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On properties of the Klimov–Shamir generator of pseudorandom numbers
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S. V. Rykov
Veröffentlicht/Copyright:
26. Mai 2011
Abstract
The pseudorandom number generator (PRNG) based on the transformation
Fc(x) = x + (x2 ∨ c) (mod 2n)
was suggested by Klimov and Shamir in 2002. The function Fc(x) is transitive modulo 2n if and only if either c ≡ 5 (mod 8) or c≡ 7 (mod 8).
We consider properties of the distribution of the pairs (xi, Fc(xi)) for various c ∈ Z/2nZ and demonstrate that their statistical properties are unsatisfactory, most notably for c ≥ 2n/3.
We show that in the case n = 32, at most 9 distinct pairs (xi, Fc(xi)) are needed to find the value of c with probability P≥ 0.999.
Received: 2010-04-16
Published Online: 2011-05-26
Published in Print: 2011-April
© de Gruyter 2011
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Artikel in diesem Heft
- Reconstruction of a linear recurrence of maximal period over a Galois ring from its highest coordinate sequence
- On properties of the Klimov–Shamir generator of pseudorandom numbers
- On the relationship between diagnostic and checking tests of the read-once functions
- Boolean functions without prediction
- Investigation of the behaviour of triangulations on simplicial structures
- On irredundant complexes of faces in the unit cube
Artikel in diesem Heft
- Reconstruction of a linear recurrence of maximal period over a Galois ring from its highest coordinate sequence
- On properties of the Klimov–Shamir generator of pseudorandom numbers
- On the relationship between diagnostic and checking tests of the read-once functions
- Boolean functions without prediction
- Investigation of the behaviour of triangulations on simplicial structures
- On irredundant complexes of faces in the unit cube
