Random number generators discussion

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thread Is the self-test valid? - Reece Pollack - 2004-03-07
last reply Yes, it is - A Fog - 2004-03-09
 
Is the self-test valid?
Author:  Date: 2004-03-07 10:40
I haven't had time to look at the theory behind your PRNG in depth, but at first blush it appears to me that the self-test is invalid.

For the self-test to be meaningful, the assertion that "only the initial state can close the circle" (page 3, just after equation 7) must be true. It is well-known that many PRNGs develop cycles that do not return to the initial state, but instead cycle through a sequence that only develops afterwards. In this case, the self-test will never detect the cycle.

It appears that the paragraph on page 4, just after equation 15, may cover this situation, but I'm not sure.

Comments?

   
Yes, it is
Author: A Fog Date: 2004-03-09 09:09
The self test is applied only to RNGs with a reversible state transition function. The RANROT generators are constructed so that it is always possible to find state (n-1) from state (n).