Results 131 to 140 of about 12,326 (180)

Factorization of the Eighth Fermat Number

Mathematics of Computation, 1981
We describe a Monte Carlo factorization algorithm which was used to factorize the Fermat number F 8 = 2 256 + 1 {F_8} = {2^{256}} + 1 . Previously F 8
Brent, Richard P., Pollard, John M.
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Factors of Fermat Numbers

2002
The factors k2 n +1, k, n ∈ ℕ of Fermat numbers have been intensively studied by many authors, e.g., [Artjuhov], [Banlie], [Bosma], [Brent, 1982], [Brillhart, Lehmer, Selfridge], [Cormack, Williams], [Golomb, 1976], [Keller 1983, 1992], [Křižek, Chleboun, 1994, 1997], [Papademetrios], [Shorey, Stewart], [Williams, 1988]. In 1878, F.
Michal Křížek, Florian Luca, Lawrence Somer   +2 more
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Divisibility of Fermat Numbers

2002
In 1878, Edouard A. Lucas established a criterion concerning the general form of prime divisors of the Fermat numbers, namely, that every prime divisor p of F m, m > 1, satisfies the congruence (see, e.g., [Lucas, 1878b], [Dickson, p. 376]) .
Michal Křížek, Florian Luca, Lawrence Somer   +2 more
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Perfect numbers, Fermat numbers

2010
Number Theory is one of the most ancient and active branches of pure mathematics. It is mainly concerned with the properties of integers and rational numbers. In recent decades, number theoretic methods are also being used in several areas of applied mathematics, such as cryptography and coding theory.
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Generalizations of Fermat Numbers

2002
We will explore generalizations of Fermat numbers that share many of the same properties of the Fermat numbers; these properties were given in earlier chapters. We will also investigate other numbers such as the Cullen numbers, which bear some resemblance to the Fermat numbers.
Michal Křížek, Florian Luca, Lawrence Somer   +2 more
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Primality of Fermat Numbers

2002
Remark 5.1. Notice that the number is prime, but the numbers 23 + 1 and are composite (cf. Appendix A). This example shows that if 2 n prime, then need not be prime and vice versa (see [Sierpinski, 1970, Problem 141]).
Michal Křížek, Florian Luca, Lawrence Somer   +2 more
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Complex Convolutions via Fermat Number Transforms

IBM Journal of Research and Development, 1976
An approach is described for computing complex convolutions modulo a Fermat number. It is shown that this technique is particularly efficient when the complex convolution is computed by means of Fermat Number Transforms and leads to improved implementation of complex digital filters.
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Fermat Number Transform diffusion's analysis

2011 IEEE GCC Conference and Exhibition (GCC), 2011
The Fermat Number Transform (FNT) has distinctive features, making it attractive for use in the design of secure cryptosystems. Advantages of FNT include parameterization; by achieving variable block size and key size, sensitivity; element values change for any changes to the input, output or key elements.
M. F. Al-Gailani, S. Boussakta, J. Neasham   +2 more
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Fermat pseudoprime numbers

2013
The purpose of the Diploma thesis at hand is to provide a proper compendium on different types of Fermat pseudoprimes. The choice of this topic is motivated by its great significance in cryptography or more precisely in primality testing. Furthermore, standard literature in number theory and cryptography seldom deals extensively with numbers of that ...
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Basic Properties of Fermat Numbers

2002
First we present a few recurrence formulae for the Fermat numbers. Most of these can be found in the paper [Grytczuk] (see also [Schram]).
Michal Křížek, Florian Luca, Lawrence Somer   +2 more
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