Analysis of Burn-in period for RC4 State Transition.
Goutam Paul, Souvik Ray · IACR Cryptology ePrint Archive · 2017
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 define 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) 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.