| Title: | a new efficient algorithm for computing all low degree annihilators of sparse polynomials with a high number of variables |
| Author: | Xu Lin
; Lin Dongdai
; Li Xin
|
| Source: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
|
| Conference Name: | 6th International Conference on Information Security Practice and Experience
|
| Conference Date: | MAY 12-13,
|
| Issued Date: | 2010
|
| Conference Place: | Seoul, SOUTH KOREA
|
| Keyword: | algebraic attack
; annihilator
; algebraic immunity
; boolean polynomial
; computational algebra
|
| Publisher: | INFORMATION SECURITY PRACTICE AND EXPERIENCE, PROCEEDINGS
|
| Publish Place: | HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY
|
| 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.
|
| Sponsorship: | Korea Internet & Security Agcy, Elect & Telecommun Res Inst, Korea Inst Informat Security & Cryptography, Korea Commun Commiss
|
| 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. |
| Content Type: | 会议论文
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| URI: | http://ir.iscas.ac.cn/handle/311060/8616
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| Appears in Collections: | 信息安全国家重点实验室_会议论文
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| a new efficient algorithm for computing all low degree annihilators of sparse polynomials with a high number of variables.pdf（264KB） | -- | -- | 限制开放 | -- | 联系获取全文 |
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| Recommended Citation: | |
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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