Re: Simple RC4 variant

Anonymous (nobody@replay.com)
Sun, 4 Apr 1999 22:20:44 +0200 (CEST)

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Keith asks:
> In the first line of RC4:
> i = (i + 1) mod 256
> 'i' cycles through 256 values.
>
> If we add in an odd number, 0 < r < 256, ie:
> i = (i + r) mod 256
> 'i' also cycles through 256 values - but in a different sequence.
>
> Does these new 127 variants of RC4 behave in a similar way with regard to
> cycle length and precautions regarding the key set-up?

Probably so. Consider setting r = 3 for specificity. Then you have
i = i + 3, j = j + s[i].

This should be similar to regular rc4 with i' * 3 = i and j' * 3 = j,
and all array elements s'[i'] * 3 = s[i]. (This is just a permutation
of the s array and a change in i, j.) These relationships should be
maintained across the state transformation i' = i' + 1, j' = j' + s'[i]'.

The output will be different, because s[s[i]+s[j]] will not be the same
as s'[s'[i']+s'[j']]. But the basic characteristics of the cipher, in
terms of cycle length, digraph frequencies, etc., should be the same.

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