共被期刊论文引用了3次
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| 1 | A new proof for the correctness of the F5 algorithm显示文摘In 2002,Faugère presented the famous F5 algorithm for computing Grbner basis where two criteria,syzygy criterion and rewritten criterion,were proposed to avoid redundant computations.He proved the correctness of the syzygy criterion,but the proof for the correctness of the rewritten criterion was left.Since then,F5 has been studied extensively.Some proofs for the correctness of F5 were proposed,but these proofs are valid only under some extra assumptions.In this paper,we give a proof for the correctness of F5B,an equivalent version of F5 in Buchberger's style.The proof is valid for both homogeneous and non-homogeneous polynomial systems.Since this proof does not depend on the computing order of the S-pairs,any strategy of selecting S-pairs could be used in F5B or F5.Furthermore,we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs. | SUN Yao WANG DingKang | 2013 | Science China Mathematics2013，56，4： | 2 |
| 2 | Algebraic-Differential Attacks on a Family of Arithmetization-Oriented Symmetric Ciphers显示文摘Motivated by applications in advanced cryptographic protocols,research on arithmetizationoriented symmetric primitives has been rising in the field of symmetric cryptography in recent years.In this paper,the authors focus on on the collision attacks for a family of arithmetization-oriented symmetric ciphers GMiMCHash.The authors firstly enhance the algebraically controlled differential attacks proposed by introducing more variables.Then,combining algebraic attacks and differential attacks,the authors propose algebraic-differential attacks on GMi MCHash.This attack method is shown to be effective by experiments on toy versions of GMi MCHash.The authors further introduce some tricks to reduce the complexities of algebraic-differential attacks and improve the success probability of finding collisions. | LI Zhengnan WU Baofeng LIN Dongdai | 2023 | Journal of Systems Science & Complexity2023，36，6： | 0 |
| 3 | Invariant G^(2)V algorithm for computing SAGBI-Grobner bases显示文摘Faugère and Rahmany have presented the invariant F5 algorithm to compute SAGBI-Grbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely, invariant G2V algorithm, to compute SAGBI-Grbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G2V algorithm; a variant of the F5 algorithm to compute Grbner bases. We have implemented our new algorithm in Maple , and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F5 algorithm. | HASHEMI Amir M.-ALIZADEH Benyamin RIAHI Monireh | 2013 | Science China Mathematics2013，56，9： | 0 |
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