Cryptology ePrint Archive: Report 2017/175

Analysis of Burn-in period for RC4 State Transition

Goutam Paul and Souvik Ray

Abstract: The internal state of RC4 stream cipher is a permutation over ${\mathbb Z}_N$ and its state transition is effectively a transposition or swapping of two elements. How the randomness of RC4 state evolves due to its state transitions has been studied for many years. As the number of swaps increases, the state comes closer to a uniform random permutation. We call the burn-in period of RC4 state transition as the number of swaps required to make the state very close to uniform random permutation under some suitably defined distance measure. Earlier, Mantin in his Master's thesis (2001) has performed an approximate analysis of the burn-in period. In this paper, we perform a rigorous analysis of the burn-in period and in the process derive the exact distribution of the RC4 state elements at any stage.

Category / Keywords: secret-key cryptography / Bias, Burn-in, Cryptography, Random Permutation, RC4, State transition, Stream cipher

Date: received 21 Feb 2017, last revised 21 Feb 2017

Contact author: goutam k paul at gmail com

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Version: 20170227:145049 (All versions of this report)

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