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Putting some of my comments into writing. This is less than an answer but too much for a comment. In the comments I had claimed to apply SMT to solve case 1 - this is false, I was mistaken. I have had cases 2 and 3 running SMT (boolector, Z3, CVC4, yices) for some time without success. The closest thing to success is the identification of seeds that ...


2

This answer addresses Cases 1 and 2 from the question to provide a baseline, leaving Case 3 (which is the one I'm most interested in), unresolved. Case 1, Zero Increment In this case we'll consider a simple Lehmer-style LCG (a.k.a. an MCG), with a seed $s_1$, multiplier $a$ and $b$ bits of state and $r$ bits returned. The modulus $M = 2^b$, and the ...


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This is a work-in-progress, mostly trying to address Case 3 in the question, since the problem of Case 2 is dealt with in another answer, and has been thoroughly researched: Jacques Stern: Secret linear congruential generators are not cryptographically secure, in proceedings of the 28th Annual Symposium on the Foundations of Computer Science, 1987 (try a ...



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