Secure pseudo-random bit sequence generation using coupled linear congruential generators

Linear congruential generators (LCGs) of the form x_i+1 = ax_i + b(mod m), have been used to generate pseudorandom numbers. However these generators have been known to be insecure. This implies that if a small sequence of numbers generated by an LCG is known then it is possible to predict the remaining numbers in the sequence that will be generated. We propose to generate a secure pseudorandom bit sequence by coupling two LCGs as follows. A 1 is output if the first LCG produces an output that is greater than the output of the second LCG and a 0 is output otherwise. The security of this sequence is shown by demonstrating the difficulty of obtaining the initial conditions of the two LCGs given the pseudorandom bit sequence output. If the modulus m is a power of 2 then efficient circuits can be designed for the proposed generators.