STATISTICAL ANALYSIS OF INTERNAL DYNAMICS OF ARC4 STREAMCIPHER

Abstract

The aim of this paper is to show, how the approach of nonlinear dynamics and statisticalphysics help to analyze pseudorandom number generators (PRNG) used incryptography. In fact, each PRNG is a highly nonlinear dynamical system, with itsinternal states, and may be analyzed as such.It is shown using PRNG of ARC4 stream cipher as example. A nonlinear phenomenon:1/fα dynamics was found in the new measure of complexity of the cipher: female count,a combinatorial quantity of direct cryptological bearing. We show that this measure canbe helpful in such tasks as measuring stationarity of internal dynamics of the PRNG andmeasuring of quality of initial condition (cryptographic key), which is statisticallyindependent from its entropy.