orz wrote:

[...]

> It's looking like state_3 combined with anything else passes all my
> tests.
>
> I am not fan of combining multiple RNGs in that way. I would rather
> have every bit of state either effect or be effected by every other
> bit of state, or both. When the RNG can be divided in to independent
> component RNGs that tends to mean both decreased overall quality and
> increased inter-state/seed correlation relative to the quality.
>
> I want to back away from my earlier statement "I could run a standard
> cryptographic RNG instead and have faster output". Really, the common
> cryptographic RNGs are pretty slow in software - to find one faster
> than this I have to basically cheat, picking ones that use larger
> integer sizes and are not well accepted as secure. And while your RNG
> is kinda slow in my book, it's still faster than mt19937 on gcc
> (though slower on MSVC), so there's plenty of people who wouldn't
> consider it slow - I have pretty high standards in that regard. Also,
> leaving out lfsr_1 and lfsr_01 has, I think, fairly little cost in
> output quality or statespace, and yields a significant improvement in
> speed. Though it would substantially worsen interstate correlation
> issues I think.

Using a block cipher was the advantage of being easy to create
a random access pseudo random number generator (just use it in counter mode).
I tried to pick one, reduce the number of rounds and overall operations,
but I wasn't able to make it fast enough.

>
> BTW, how did you choose the constants for the state_* LFSR? I'm
> familiar with methods of finding maximal period constants and have a
> few rules of thumb / common sense to avoid bad constants, but after
> that I mostly stick to either empirical testing or avalanche-style
> testing to distinguish good constants from bad constants. If I had a
> better feel for where the constants came from I might scale it down to
> working on 16 or 8 bit integers for testing purposes, as it's a lot
> easier to find flaws when corner cases are more frequent and the state
> size is closer to the log of the number of bins in my chi squared
> tests.

I'm using the same method.

Pedro Pereira