Rainbow table reduction function

[fedaykin]

I recently did some personal research into the aforementioned functions.

I created a few simple functions based in part on sine (and cosine).
Anyway, the basic idea was to get a seed from the sine of some number, since -1 =< sin N =< 1.

However, I think that sine is not an ideal function to get a pseudo-random seed (assuming a pseudo-random input). If f(x) = sin x, then f'(x) = cos x.

Since the derivative is non-linear, and sine is a smooth function (and also non-linear), then there is a greater chance of picking picking some numbers relative to others.

EX: for some interval of the function, a small change in x will result in a disproportionate change in f(x) relative to a different interval.
I would be overjoyed if someone could debunk or backup my assumptions.

 

[CRGreathouse]

Since cos(x) is smooth, a small change in x may result in only a small change in sin(x), yes.