Results 141 to 150 of about 195 (180)
Some of the next articles are maybe not open access.
Related searches:
Related searches:
Russian Mathematics, 2022
This article studies a combined primality test for natural numbers, called \textit{L2 test}, by combining the Lucas test and the Fermat condition test. The efficiency and complexity of this test are also analyzed, and a methodology for identifying composite numbers that pass the L2 test (called L2 pseudoprimes) is presented.
Ishmukhametov, S. T. +3 more
openaire +1 more source
This article studies a combined primality test for natural numbers, called \textit{L2 test}, by combining the Lucas test and the Fermat condition test. The efficiency and complexity of this test are also analyzed, and a methodology for identifying composite numbers that pass the L2 test (called L2 pseudoprimes) is presented.
Ishmukhametov, S. T. +3 more
openaire +1 more source
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
, 2013 With the boom in information technology and the penetration of these technologies in an increasing number of areas, such as electronic business, many questions about security arise. Data in electronic form bring many benefits, but they are vulnerable to various abuses. Therefore, data need to be adequately protected.
Lynn Margaret Batten
exaly +3 more sources
Fooling Primality Tests on Smartcards
2020We analyse whether the smartcards of the JavaCard platform correctly validate primality of domain parameters. The work is inspired by Albrecht et al. [1], where the authors analysed many open-source libraries and constructed pseudoprimes fooling the primality testing functions.
Vladimir Sedlacek +2 more
openaire +2 more sources
ACM Communications in Computer Algebra, 2020
In 1879, Laisant-Beaujeux gave the following result without proof: If n is a prime, then [EQUATION] This paper provides proofs of the result of Laisant-Beaujeux in two cases explicitly: (1) If an integer of the form n = 4k + 1, k > 0 is prime, then ([EQUATION]) and (2) If an integer of the form n = 4k + 3, k ≥ 0 is prime, then ...
openaire +1 more source
In 1879, Laisant-Beaujeux gave the following result without proof: If n is a prime, then [EQUATION] This paper provides proofs of the result of Laisant-Beaujeux in two cases explicitly: (1) If an integer of the form n = 4k + 1, k > 0 is prime, then ([EQUATION]) and (2) If an integer of the form n = 4k + 3, k ≥ 0 is prime, then ...
openaire +1 more source
Pseudocubes and Primality Testing
2004The recent ideas of Agrawal, Kayal, and Saxena have produced a milestone in the area of deterministic primality testing. Unfortunately, their method, as well as their successors are mainly of theoretical interest, as they are much too slow for practical applications.
Pedro Berrizbeitia +2 more
openaire +1 more source
On a Modification of The Lucas Primality Test
Lobachevskii Journal of Mathematics, 2023Let \(F_n\) be the Fibonacci series defined by \(F_0 = 0\), \(F_1 = 1\), and \(F_{n+2} = F_n + F_{n+1}\). Set \(e(n) = (n/5)\), where \((\cdot/5)\) is the usual Legendre symbol. The classical Lucas primality test is based on the following result: If \(n > 5\), then \(F_{n-e(n)} \equiv 0 \pmod n\).
Ishmukhametov, Sh. +2 more
openaire +2 more sources
Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92, 1992
Rabin’s algorithm is commonly used in computer algebra systems and elsewhere for primality testing. This paper presents an experience with this in the Axiom* computer algebra system. As a result of this experience, we suggest certain strengthenings of the algorithm.
openaire +1 more source
Rabin’s algorithm is commonly used in computer algebra systems and elsewhere for primality testing. This paper presents an experience with this in the Axiom* computer algebra system. As a result of this experience, we suggest certain strengthenings of the algorithm.
openaire +1 more source