Results 21 to 30 of about 6,542 (225)
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 +1 more source
A faster pseudo-primality test [PDF]
, 2012 We propose a pseudo-primality test using cyclic extensions of $\mathbb Z/n \mathbb Z$. For every positive integer $k \leq \log n$, this test achieves the security of $k$ Miller-Rabin tests at the cost of $k^{1/2+o(1)}$ Miller-Rabin tests.Comment ...
C.M. Papadimitriou +15 more
core +9 more sources
On primality of Cartesian product of graphs [PDF]
Arab Journal of Mathematical SciencesPurposeThe present work focuses on the primality and the Cartesian product of graphs.Design/methodology/approachGiven a graph G, a subset M of V (G) is a module of G if, for a, b ∈ M and x ∈ V (G) \ M, xa ∈ E(G) if and only if xb ∈ E(G).
Nadia El Amri +2 more
doaj +1 more source
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
doaj +1 more source
Two Compact Incremental Prime Sieves [PDF]
, 2015 A prime sieve is an algorithm that finds the primes up to a bound $n$. We say that a prime sieve is incremental, if it can quickly determine if $n+1$ is prime after having found all primes up to $n$. We say a sieve is compact if it uses roughly $\sqrt{n}$
Sorenson, Jonathan P.
core +3 more sources
Constructing elliptic curves of prime order [PDF]
, 2007 We present a very efficient algorithm to construct an elliptic curve E and a finite field F such that the order of the point group E(F) is a given prime number N.
Broker, Reinier, Stevenhagen, Peter
core +3 more sources
Learned Primal-Dual Reconstruction [PDF]
IEEE Transactions on Medical Imaging, 2018 We propose the Learned Primal-Dual algorithm for tomographic reconstruction. The algorithm accounts for a (possibly non-linear) forward operator in a deep neural network by unrolling a proximal primal-dual optimization method, but where the proximal operators have been replaced with convolutional neural networks.
Jonas Adler, Ozan Oktem
openaire +3 more sources
Characterization of prime and composite numbers using the notion of successive sum of integers and the consequence in primality testing [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we give a characterization of primes and composite natural numbers using the notion of the sum of successive natural numbers. We prove essentially that an odd natural number N≥3 is prime if and only if the unique decomposition of N as a ...
Fateh Mustapha Dehmeche +2 more
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S-PRIMALITY DEGREE OF A NUMBER AND S-PRIME NUMBERS [PDF]
, 1999 Defining the S-Primality Degree of a Number, the 5-Prime Numbers, and make some considerations on ...
Burton, Emil
core +1 more source
Primality proving with Gauss and Jacobi sums
Journal of Telecommunications and Information Technology, 2004 This article presents a primality test known as APR (Adleman, Pomerance and Rumely) which was invented in 1980. It was later simplified and improved by Cohen and Lenstra.
Andrzej Chmielowiec
doaj +1 more source