On Implementing the Symbolic Preprocessing Function over Boolean Polynomial Rings in Grobner Basis Algorithms Using Linear Algebra
文献类型：期刊论文
| 作者 | Sun Yao1; Huang Zhenyu1; Lin Dongdai1; Wang Dingkang2
|
| 刊名 | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| 出版日期 | 2016-06-01 |
| 卷号 | 29期号:3页码:789-804 |
| 关键词 | Boolean polynomial rings Grobner basis implementation linear algebra |
| ISSN号 | 1009-6124 |
| DOI | 10.1007/s11424-015-4085-1 |
| 英文摘要 | Some 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. |
| 资助项目 | National 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研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000379826000013 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/23224]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Huang Zhenyu |
| 作者单位 | 1.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 |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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