Randomized Stopping Times And Provably Secure Pseudorandom Permutation Generators

Conventionally, key-scheduling algorithm (KSA) of a cryptographic scheme runs for predefined number of steps. We suggest a different approach by utilization of randomized stopping rules to generate permutations which are indistinguishable from uniform ones. We explain that if the stopping time of such a shuffle is a Strong Stationary Time and bits of the secret key are not reused then these algorithms are immune against timing attacks.We also revisit the well known paper of Mironov [15] which analyses a card shuffle which models KSA of RC4. Mironov states that expected time till reaching uniform distribution is 2nH(n) - n while we prove that nH(n) + n steps are enough (by finding a new strong stationary time for the shuffle).Nevertheless, both cases require O(n log(2) n) bits of randomness while one can replace the shuffle used in RC4 (and in Spritz) with a better shuffle which is optimal and needs only O(n log n) bits.