Results 1 to 10 of about 115 (102)
On Fibonacci and Lucas sequences modulo a prime and primality testing [PDF]
Arab Journal of Mathematical Sciences, 2018 We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p∣Fp−p5. We then discuss these results in the context of primality testing.
Dorin Andrica +2 more
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Recent Breakthrough in Primality Testing
Nonlinear Analysis, 2004 This paper briefly surveys the history of primality tests. The recently discovered deterministic polynomial time primality test due to Agrawal, Kayal and Saxena is presented and some improvements are shortly discussed.
R. Šleževičienė +2 more
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Information Processing Letters, 1979 The author presents the following simplification of G. L. Miller's primality criterion [J. Comput. Syst. Sci. 13, 300--317 (1976; Zbl 0349.68025)]. Assume that for every integer \(d\equiv 1\pmod 4\), which is either prime or the product of two primes, the \(L\)-function \(\sum_{k=1}^\infty (k\mid d) k^{-s}\) satisfies the generalized Riemann hypothesis,
exaly +4 more sources
Arab Journal of Basic and Applied Sciences, 2023 Lucas-Lehmer test is the current standard algorithm used for testing the primality of Mersenne numbers, but it may have limitations in terms of its efficiency and accuracy.
Moustafa Ibrahim
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A Simple Algorithm for Prime Factorization and Primality Testing
Journal of Mathematics, 2022 We propose a new simple and faster algorithm to factor numbers based on the nature of the prime numbers contained in such composite numbers. It is well known that every composite number has a unique representation as a product of prime numbers.
Kabenge Hamiss
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Optimized AKS Primality Testing: A Fluctuation Theory Perspective
Cryptography, 2019 The AKS algorithm is an important breakthrough in showing that primality testing of an integer can be done in polynomial time. In this paper, we study the optimization of its runtime. Namely, given a finite cardinality set of alphabets of a deterministic
Bhupendra Nath Tiwari +3 more
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Integer factoring and compositeness witnesses
Journal of Mathematical Cryptology, 2020 We describe a reduction of the problem of factorization of integers n ≤ x in polynomial-time (log x)M+O(1) to computing Euler’s totient function, with exceptions of at most xO(1/M) composite integers that cannot be factored at all, and at most x exp −cM ...
Pomykała Jacek, Radziejewski Maciej
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An RSA Scheme based on Improved AKS Primality Testing Algorithm
MATEC Web of Conferences, 2016 In applied cryptography, RSA is a typical asymmetric algorithm, which is used in electronic transaction and many other security scenarios. RSA needs to generate large random primes.
Wu Han Wei +4 more
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Solving some specific tasks by Euler's and Fermat's Little theorem
Ratio Mathematica, 2019 Euler's and Fermat's Little theorems have a great use in number theory. Euler's theorem is currently widely used in computer science and cryptography, as one of the current encryption methods is an exponential cipher based on the knowledge of number ...
Viliam Ďuriš
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