Results 1 to 10 of about 104 (91)
Primality deterministic and primality probabilistic tests
Statistica, 2007 In this paper the A. comments the importance of prime numbers in mathematics and in cryptography. He remembers the very important researches of Eulero, Fermat, Legen-re, Rieman and others scholarships.
Alfredo Rizzi
doaj +2 more sources
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
doaj +4 more sources
SIAM Journal on Computing, 1982 Whether an odd number m is prime can be decided on the knowledge of the image of the function $a \mapsto a^{(m - 1)/2} (m)$. As a consequence, an algorithm for testing primality is proposed (under the extended Riemann hypothesis) which is more efficient than ones proposed by Miller [Pros. 7th ACM Symp. Theory of Computing, 1975, pp.
James Finn, Karl J. Lieberherr
+14 more sources
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
A primality test for Kpⁿ⁺¹ numbers and a generalization of Safe primes and Sophie Germain primes [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we provide a generalization of Proth's theorem for integers of the form Kpⁿ⁺¹. In particular, a primality test that requires a modular exponentiation (with a proper base a) similar to that of Fermat's test without the computation of any ...
Abdelrahman Ramzy
doaj +1 more source
مجلة بغداد للعلوم, 2023 In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test.
Yahia Awad, Ramiz Hindi, Haissam Chehade
doaj +1 more source
A Practical Collision-Based Power Analysis on RSA Prime Generation and Its Countermeasure
IEEE Access, 2019 We analyze the security of RSA prime generation implemented on embedded devices by a practical power analysis attack. Unlike previous differential power analysis-based attack on primality tests of RSA prime generation exploiting the deterministic ...
Sangyub Lee +3 more
doaj +1 more source
Genefer: Programs for Finding Large Probable Generalized Fermat Primes
Journal of Open Research Software, 2015 Genefer is a suite of programs for performing Probable Primality (PRP) tests of Generalised Fermat numbers 'b'2'n'+1 (GFNs) using a Fermat test. Optimised implementations are available for modern CPUs using single instruction, multiple data (SIMD ...
Iain Arthur Bethune, Yves Gallot
doaj +1 more source
Partitions of numbers and the algebraic principle of Mersenne, Fermat and even perfect numbers [PDF]
Notes on Number Theory and Discrete MathematicsLet ρ be an odd prime greater than or equal to 11. In a previous work, starting from an M-cycle in a finite field 𝔽_ρ, it has been established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
doaj +1 more source