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Multivariate permutation polynomial systems and nonlinear pseudorandom number generators
 FINITE FIELDS AND THEIR APPL
, 2009
"... In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques studied previously for inversive generators, we bound exponenti ..."
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In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques studied previously for inversive generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates “on average” over all initial values v ∈ F m+1 p than in the general case and thus can be of use for pseudorandom number generation.
Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators’, Submitted
, 2012
"... Abstract. We present several general results that show how algebraic dynamical systems with a slow degree growth and also rational automorphisms can be used to construct stronger pseudorandom number generators. We then give several concrete constructions that illustrate the applicability of these ..."
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Abstract. We present several general results that show how algebraic dynamical systems with a slow degree growth and also rational automorphisms can be used to construct stronger pseudorandom number generators. We then give several concrete constructions that illustrate the applicability of these general results. 1.
Open Problems on Exponential and Character Sums
, 2010
"... This is a collection of mostly unrelated open questions, at various levels of difficulty, related to exponential and multiplicative character sums. One may certainly notice a large proportion of selfreferences in the bibliography. By no means should this be considered as an indication of anything e ..."
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This is a collection of mostly unrelated open questions, at various levels of difficulty, related to exponential and multiplicative character sums. One may certainly notice a large proportion of selfreferences in the bibliography. By no means should this be considered as an indication of anything else than
COLLISIONS IN COMPOSITIONS OF TRIANGULAR POLYNOMIAL SYSTEMS AND HASH FUNCTIONS
"... Abstract. We study collisions in compositions of triangular polynomial systems with two favourable effects under iterations: polynomial degree growth or sparse representation. We construct classes of such polynomial systems that do not have collisions. This property makes them suitable for the co ..."
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Abstract. We study collisions in compositions of triangular polynomial systems with two favourable effects under iterations: polynomial degree growth or sparse representation. We construct classes of such polynomial systems that do not have collisions. This property makes them suitable for the construction of a recently proposed hash function. We also give estimates for the number of collisions in the hash function using these systems. 1.