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Ledoan, Robert J. Miller, Hugh L.

Montgomery, Melvyn B. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Mathematics Number Theory and Discrete Mathematics. Free Preview. Buy eBook.

Buy Hardcover. Buy Softcover. FAQ Policy. About this book This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field.

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On Conjectures of T. Combinatorial number theory : proceedings of the "Integers Conference " in celebration of the 70th birthday of Ronald Graham, Carrollton, Georgia, USA, October , by Bruce M Landman 12 editions published between and in English and held by 72 WorldCat member libraries worldwide This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference ", an international conference in combinatorial number theory.

The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics. Cryptology and computational number theory : [lecture notes prepared for the American Mathematical Society Short Course Cryptology and Computational Number Theory, held in Boulder, Colorado, August , ] Book 1 edition published in in English and held by 23 WorldCat member libraries worldwide.

Prime numbers : a computational persprective by Richard E Crandall Book 1 edition published in in English and held by 20 WorldCat member libraries worldwide. Advances in Cryptology - Crypto '87 by Carl Pomerance 1 edition published in in English and held by 19 WorldCat member libraries worldwide Zero-knowledge interactive proofsystems are a new technique which can be used as a cryptographic tool for designing provably secure protocols.

Goldwasser, Micali, and Rackoff originally suggested this technique for controlling the knowledge released in an interactive proof of membership in a language, and for classification of languages [19].

Pomerance, Mathematika 26 , — Dilworth, K. Luca, and C. See also this. Pokhozhaev, V. Lapidus and C. Doesn't matter if it's a 10th birthday, 18th birthday, 21st

In this approach, knowledge is defined in terms of complexity to convey knowledge if it gives a computational advantage to the receiver, theory, and a message is said for example by giving him the result of an intractable computation. The formal model of interacting machines is described in [19, 15, A proof-system for a language L is an interactive protocol by which one user, the prover, attempts to convince another user, the verifier, that a given input x is in L. We assume that the verifier is a probabilistic machine which is limited to expected polynomial-time computation, while the prover is an unlimited probabilistic machine.

In cryptographic applications the prover has some trapdoor information, or knows the cleartext of a publicly known ciphertext A correct proof-system must have the following properties: If XE L, the prover will convince the verifier to accept the pmf with very high probability. If XP L no prover, no matter what program it follows, is able to convince the verifier to accept the proof, except with vanishingly small probability.

Prime Numbers : a Computational Perspective by Richard E Crandall 2 editions published in in Undetermined and English and held by 13 WorldCat member libraries worldwide Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more.

The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added. Though he publishes in quantum physics, biology, mathematics, and chemistry, and holds various engineering patents, his primary interest is interdisciplinary scientific computation.

Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for expository mathematical writing. He is currently a mathematics professor at Dartmouth College, having previously been at the University of Georgia and Bell Labs. A popular lecturer, he is well known for his research in computational number theory, his efforts having produced important algorithms now in use.

Philippe Michel - Some applications of trace functions to analytic number theory

From the reviews of the first edition: "Destined to become a definitive textbook conveying the most modern computational ideas about prime numbers and factoring, this book will stand as an excellent reference for this kind of computation, and thus be of interest to both educators and researchers. Prime Numbers is a welcome addition to the literature of number theory--comprehensive, up-to-date and written with style.

Crandall and Pomerance have written a terrific book. Cryptology and computational number theory Book 1 edition published in in English and held by 9 WorldCat member libraries worldwide.

Average case error estimates for the strong probable prime test by I. Sosu zensho : Keisan karano apurochi by Richard E Crandall Book 2 editions published in in Japanese and held by 3 WorldCat member libraries worldwide. A pipe-line architecture for factoring large integers with the quadratic sieve algorithm by Carl Pomerance Book 1 edition published in in English and held by 1 WorldCat member library worldwide. The smallest n-uniform hypergraph with positive discrepancy by Noga Alon Book 1 edition published in in English and held by 1 WorldCat member library worldwide.