION SECURITY PRACTICE AND EXPERIENCE, PROCEEDINGS |
| ISSN | 0302-9743 |
| ISBN | 978-3-642-12826-4 |
| Department | Xu, Lin; Lin, Dongdai; Li, Xin Chinese Acad Sci, State Key Lab Informat Secur, Inst Software, Beijing 100080, Peoples R China. |
| English Abstract | 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. |
| Keyword | Algebraic Attack Annihilator Algebraic Immunity Boolean Polynomial Computational Algebra |
| Sponsorship | Korea Internet & Security Agcy, Elect & Telecommun Res Inst, Korea Inst Informat Security & Cryptography, Korea Commun Commiss |
| Content Type | 会议论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/8616 |
| Collection | 信息安全国家重点实验室 |
| Recommended Citation 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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| a new efficient algo（264KB） | 开放获取 | -- | Application Full Text | |||
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