检索结果-内蒙古大学图书馆

MATHEMATICS OF COMPUTATION 2023年第342期92卷 1779-1790页

作者： Chen, Qiong Wu, Qiang Southwest Univ China Dept Math 2 Tiansheng Rd Chongqing 400715 Peoples R China

In this paper, a new method to compute lower and upper bounds for Salem numbers with a given trace and a given degree is given. With this method, it is proven that the smallest trace of Salem numbers of degree 22 is -1. Further, new lower bounds for degree of Salem numbers with minimal trace -5 and -6 are given. All Salem numbers of trace -2 and degree 24, 26 are given. This includes 7 additional Salem numbers of degree 26 beyond what was previously known. The auxiliary functions related to Chebyshev polynomials, which are adapted to Salem number, are used in this work.

关键词： Salem number Chebyshev polynomial explicit auxiliary function integer transfinite diameter semi-infinite linear programming lll algorithm

来源：评论

学校读者我要写书评

暂无评论

THE TRACE PROBLEM FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS

引用

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY 2011年第3期90卷 341-354页

作者： Liang, Yanhua Wu, Qiang SW Univ China Dept Math Chongqing 400715 Peoples R China

Let a be a totally positive algebraic integer of degree d >= 2 and alpha(1) = alpha, alpha(2), ... alpha(d), be all its conjugates. We use explicit auxiliary functions to improve the known lower bounds of S-k/d, where S-k = Sigma(d)(i=1) alpha(k)(i) and k = 1, 2, 3. These improvements have consequences for the search of Salem numbers with negative traces.

关键词： absolute trace totally positive algebraic integer Salem number explicit auxiliary function semi-infinite linear programming lll algorithm

来源：评论

学校读者我要写书评

暂无评论

Revisiting Modular Inversion Hidden Number Problem and Its Applications

引用

IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第8期69卷 5337-5356页

作者： Xu, Jun Sarkar, Santanu Hu, Lei Wang, Huaxiong Pan, Yanbin Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100085 Peoples R China Univ Chinese Acad Sci Sch Cyber Secur Beijing 100049 Peoples R China Indian Inst Technol Madras Chennai 600036 India Nanyang Technol Univ Sch Phys & Math Sci Div Math Sci Singapore 637371 Singapore Chinese Acad Sci Acad Math & Syst Sci Key Lab Math Mechanizat NCMIS Beijing 100190 Peoples R China

The Modular Inversion Hidden Number Problem (MIHNP), which was proposed at Asiacrypt 2001 by Boneh, Halevi, and Howgrave-Graham, is summarized as follows: Assume that the delta most significant bits of z are denoted by MSB delta(z). The goal is to retrieve the hidden number alpha is an element of Z(p) given many samples (t(i), MSB delta((alpha + t(i))(-1) mod p)) for random t(i) is an element of Z(p). MIHNP is a significant subset of Hidden Number Problems. Eichenauer and Lehn introduced the Inversive Congruential Generator (ICG) in 1986. It is basically characterized as follows: For iterated relations v(i+1) = (av(i)(-1) + b) mod p with a secret seed v(0) is an element of Z(p), each iteration produces MSB delta(v(i)+1) where i >= 0. The ICG family of pseudorandom number generators is a significant subclass of number-theoretic pseudorandom number generators. Sakai-Kasahara scheme is an identity-based encryption (IBE) system proposed by Sakai and Kasahara. It is one of the few commercially implemented identity-based encryption schemes. We explore the Coppersmith approach for solving a class of modular polynomial equations, which is derived from the recovery issue for the hidden number alpha in MIHNP and the secret seed v(0) in ICG, respectively. Take a positive integer n = d(3+o(1)) for some positive integer constant d. We propose a heuristic technique for recovering the hidden number a or secret seed v(0) with a probability close to 1 when delta/log(2) p > 1\d+1 + o(1\d). The attack's total time complexity is polynomial in the order of log(2) p, with the complexity of the lll algorithm increasing as d(O)(d) and the complexity of the Grobner basis computation increasing as d(O)(n). When d > 2, this asymptotic bound surpasses the asymptotic bound delta/log(2) p > 1\3 established by Boneh, Halevi, and Howgrave-Graham at Asiacrypt 2001. This is the first time a more precise constraint for solving MIHNP is established, implying that the claim that MIHNP is difficult is v

关键词： Modular inversion hidden number problem inversive congruential generator signature schemes lattice lll algorithm coppersmith technique

来源：评论

学校读者我要写书评

暂无评论

TOTALLY POSITIVE ALGEBRAIC INTEGERS WITH SMALL TRACE

引用

MATHEMATICS OF COMPUTATION 2021年第331期90卷 2317-2332页

作者： Wang, Cong Wu, Jie Wu, Qiang Southwest Univ China Dept Math 2 Tiansheng Rd Chongqing 400715 Peoples R China Univ Paris Est Creteil CNRS UMR 8050 Lab Anal & Math Appl 61 Ave Gen Gaulle F-94010 Creteil France

The "Schur-Siegel-Smyth trace problem" is a famous open problem that has existed for nearly 100 years. To study this problem with the known methods, we need to find all totally positive algebraic integers with small trace. In this work, on the basis of the classical algorithm, we construct a new type of explicit auxiliary functions related to Chebyshev polynomials to give better bounds for Sk, and reduce sharply the computing time. We are then able to push the computation to degree 15 and prove that there is no such totally positive algebraic integer with absolute trace 1.8. As an application, we improve the lower bound for the absolute trace of totally positive algebraic integers to 1.793145 . . . .

关键词： Absolute trace totally positive algebraic integers Chebyshev polynomial explicit auxiliary function semi-infinite linear programming lll algorithm

来源：评论

学校读者我要写书评

暂无评论

Some bounds and limits in the theory of Riemann's zeta function

引用

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2012年第1期396卷 199-214页

作者： Arias de Reyna, Juan van de Lune, Jan Univ Seville Fac Matemat E-41080 Seville Spain CWI NL-1009 AB Amsterdam Netherlands

For any real a > 0 we determine the supremum of the real sigma such that zeta(sigma + it) = a for some real t. For 0 1 the results turn out to be quite different. We also determine the supremum E of the real parts... 详细信息

For any real a > 0 we determine the supremum of the real sigma such that zeta(sigma + it) = a for some real t. For 0 < a < 1, a = 1, and a > 1 the results turn out to be quite different. We also determine the supremum E of the real parts of the 'turning points', that is points sigma + it where a curve lm zeta(sigma + it) = 0 has a vertical tangent. This supremum E (also considered by Titchmarsh) coincides with the supremum of the real sigma such that zeta'(sigma + it) = 0 for some real t. We find a surprising connection between the three indicated problems: zeta(s) = 1, zeta'(s) = 0 and turning points of zeta(s). The almost extremal values for these three problems appear to be located at approximately the same height. (C) 2012 Elsevier Inc. All right reserved.

关键词： Zeta function lll algorithm Extreme values

来源：评论

学校读者我要写书评

暂无评论

Cryptanalysis of RSA for a special case with d>e

引用

Science in China(Series F) 2009年第4期52卷 609-616页

作者： LUO Ping ZHOU HaiJian WANG DaoShun DAI YiQi Tsinghua National Laboratory for Information Science and Technology (TNlist) Department of Computer Science and TechnologyTsinghua University Beijing 100084 China

In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can perform cryptanalytic attacks based on the lll lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee＇s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.

关键词： RSA cryptanalysis lattice basis reduction lll algorithm

来源：评论

学校读者我要写书评

暂无评论

A new lower bound for the football pool problem for six matches

引用

JOURNAL OF COMBINATORIAL THEORY SERIES A 2002年第1期99卷 175-179页

作者： Östergård, PRJ Wassermann, A Helsinki Univ Technol Dept Comp Sci & Engn Helsinki 02015 Finland

In the football pool problem one wants to minimize the cardinality of a tertiary code, C subset of or equal to F-3(n), with covering radius one, and the size of a minimum code is denoted by a,. The smallest unsettled case is 63 less than or equal to sigma(b) less than or equal to 73, The lower bound is here improved to 65 in a coordinate-by-coordinate backtrack search using the lll algorithm and complete equivalence checking of subcodes. (C) 2002 Elsevier Science (USA).

关键词： covering radius football pool problem lll algorithm ternary code

来源：评论

学校读者我要写书评

暂无评论

The Mahler measure and its areal analog for totally positive algebraic integers

引用

JOURNAL OF NUMBER THEORY 2015年 151卷 211-222页

作者： Flammang, V. Univ Lorraine Dept Math UMR CNRS 7502 IECLUFR MIM F-57045 Metz 01 France

Using the method of explicit auxiliary functions, we first improve the known lower bounds of the absolute Mahler measure of totally positive algebraic integers. In 2008, I. Pritsker defined a natural areal analog of the Mahler measure that we call the Pritsker measure. We study the spectrum of the absolute Pritsker measure for totally positive algebraic integers and find the four smallest points. Finally, we give inequalities involving the Mahler measure and the Pritsker measure of totally positive algebraic integers. The polynomials involved in the auxiliary functions are found by our recursive algorithm. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Mahler measure Totally positive algebraic integers Explicit auxiliary functions lll algorithm

来源：评论

学校读者我要写书评

暂无评论

Small CRT-Exponent RSA Revisited 36th

Small CRT-Exponent RSA Revisited

引用

36th Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT)

作者： Takayasu, Atsushi Lu, Yao Peng, Liqiang Univ Tokyo Tokyo Japan Natl Inst Adv Ind Sci & Technol Tokyo Japan Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing Peoples R China

ISBN: (纸本)9783319566146;9783319566139

SinceMay (Crypto'02) revealed the vulnerability of the small CRT-exponent RSA using Coppersmith's lattice-based method, several papers have studied the problem and two major improvements have been made. Bleichenbacher and May (PKC'06) proposed an attack for small d(q) when the prime factor p is significantly smaller than the other prime factor q;the attack works for p < N-0.468. Jochemsz and May (Crypto'07) proposed an attack for small d(p) and d(q) where the prime factors p and q are balanced;the attack works for d(p), d(q) < N-0.073. Even after a decade has passed since their proposals, the above two attacks are still considered to be the state-of-the-art, and no improvements have been made thus far. A novel technique seems to be required for further improvements since the attacks have been studied with all the applicable techniques for Coppersmith's methods proposed by Durfee-Nguyen (Asiacrypt'00), Jochemsz-May (Asiacrypt'06), and Herrmann-May (Asiacrypt'09, PKC'10). In this paper, we propose two improved attacks on the small CRT-exponent RSA: a small d(q) attack for p < N-0.5 (an improvement of Bleichenbacher-May's) and a small dp and d(q) attack for d(p), d(q) < N-0.091 (an improvement of Jochemsz-May's). We use Coppersmith's lattice-based method to solve modular equations and obtain the improvements from a novel lattice construction by exploiting useful algebraic structures of the CRT-RSA key generation. We explicitly show proofs of our attacks and verify the validities by computer experiments. In addition to the two main attacks, we propose small d(q) attacks on several variants of RSA.

关键词： CRT-RSA Cryptanalysis Coppersmith's method Lattices lll algorithm

来源：评论

学校读者我要写书评

暂无评论

A New Class of Weak Encryption Exponents in RSA

引用

9th Annual International Conference on Cryptology in India

作者： Maitra, Subhamoy Sarkar, Santanu Indian Stat Inst Kolkata 700108 India

Consider RSA with N = pq, q 0 is arbitrarily small for suitably large N.

ISBN: (纸本)9783540897538

Consider RSA with N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. We concentrate on the cases when e(= N-alpha) satisfies eX-ZY = 1, given vertical bar N-Z vertical bar = N-tau. Using the idea of Boneh and Durfee (Eurocrypt 1999, IEEE-IT 2000) we show that the lll algorithm can be efficiently applied to get Z when vertical bar Y vertical bar = N-gamma and gamma < 4 alpha tau (1/4 tau + 1/12 alpha - root(1/4 tau + 1/12 alpha)(2) + 1/2 alpha tau (1/12 + tau/24 alpha - alpha/8 tau)). This idea substantially extends the class of weak keys presented by Nitaj (Africacrypt 2008) when Z = psi(p,q,u,v) = (p - u)(q - v). Further, we consider Z = psi(p, q, u, v) = N - pu - v to provide a new class of weak keys in RSA. This idea does not require any kind of factorization as used in Nitaj's work. A very conservative estimate for the number of such weak exponents is N0.75-epsilon, where epsilon > 0 is arbitrarily small for suitably large N.

关键词： Cryptanalysis Factorization Lattice lll algorithm

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：