The cryptographic security of truncated linearly related variables
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
How to Predict Congruential Generators
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Secret linear congruential generators are not cryptographically secure
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
A new elliptic curve cryptosystem for securing sensitive data applications
International Journal of Electronic Security and Digital Forensics
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In this brief, we propose the generation of a pseudo-random 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 log2m2 (m being the LCG modulus) bits of the output sequence and 2) the solution of at least log2m2 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 = log2m is the number of bits in m) with complexity O(22n). 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.