Abstract
In this paper we study a new class of dynamical systems generated by iterations of a class of multivariate permutation polynomial systems. Using the same techniques studied previously for other generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit stronger estimates than in the general case and thus can be of use for pseudorandom number generation. We also prove a nontrivial bound “on average” over all initial values \({\rm v} \epsilon \mathbb{F}_p^{m}\) on the discrepancy for pseudorandom vectors generated by these iterations.
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Ostafe, A. (2010). Pseudorandom Vector Sequences Derived from Triangular Polynomial Systems with Constant Multipliers. In: Hasan, M.A., Helleseth, T. (eds) Arithmetic of Finite Fields. WAIFI 2010. Lecture Notes in Computer Science, vol 6087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13797-6_5
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DOI: https://doi.org/10.1007/978-3-642-13797-6_5
Publisher Name: Springer, Berlin, Heidelberg
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