Modification of Linear Congruential Generator

[ttw]

Implicit in all the stuff I wrote is a simpler suggestion. (It does not take advantage of the "independence" of quadratic residues though.) When using a prime modulus and primitive element for multiplier X = X*A mod (M), M should be taken to be a prime of the form 4*k+1 rather than 2*k+1. (This means not using Sophie Germain primes and similar). In the case of 4*k+1 primes, the odd and even calls to the RNG are both uniformly distributed.