Results 41 to 50 of about 391,497 (318)
Factorization of big integer and the security of RSA
网络与信息安全学报, 2017 Three kinds of methods for integer factorization were proposed and the security of RSA was demarcated.RSA is a well-known cryptographic algorithm,using the analysis result of those methods.Through the work,readers could easily realize that if merely ...
Yan-bing REN
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Cryptography, 2023 This article proposes a new method to inject backdoors in RSA (the public-key cryptosystem invented by Rivest, Shamir, and Adleman) and other cryptographic primitives based on the integer factorization problem for balanced semi-primes.
Marco Cesati
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Linear Algebra and its Applications, 1991 AbstractLet A be an m-by-n integer matrix and r = rank(A). A necessary and sufficient condition is given for A to have an integer LU-factorization, and a modification of Gaussian elimination is given for finding such factorizations when the first r leading principal minors are nonzero.
Frank J. Hall, Jean H. Bevis
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Mersenne version of Brocard-Ramanujan equation
Journal of New Results in Science, 2023 In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one of the interesting and still open problems of Diophantine analysis.
Ayşe Nalli, Seyran İbrahimov
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Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography
Journal of Applied Mathematics, 2014 To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over
Lize Gu, Shihui Zheng
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A Practical Analysis of the Fermat Factorization and Pollard Rho Method for Factoring Integers
Lontar Komputer, 2021 The development of public-key cryptography generation using the factoring method is very important in practical cryptography applications. In cryptographic applications, the urgency of factoring is very risky because factoring can crack public and ...
Aminudin Aminudin, Eko Budi Cahyono
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On factoring of unlimited integers
Journal of Logic and Analysis, 2020 Abdelmadjid Boudaoud asked whether every unlimited integer is a sum of a limited integer and a product of two unlimited integers. Assuming Dickson's conjecture, the answer is negative.
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On the number of prime factors of an integer
Duke Mathematical Journal, 1988 The authors prove the remarkable asymptotic formula \[ (1)\quad \pi (x,k)=\frac{\rho^{-k} x^{\alpha} F(\rho,\alpha)}{(\log x) kw(k) w(\rho)}(1+O(1/L)), \] which is uniform for \(x\geq x_ 0\), \(1\leq k\ll (\log x)/(\log \log x)^ 2\), where \(\pi\) (x,k) denotes the number of integers \(1\leq n\leq x\) which have exactly k distinct prime factors ...
Hildebrand, Adolf, Tenenbaum, Gérald
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A factorization formula for power series [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Given an odd prime p, we give an explicit factorization over the ring of formal power series with integer coefficients for certain reducible polynomials whose constant term is of the form $p^w$ with $w>1$.
Daniel Birmajer +2 more
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Hardware Acceleration of Large-Scale CMOS Invertible Logic Based on Sparse Hamiltonian Matrices
IEEE Open Journal of Circuits and Systems, 2021 Invertible logic has been recently presented that can realize bidirectional computing based on Hamiltonians for solving several critical issues, such as integer factorization and training neural networks.
Naoya Onizawa +2 more
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