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On Implementing the Symbolic Preprocessing Function over Boolean Polynomial Rings in Grobner Basis Algorithms Using Linear Algebra
Sun Yao1; Huang Zhenyu1; Lin Dongdai1; Wang Dingkang2
2016-06-01
Source PublicationJOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN1009-6124
Volume29Issue:3Pages:789-804
AbstractSome techniques using linear algebra was introduced by Faugere in F4 to speed up the reduction process during Grobner basis computations. These techniques can also be used in fast implementations of F5 and some other signature-based Grobner basis algorithms. When these techniques are applied, a very important step is constructing matrices from critical pairs and existing polynomials by the Symbolic Preprocessing function ( given in F4). Since multiplications of monomials and polynomials are involved in the Symbolic Preprocessing function, this step can be very costly when the number of involved polynomials/monomials is huge. In this paper, multiplications of monomials and polynomials for a Boolean polynomial ring are investigated and a specific method of implementing the Symbolic Preprocessing function over Boolean polynomial rings is reported. Many examples have been tested by using this method, and the experimental data shows that the new method is very efficient.
KeywordBoolean polynomial rings Grobner basis implementation linear algebra
DOI10.1007/s11424-015-4085-1
Language英语
Funding ProjectNational Key Basic Research Program of China[2013CB834203] ; National Key Basic Research Program of China[2011CB302400] ; National Nature Science Foundation of China[11301523] ; National Nature Science Foundation of China[11371356] ; National Nature Science Foundation of China[61121062] ; Strategic Priority Research Program of the Chinese Academy of Sciences[XDA06010701] ; IEE's Research Project on Cryptography Grant[Y3Z0013102] ; IEE's Research Project on Cryptography Grant[Y3Z0018102] ; IEE's Research Project on Cryptography Grant[Y4Z0061A02]
WOS Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000379826000013
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23225
Collection系统科学研究所
Affiliation1.Chinese Acad Sci, Inst Informat Engn, SKLOIS, Beijing 100093, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100090, Peoples R China
Recommended Citation
GB/T 7714
Sun Yao,Huang Zhenyu,Lin Dongdai,et al. On Implementing the Symbolic Preprocessing Function over Boolean Polynomial Rings in Grobner Basis Algorithms Using Linear Algebra[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2016,29(3):789-804.
APA Sun Yao,Huang Zhenyu,Lin Dongdai,&Wang Dingkang.(2016).On Implementing the Symbolic Preprocessing Function over Boolean Polynomial Rings in Grobner Basis Algorithms Using Linear Algebra.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,29(3),789-804.
MLA Sun Yao,et al."On Implementing the Symbolic Preprocessing Function over Boolean Polynomial Rings in Grobner Basis Algorithms Using Linear Algebra".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 29.3(2016):789-804.
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