The Rc4 Key Expansion Algorithm Is Not Fixed Points Analysis

The probabilities of the state transitions of the initial value S₀in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.In the first chapter, at first we introduce the research of Finney Mantin and Shamir, then we describe the key extending algorithm of RC4, we use a kind of bistochastic matrices to describe the probabilities of the state transitions of initial value S table of RC4.In the second chapter, we give a computational formula for such bistochastic matrices, by which we prove that the limiting value of mathematical expectation of the number of fixed points in the key extended algorithm of RC4 is about 0.896362 which implies that the key extending algorithm of RC4 is imperfect.