3 ms·
I'm not sure that the claim "the mix function is injective" is sufficient to support the claim "The period is at least 2^128". If the mix is reversible then it
by aappleby 1y ago
I'm not sure that the claim "the mix function is injective" is sufficient to support the claim "The period is at least 2^128". If the mix is reversible then it forms a permutation on 2^192, but that does not imply that it forms a single cyclic permutation.
For example, if f(0) = 1 and f(1) = 0, even if the rest of f's domain is injective the period of f is still only 2 when the initial value is 0 or 1.
- the_othernet 1y agoI wasn't able to analyze the cyclic behavior of the mix directly, but for the purpose of minimal period only fast_loop and slow_loop are used (as a 128bit counter).
- grumbelbart 1y agoThat is correct. The permutations will likely break up into multiple cycles, and the cycle lengths follow a poisson distribution. https://dms.umontreal.ca/~andrew/PDF/CycleLengths1.pdf https://dms.umontreal.ca/~andrew/PDF/CycleLengths1.pdf