Pseudorandom Bit Generation Using Coupled Congruential Generators

In this brief, we propose the generation of a pseudorandom bit sequence (PRBS) using a comparative linear congruential generator (CLCG) as follows. A bit ¿1¿ is output if the first linear congruential generator (LCG) produces an output that is greater than the output of the second LCG, and a bit ¿0¿ is output otherwise. Breaking this scheme would require one to obtain the seeds of the two independent generators given the bits of the output bit sequence. We prove that the problem of uniquely determining the seeds for the CLCG requires the following: 1) knowledge of at least log
₂

m

²
(
m
being the LCG modulus) bits of the output sequence and 2) the solution of at least log
₂

m

²

inequalities
, where each inequality (dictated by the output bit observed) is applied over positive integers. Computationally, we show that this task is exponential in
n
(where
n
= log
₂

m
is the number of bits in
m
) with complexity
O
(2
²

n
). The quality of the PRBS so obtained is assessed by performing a suite of statistical tests (National Institute of Standards and Technology (NIST) 800-22) recommended by NIST. We observe that a variant of our generator that uses two CLCGs (called dual CLCG) pass all the NIST pseudorandomness tests with a high degree of consistency.