An improvement over the GVW algorithm for inhomogeneous polynomial systems

doi:10.1016/j.ffa.2016.06.002

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	An improvement over the GVW algorithm for inhomogeneous polynomial systems
	Sun, Yao 1; Huang, Zhenyu 1; Wang, Dingkang2 ; Lin, Dongdai 1
刊名	FINITE FIELDS AND THEIR APPLICATIONS
	2016-09-01
卷号	41 页码:174-192
关键词	Grobner basis The GVW algorithm Signature-based algorithm Linear algebra Boolean polynomial ring
ISSN号	1071-5797
DOI	10.1016/j.ffa.2016.06.002
英文摘要	The GVW algorithm provides a new framework for computing Grobner bases efficiently. If the input system is not homogeneous, some J-pairs with larger signatures but lower degrees may be rejected by GVW's criteria, and instead, GVW has to compute some J-pairs with smaller signatures but higher degrees. Consequently, degrees of polynomials appearing during the computations may unnecessarily grow up higher, and hence, the total computations become more expensive. This phenomenon happens more frequently when the coefficient field is a finite field and the field polynomials are involved in the computations. In this paper, a variant of the GVW algorithm, called M-GVW, is proposed. The concept of mutant pairs is introduced to overcome the inconveniences brought by inhomogeneous inputs. In aspects of implementations, to obtain efficient implementations of GVW/M-GVW over boolean polynomial rings, we take advantages of the famous library M4RI. We propose a new rotating swap method of adapting efficient routines in M4RI to deal with the one-direction reductions in GVW/M-GVW. Our implementations are tested with many examples from Boolean polynomial rings, and the timings show M-GVW usually performs much better than the original GVW algorithm if mutant pairs are found. (C) 2016 Elsevier Inc. All rights reserved.
资助项目	National Key Basic Research Program of China[2013CB834203] ; National Natural Science Foundation of China[11301523] ; National Natural Science Foundation of China[61502485] ; Strategic Priority Research Program of the Chinese Academy of Sciences[XDA06010701] ; IEE's Research Project on Cryptography[Y4Z0061A02]
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000381062900012
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/23472]
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 100190, Peoples R China
推荐引用方式 GB/T 7714	Sun, Yao,Huang, Zhenyu,Wang, Dingkang,et al. An improvement over the GVW algorithm for inhomogeneous polynomial systems[J]. FINITE FIELDS AND THEIR APPLICATIONS,2016,41:174-192.
APA	Sun, Yao,Huang, Zhenyu,Wang, Dingkang,&Lin, Dongdai.(2016).An improvement over the GVW algorithm for inhomogeneous polynomial systems.FINITE FIELDS AND THEIR APPLICATIONS,41,174-192.
MLA	Sun, Yao,et al."An improvement over the GVW algorithm for inhomogeneous polynomial systems".FINITE FIELDS AND THEIR APPLICATIONS 41(2016):174-192.