Dynamical systems as the main instrument for the constructions of new quadratic families and their usage in cryptography

Vasyl Ustimenko, Aneta Wroblewska
2012 Annales UMCS Informatica  
Let K be a finite commutative ring and f = f (n) a bijective polynomial map f (n) of the Cartesian power K n onto itself of a small degree c and of a large order. Let f y be a multiple composition of f with itself in the group of all polynomial automorphisms, of free module K n . The discrete logarithm problem with the "pseudorandom" base f (n) (solve f y = b for y) is a hard task if n is "sufficiently large". We will use families of algebraic graphs defined over K and corresponding dynamical
more » ... ponding dynamical systems for the explicit constructions of such maps f (n) of a large order with c = 2 such that all nonidentical powers f y are quadratic polynomial maps. The above mentioned result is used in the cryptographical algorithms based on the maps f (n) -in the symbolic key exchange protocols and public keys algorithms.
doi:10.2478/v10065-012-0030-2 fatcat:uxqalhfbvfao7kgvuwht4dpjye