Titlebook: Cryptography and Computational Number Theory; Kwok-Yan Lam,Igor Shparlinski,Chaoping Xing Conference proceedings 2001 Springer Basel AG 20

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Counting the Number of Points on Affine Diagonal CurvesEvans and Williams [1] is to express the number of points in terms of generalized Jacobi sums, then to relate the Jacobi sums .(..,..) to cyclotomic numbers. In this article we present the direct elementary method for the number of points on the affine curves .. + .. = . over finite fields in terms

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Algorithms for Generating, Testing and Proving Primes: A Surveyf primality tests of theoretical or practical relevance, the focus is on criteria for practical use..We give a new model for sources producing prime numbers with biased distributions and use it for measuring the security of biases against unknown attacks (adapted solutions to the discrete logarithm

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The Hermite-Serret Algorithm and 122 + 332uares, given (or having already found) a square root ., say, of -1 modulo n. In brief, one applies the Euclidean algorithm to n and ., stopping at the first pair . and . of remainders that are smaller than . Then, lo! it happens that . = .. + ... Naturally, square roots of -1 properly different from

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