Cryptology ePrint Archive: Report 2016/1049

Randomized stopping times and provably secure pseudorandom permutation generators

Michal Kulis and Pawel Lorek and Filip Zagorski

Abstract: 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~\cite{Mironov2002} which analyses a card shuffle which models KSA of RC4. Mironov states that expected time till reaching uniform distribution is $2n H_n - n$ while we prove that $n H_n+ n$ 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.

Category / Keywords: foundations /

Original Publication (with minor differences): Proceedings of Mycrypt 2016: Paradigm-shifting Crypto

Date: received 7 Nov 2016

Contact author: filip zagorski at pwr edu pl

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Version: 20161107:193330 (All versions of this report)

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