II, by Donald Knuth, 1969. M must be relatively prime. In this special case, the LCG degenerates from a geometric summation into an arithmatic summation. It is my belief that one of the best ways to achieve encryption security is by individuals creating their own pseudo-random number generators, and keeping the source code private.
Encryption is, after all, a private matter.
Thusly, you want your pseudo-random number generators to be as good as possible. Confidentially distributing the keys and compiled generators should allow for a highly secure, personal, private-key system. I have seen books which advise that M simply be a prime number. It is thusly potentially easy to construct an LCG which is really an additive hash by accident. That is exactly what happened to me a few years ago.