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? |