Article
Exponential Sums and Linear Complexity of Nonlinear Pseudorandom Number Generators With Polynomials of Small P-Weight Degree
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Abstract
For a class of polynomials f (X) of small p-weight degree over a finite field of characteristic p we improve the general bounds on exponential sums and linear complexity of nonlinear pseudorandom number generators defined by µn+1 = f (µn), n = 0, 1, . . . with some initial value µ0. This extends the class of polynomials where a nontrivial exponential sum bound is known. From the bound on exponential sums we derive discrepancy bounds for nonlinear pseudorandom vectors.
Keywords
Finite fields, pseudorandom numbers, discrepancy, exponential sums.
Citation
Ibeas, A. & Winterhof, A. (2010). Exponential sums and linear complexity of nonlinear pseudorandom number generators with polynomials of small p-weight degree. Uniform Distribution Theory, 5(1), 79–93.
A. Ibeas and A. Winterhof, “Exponential sums and linear complexity of nonlinear pseudorandom number generators with polynomials of small p-weight degree,” Uniform Distribution Theory, vol. 5, no. 1, pp. 79–93, 2010.
Ibeas A, Winterhof A. Exponential sums and linear complexity of nonlinear pseudorandom number generators with polynomials of small p-weight degree. Uniform Distribution Theory. 2010;5(1):79–93.
Ibeas, A. and Winterhof, A. (2010), ‘Exponential sums and linear complexity of nonlinear pseudorandom number generators with polynomials of small p-weight degree’, Uniform Distribution Theory, 5(1), pp. 79–93.
Ibeas, Alvar, and Arne Winterhof. “Exponential Sums and Linear Complexity of Nonlinear Pseudorandom Number Generators with Polynomials of Small P-weight Degree.” Uniform Distribution Theory, vol. 5, no. 1, 2010, pp. 79–93.
Ibeas, Alvar, and Arne Winterhof. “Exponential Sums and Linear Complexity of Nonlinear Pseudorandom Number Generators with Polynomials of Small P-weight Degree.” Uniform Distribution Theory 5, no. 1 (2010): 79–93.
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Published by: Engineering Journals
