[Python-ideas] Should our default random number generator be secure?

[Robert Kern]

On 2015-09-14 21:56, Sturla Molden wrote:
> On 14/09/15 22:45, Robert Kern wrote:
>> On 2015-09-14 20:07, Sturla Molden wrote:
>>> On 14/09/15 19:15, M.-A. Lemburg wrote:
>>>
>>>> I am well aware that MT doesn't satisfy all empirical tests
>>>> and also that it is not a CSPRNG
>>>
>>>> However, it has been extensively studied and it is proven to be
>>>> equidistributed which is a key property needed for it to be used as
>>>> basis for other derived probability distributions (as it done by the
>>>> random module).
>>>
>>> And with this criterion, only MT and certain PCG generators are
>>> acceptable.
>>> Those are (to my knowledge) the only ones with proven equidistribution.
>>
>> Do not confuse k-dimensional equidistribution with "equidistribution".
>> The latter property (how uniformly a single draw is distributed) is the
>> one that the derived probability distributions rely upon, not the
>> former.
>
> Yes, there was something fishy about this. k-dimensional equidistribution
> matters if we simulate a k-dimensional tuple, as I understand it.

Yeah, but we do that every time we draw k numbers in a simulation at all. And we 
usually draw millions. In that case, perfect k=623-dimensional equidistribution 
is not really any better than k=1, provided that the PRNG is otherwise good.

The requirement for a good PRNG for simulation work is that it be *well* 
distributed in reasonable dimensions, not that it be *exactly* equidistributed 
for some k. And well-distributedness is exactly what is tested in TestU01. It is 
essentially a collection of simulations designed to expose known statistical 
flaws in PRNGs. So to your earlier question as to which is more damning, failing 
TestU01 or not being perfectly 623-dim equidistributed, failing TestU01 is.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco