Spectral properties of a linear congruent generator in special cases
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A. S. Rybakov
In this paper for the linear congruent generator
zN + 1 = G (zN), N = 1,2, ... ,
where G(x) = λx + c (mod W), W = pF, p is a prime number, we find a non-trivial lower bound for the least non-zero wave number eL(λ), the fundamental characteristic introduced in the spectral test to check for randomness on the base of analysis of the frequence of occurrences of L-tuples (t1, ... ,tL) in the sequence (zN).
The lower bound obtained is of the form W1/L– δ, where δ is some variable explicitly depending on parameters which determine the factor λ. Under an appropriate choice of the parameters, δ can be made as small as desired. The factor 1/L cannot be changed for a greater one. Such bounds are necessary in studying classes of multipliers that pass the spectral test.
Copyright 2004, Walter de Gruyter
Articles in the same Issue
- On the number of closure-type mappings
- Spectral properties of a linear congruent generator in special cases
- On the key space of the McEliece cryptosystem based on binary Reed–Muller codes
- On the complexity of polarised polynomials of multi-valued logic functions in one variable
- Simulation of circuits of functional elements by the universal Turing machine
- Implementation of Markov chains over Galois fields
- On solving automaton equations
- Boundaries of random triangulation of a disk
- On the accuracy of approximation in the Poisson limit theorem
Articles in the same Issue
- On the number of closure-type mappings
- Spectral properties of a linear congruent generator in special cases
- On the key space of the McEliece cryptosystem based on binary Reed–Muller codes
- On the complexity of polarised polynomials of multi-valued logic functions in one variable
- Simulation of circuits of functional elements by the universal Turing machine
- Implementation of Markov chains over Galois fields
- On solving automaton equations
- Boundaries of random triangulation of a disk
- On the accuracy of approximation in the Poisson limit theorem
