Inferring a sequence generated by a linear congruence

Abstract

Suppose it is known that {X₀, X₁,...,X_n} is produced by a pseudo-random number generator of the form X_i+1 = aX_i + b mod m, but a, b, and m are unknown. Can one efficiently predict the remainder of the sequence with knowledge of only a few elements from that sequence? This question is answered in the affirmative and an algorithm is given.