• #### How is it possible that 8-bit PRNG output pass statistical tests

From William Unruh@21:1/5 to Karl-Uwe Frank on Fri Sep 4 22:57:06 2015
On 2012-01-24, Karl-Uwe Frank <karl.frank@freecx.co.uk> wrote:
On 24.01.12 17:38, Peter Pearson wrote:
On Tue, 24 Jan 2012 15:11:47 +0000, Karl-Uwe Frank wrote:
I am stuck at the point where to understand why the 8-bit binary output
of a PRNG can pass all statistical test, like ENT, diehard and TestU01.
Based on my current understanding this should not be possible.

I don't know your current understanding, and I don't see why
it should not be possible. Would you care to elaborate on
why it should not be possible?

Because I was told and read in several articles that the LSB of a 32-bit integer is to weak to be considered as output, so it's far better to use
the MSB instead. In contrary my tests show that the results with only
the LSB 8-bit output are quit reasonable. So I am wondering if this is correct.

You either midunderstood, or the person was ignorant. A random stream
(which a pseudo random stream should immitate) is randome in each and
every bit, no matter where that bit is located.
The advice you read is good for certain kinds of physical input which is
used as a random input. Thus clock times from the computer can well have
the lowest order bits by highly non-random (eg always 0). But the high
order bits will also be highly non-random (eg every time you query the
clock for 100 years, the upper bit of the time it is always zero).

The question arising now is, if the simple 8-bit output of "tt32" could reveal any way to figure out the next 32-bit values, or perhaps the
internal state of the PRNG.

I have no idea what tt32 is, but if you could do what you suggests it is
a really really lousy PRNG.

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• From Karl-Uwe Frank@21:1/5 to William Unruh on Sun Sep 6 16:39:22 2015
On 05.09.15 00:57, William Unruh wrote:
On 2012-01-24, Karl-Uwe Frank<karl.frank@freecx.co.uk> wrote:
On 24.01.12 17:38, Peter Pearson wrote:
On Tue, 24 Jan 2012 15:11:47 +0000, Karl-Uwe Frank wrote:
I am stuck at the point where to understand why the 8-bit binary output >>>> of a PRNG can pass all statistical test, like ENT, diehard and TestU01. >>>> Based on my current understanding this should not be possible.

I don't know your current understanding, and I don't see why
it should not be possible. Would you care to elaborate on
why it should not be possible?

Because I was told and read in several articles that the LSB of a 32-bit
integer is to weak to be considered as output, so it's far better to use
the MSB instead. In contrary my tests show that the results with only
the LSB 8-bit output are quit reasonable. So I am wondering if this is
correct.

You either midunderstood, or the person was ignorant. A random stream
(which a pseudo random stream should immitate) is randome in each and
every bit, no matter where that bit is located.
The advice you read is good for certain kinds of physical input which is
used as a random input. Thus clock times from the computer can well have
the lowest order bits by highly non-random (eg always 0). But the high
order bits will also be highly non-random (eg every time you query the
clock for 100 years, the upper bit of the time it is always zero).

The question arising now is, if the simple 8-bit output of "tt32" could
reveal any way to figure out the next 32-bit values, or perhaps the
internal state of the PRNG.

I have no idea what tt32 is, but if you could do what you suggests it is
a really really lousy PRNG.

Yes tt32 is somewhat a bizarre 32bit PRNG algorithm.

Meanwhile I am more in favour for 8bit permutation based algorithms as
they, if proper designed, are easy to memorize, useful as CSPRNG, for
building a stream cipher and even with some modification, according the
nature of hashes, as cryptographically secure hash, as PBKDF and MAC
function.

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