Abstract
In this paper we provide several theoretical evidences that the pseudo-random index j of RC4 is indeed not pseudo-random. First we show that in long term \(\Pr (j = i+1) = \frac{1}{N} - \frac{1}{N^2}\), instead of the random association \(\frac{1}{N}\) and this happens for the non-existence of the condition \(S[i] = 1 \text{ and } j = i+1\) that is mandatory for the non-existence of the Finney cycle. Further we also identify several results on non-existence of certain sequences of j. We further discuss the cycle structure in RC4 and provide several theoretical results. The results are supported by experimental observations with reduced versions of RC4. In this direction we point out that certain non-randomness in j is closely related to the short cycles in RC4.
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Chakraborty, C., Chakraborty, P., Maitra, S. (2019). RC4: Non-randomness in the Index j and Some Results on Its Cycles. In: Hao, F., Ruj, S., Sen Gupta, S. (eds) Progress in Cryptology – INDOCRYPT 2019. INDOCRYPT 2019. Lecture Notes in Computer Science(), vol 11898. Springer, Cham. https://doi.org/10.1007/978-3-030-35423-7_5
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DOI: https://doi.org/10.1007/978-3-030-35423-7_5
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