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Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/202794
Description: We give a survey of a variety of recent results about the distribution and some geometric properties of points (x, y) on modular hyperbolas xy ≡ a (mod m). We also outline a very diverse range of appl ... More
Reviewed: Reviewed
Date: 2005
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/80598
Description: We show that the elliptic curve analogue of the linear congruential generator produces sequences with high linear complexity and good multidimensional distribution.
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332390
Description: 10 page(s)
Reviewed: Reviewed
Date: 2000
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/118576
Description: One of the long-standing open questions in the theory of parallel computation is the parallel complexity of the integer gcd and related problems, such as modular inversion. We present a lower bound Ω ... More
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Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/271249
Description: We show that for any integers a and m with m ≥ 1 and gcd(a,m) = 1, there is a solution to the congruence pr ≡ a (modm) where p is prime, r is a product of at most k = 17 prime factors and p, r ≤ m. Th ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/18914
Description: Nonlinear congruential pseudorandom number generators can have unexpectedly short periods. Shamir and Tsaban introduced the class of counter-dependent generators which admit much longer periods. In th ... More
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195130
Description: We use new bounds of double exponential sums with ratios of integers from prescribed intervals to get an asymptotic formula for the number of solutions to congruences [equation presented here], with v ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20113
Description: Let Fp be a finite field of p elements, where p is prime. The bit security of the Diffie-Hellman function over subgroups of F*p and of an elliptic curve over Fp, is considered. It is shown that if the ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/7831
Description: We obtain an upper bound on exponential sums of a new type with linear recurrence sequences. We apply this bound to estimate the Fourier coefficients, and thus the nonlinearity, of a Boolean function ... More
Reviewed: Reviewed
Date: 2003
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/79990
Description: 17 page(s)
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130407
Description: Given two relatively prime positive integers m < n we consider the smallest positive solution (x0, y0) to the equation mx - ny = 1. E. I. Dinaburg and Y. G. Sinai have used continued fractions to show ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/9952
Description: The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present a new bound on the s-dimensional ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197843
Description: We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form [x,x+x¹/²] contains an integral multiple m²r ∈ [x,x+x¹/²] of a perfect square m² with an integer m > x⁰ ... More
Reviewed: Reviewed
Date: 2005
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/146589
Description: 8 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/133006
Description: We show how to accelerate the subset sum pseudorandom number generator with arbitrary weights. Some special choices of weights speed up the naive usage of this generator without losing the property of ... More
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Reviewed: Reviewed