发布求助
文献互助 智能选刊 最新文献

Groups Complexity Cryptology最新文献

筛选
英文 中文
Memory-saving computation of the pairing final exponentiation on BN curves BN曲线上配对最终幂的内存节省计算
Groups Complexity Cryptology Pub Date : 2016-05-01 DOI: 10.1515/gcc-2016-0006
S. Duquesne, Loubna Ghammam
{"title":"Memory-saving computation of the pairing final exponentiation on BN curves","authors":"S. Duquesne, Loubna Ghammam","doi":"10.1515/gcc-2016-0006","DOIUrl":"https://doi.org/10.1515/gcc-2016-0006","url":null,"abstract":"Abstract Tate pairing computation is made of two steps. The first one, the Miller loop, is an exponentiation in the group of points of an elliptic curve. The second one, the final exponentiation, is an exponentiation in the multiplicative group of a large finite field extension. In this paper, we describe and improve efficient methods for computing the hardest part of this second step for the most popular curves in pairing-based cryptography, namely Barreto–Naehrig curves. We present the methods given in the literature and their complexities. However, the necessary memory resources are not always given whereas it is an important constraint in restricted environments for practical implementations. Therefore, we determine the memory resources required by these known methods and we present new variants which require less memory resources (up to 37 %). Moreover, some of these new variants are providing algorithms which are also more efficient than the original ones.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"27 1","pages":"75 - 90"},"PeriodicalIF":0.0,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77759698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
The automorphism group of a finitely generated virtually abelian group 有限生成虚阿贝尔群的自同构群
Groups Complexity Cryptology Pub Date : 2016-05-01 DOI: 10.1515/gcc-2016-0007
B. Eick
{"title":"The automorphism group of a finitely generated virtually abelian group","authors":"B. Eick","doi":"10.1515/gcc-2016-0007","DOIUrl":"https://doi.org/10.1515/gcc-2016-0007","url":null,"abstract":"Abstract We describe a practical algorithm to compute the automorphism group of a finitely generated virtually abelian group. As application, we describe the automorphism groups of some small-dimensional crystallographic groups.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"100 1","pages":"35 - 45"},"PeriodicalIF":0.0,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79297509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On irreducible algebraic sets over linearly ordered semilattices 关于线性有序半格上的不可约代数集
Groups Complexity Cryptology Pub Date : 2016-01-15 DOI: 10.1515/gcc-2016-0014
A. Shevlyakov
{"title":"On irreducible algebraic sets over linearly ordered semilattices","authors":"A. Shevlyakov","doi":"10.1515/gcc-2016-0014","DOIUrl":"https://doi.org/10.1515/gcc-2016-0014","url":null,"abstract":"Abstract Equations over linearly ordered semilattices are studied. For any equation t ⁢ ( X ) = s ⁢ ( X ) ${t(X)=s(X)}$ we find irreducible components of its solution set and compute the average number of irreducible components of all equations in n variables.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"1 1","pages":"187 - 195"},"PeriodicalIF":0.0,"publicationDate":"2016-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77206902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A PTIME solution to the restricted conjugacy problem in generalized Heisenberg groups 广义Heisenberg群中受限共轭问题的PTIME解
Groups Complexity Cryptology Pub Date : 2016-01-01 DOI: 10.1515/gcc-2016-0003
Kenneth R. Blaney, Andrey Nikolaev
{"title":"A PTIME solution to the restricted conjugacy problem in generalized Heisenberg groups","authors":"Kenneth R. Blaney, Andrey Nikolaev","doi":"10.1515/gcc-2016-0003","DOIUrl":"https://doi.org/10.1515/gcc-2016-0003","url":null,"abstract":"Abstract We examine the Anshel–Anshel–Goldfeld key exchange protocol with a generalized Heisenberg group, Hm, as a platform. We show that subgroup-restricted simultaneous conjugacy search problem in Hm can be solved in quasi-quintic time, which allows the computation of the private keys of the parties.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"32 1","pages":"69 - 74"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73798441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Faster Ate pairing computation on Selmer's model of elliptic curves 椭圆曲线Selmer模型的快速配对计算
Groups Complexity Cryptology Pub Date : 2016-01-01 DOI: 10.1515/gcc-2016-0005
Emmanuel Fouotsa, Abdoul Aziz Ciss
{"title":"Faster Ate pairing computation on Selmer's model of elliptic curves","authors":"Emmanuel Fouotsa, Abdoul Aziz Ciss","doi":"10.1515/gcc-2016-0005","DOIUrl":"https://doi.org/10.1515/gcc-2016-0005","url":null,"abstract":"Abstract This paper revisits the computation of pairings on a model of elliptic curve called Selmer curves. We extend the work of Zhang, Wang, Wang and Ye [17] to the computation of other variants of the Tate pairing on this curve. Especially, we show that the Selmer model of an elliptic curve presents faster formulas for the computation of the Ate and optimal Ate pairings with respect to Weierstrass elliptic curves. We show how to parallelise the computation of these pairings and we obtained very fast results. We also present an example of optimal pairing on a pairing-friendly Selmer curve of embedding degree k = 12.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"48 1","pages":"55 - 67"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80606506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A parallel evolutionary approach to solving systems of equations in polycyclic groups 求解多环群方程组的平行进化方法
Groups Complexity Cryptology Pub Date : 2016-01-01 DOI: 10.1515/gcc-2016-0012
M. J. Craven, D. Robertz
{"title":"A parallel evolutionary approach to solving systems of equations in polycyclic groups","authors":"M. J. Craven, D. Robertz","doi":"10.1515/gcc-2016-0012","DOIUrl":"https://doi.org/10.1515/gcc-2016-0012","url":null,"abstract":"Abstract The Anshel–Anshel–Goldfeld (AAG) key exchange protocol is based upon the multiple conjugacy problem for a finitely-presented group. The hardness in breaking this protocol relies on the supposed difficulty in solving the corresponding equations for the conjugating element in the group. Two such protocols based on polycyclic groups as a platform were recently proposed and were shown to be resistant to length-based attack. In this article we propose a parallel evolutionary approach which runs on multicore high-performance architectures. The approach is shown to be more efficient than previous attempts to break these protocols, and also more successful. Comprehensive data of experiments run with a GAP implementation are provided and compared to the results of earlier length-based attacks. These demonstrate that the proposed platform is not as secure as first thought and also show that existing measures of cryptographic complexity are not optimal. A more accurate alternative measure is suggested. Finally, a linear algebra attack for one of the protocols is introduced.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"44 1","pages":"109 - 125"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75099513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Factoring multi-power RSA moduli with primes sharing least or most significant bits 质数共享最小有效位或最高有效位的多幂RSA模的分解
Groups Complexity Cryptology Pub Date : 2016-01-01 DOI: 10.1515/gcc-2016-0002
Omar Akchiche, O. Khadir
{"title":"Factoring multi-power RSA moduli with primes sharing least or most significant bits","authors":"Omar Akchiche, O. Khadir","doi":"10.1515/gcc-2016-0002","DOIUrl":"https://doi.org/10.1515/gcc-2016-0002","url":null,"abstract":"Abstract We study the factorization of a balanced multi-power RSA moduli N = prq when the unknown primes p and q share t least or most significant bits. We show that if t ≥ 1/(1+r)log p, then it is possible to compute the prime decomposition of N in polynomial time in log N. This result can be used to mount attacks against several cryptographic protocols that are based on the moduli N.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"27 1","pages":"47 - 54"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74168414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Computing discrete logarithms using 𝒪((log q)2) operations from {+,-,×,÷,&} 用{+，-，x，÷，&}的操作计算离散对数((log q)2)
Groups Complexity Cryptology Pub Date : 2016-01-01 DOI: 10.1515/gcc-2016-0009
C. Schridde
{"title":"Computing discrete logarithms using 𝒪((log q)2) operations from {+,-,×,÷,&}","authors":"C. Schridde","doi":"10.1515/gcc-2016-0009","DOIUrl":"https://doi.org/10.1515/gcc-2016-0009","url":null,"abstract":"Abstract Given a computational model with registers of unlimited size that is equipped with the set { + , - , × , ÷ , & } = : 𝖮𝖯 ${{+,-,times,div,&}=:mathsf{OP}}$ of unit cost operations, and given a safe prime number q, we present the first explicit algorithm that computes discrete logarithms in ℤ q * ${mathbb{Z}^{*}_{q}}$ to a base g using only 𝒪 ⁢ ( ( log ⁡ q ) 2 ) ${mathcal{O}((log q)^{2})}$ operations from 𝖮𝖯 ${mathsf{OP}}$ . For a random n-bit prime number q, the algorithm is successful as long as the subgroup of ℤ q * ${mathbb{Z}^{*}_{q}}$ generated by g and the subgroup generated by the element p = 2 ⌊ log 2 ⁡ ( q ) ⌋ ${p=2^{lfloorlog_{2}(q)rfloor}}$ share a subgroup of size at least 2 ( 1 - 𝒪 ⁢ ( log ⁡ n / n ) ) ⁢ n ${2^{(1-mathcal{O}(log n/n))n}}$ .","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"1 1","pages":"107 - 91"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76714815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Authenticated commutator key agreement protocol 认证换向器密钥协议协议
Groups Complexity Cryptology Pub Date : 2016-01-01 DOI: 10.1515/gcc-2016-0011
A. Ushakov
{"title":"Authenticated commutator key agreement protocol","authors":"A. Ushakov","doi":"10.1515/gcc-2016-0011","DOIUrl":"https://doi.org/10.1515/gcc-2016-0011","url":null,"abstract":"Abstract The original commutator key agreement (CKA) protocol is a two party anonymous key agreement protocol invented by I. Anshel, M. Anshel and D. Goldfeld. In this paper we propose a modification of the CKA protocol with mutual authentication without introducing any additional computational assumptions. In addition, we propose a new zero-knowledge Feige–Fiat–Shamir-type authentication protocol.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"89 1","pages":"127 - 133"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79392315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Generic case complexity of the Graph Isomorphism Problem 图同构问题的一般情形复杂度
Groups Complexity Cryptology Pub Date : 2016-01-01 DOI: 10.1515/gcc-2016-0008
G. A. Noskov, A. Rybalov
{"title":"Generic case complexity of the Graph Isomorphism Problem","authors":"G. A. Noskov, A. Rybalov","doi":"10.1515/gcc-2016-0008","DOIUrl":"https://doi.org/10.1515/gcc-2016-0008","url":null,"abstract":"Abstract The edge test is a partial algorithm for the Graph Isomorphism Problem based on comparison the number of edges. We perform a probabilistic analysis of the efficiency of the edge test. With the binomial distribution B(n,p) on the set of inputs, we estimate the asymptotic failure probability of the edge test depending on the rate of decay of parameter p. In particular, if p ≤ 1/2, np → λ > 0, then the asymptotic failure probability is nonzero, so that the edge test does not solve generically the Graph Isomorphism Problem. On the other hand, if p ≤ 1/2, np → ∞, then the failure set is negligible and the edge test generically solves the Graph Isomorphism Problem in polynomial time.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"4 1","pages":"20 - 9"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80330258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信