Pseudo Random Binary Sequence Based on Cyclic Difference Set

Abstract

With the increasing reliance on technology, it has become crucial to secure every aspect of online information where pseudo random binary sequences (PRBS) can play an important role in today’s world of Internet. PRBS work in the fundamental mathematics behind the security of different protocols and cryptographic applications. This paper proposes a new PRBS namely MK (Mamun, Kumu) sequence for security applications. Proposed sequence is generated by primitive polynomial, cyclic difference set in elements of the field and binarized by quadratic residue (QR) and quadratic nonresidue (QNR). Introduction of cyclic difference set makes a special contribution to randomness of proposed sequence while QR/QNR-based binarization ensures uniformity of zeros and ones in sequence. Besides, proposed sequence has maximum cycle length and high linear complexity which are required properties for sequences to be used in security applications. Several experiments are conducted to verify randomness and results are presented in support of robustness of the proposed MK sequence. The randomness of proposed sequence is evaluated by popular statistical test suite, i.e., NIST STS 800-22 package. The test results confirmed that the proposed sequence is not affected by approximations of any kind and successfully passed all statistical tests defined in NIST STS 800-22 suite. Finally, the efficiency of proposed MK sequence is verified by comparing with some popular sequences in terms of uniformity in bit pattern distribution and linear complexity for sequences of different length. The experimental results validate that the proposed sequence has superior cryptographic properties than existing ones.