Another problem with IPG algorithm

[wichita at cyberstation.net]

On Sun, 1 Dec 1996, Igor Chudov @ home wrote:

> Don and others,
> 
> At the heart of IPG algorithm there is a pseudo-random number generator
> which generates values of A(JV). (see http://www.netprivacy.com/algo.html)
> 
>        DO
>          JV=JV+1
>          IF JV=53 THEN JV=0
>          A(JV)=(A(JV)+B(JV)) MOD C(JV)
>        UNTIL A(JV)<16384
> 
> Note that if B(JV) and C(JV) in a triplet (A(JV), B(JV), C(JV)) are not
> mutually prime, they will generate very few numbers and not a whole set
> 0-16383. For example, if C(JV) is 20000, and B(JV) is 10000, and initial
> A is (for example) 57, the only two numbers that this triplet will
> generate will be 57 and 10057.
> 
> This refutes Don Wood's claim that the distribution of results
> approaches even. Even if only ONE triplet is such as I described (and it
> is VERY likely to happen statistically), the distribution will be
> skewed.
> 
> Don, what do you think about it?
> 
> igor
> 
Igor, 

Also included in the more detailed explanation is the set of As, Bs, and
Cs that are used. Either the B or a C is prime in all instances,
I would agree with you if that was not the case. All 16384 numbers, 0
through 16383, are always generated. In addition of course, the numbers
between 16384 and each of the Cs are also generated but not used. 

Thus each of the C(JV) values are operating at different speeds and
produce a staccato, meaning in this case, something that is discontinious
or disjointed. However, the sum of series approaches an even distribution
in the almost precisely same manner as a true random number generator
approaches an even distribution. Thus over short frames variance is great
but over long frames, the frequency of occurrence tends to approach a
perfectly even distribution.

Also, keep in mind, that the values are never used directly - they are
only used as a variable for a three dimensional table lookup, where all 
three of the 4096 element tables are constantly changing depending upon
the the sum of the A(JV) variables combined with the initial settings,
which were initally determined determined by the user generated key, and 
other related information.   

Also, remember that the order and the actual As, Bs, and Cs used are also
randomly arrived at by using the user defined key, 256 bytes or 8192
bytes.

There is a lot more revealed at the web site. If you have further
interest, I would provide you, Igor, with source code for the 
algorithm, subject to a binding NDA. I think you will be suprised if
you examined it in detail.

With kindest regards,

Don Wood