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.
Highlights
Pseudo random binary sequences (PRBS) are widely used in many applications such as wireless communications and cryptography [1,2,3,4]
PRBS is adopted in many applications as the primary security component
We proposed a new pseudo random binary sequence, i.e., MK sequence with an aim to use in security of applications
Summary
Pseudo random binary sequences (PRBS) are widely used in many applications such as wireless communications and cryptography [1,2,3,4]. Randomness of a sequence indicates the degree of difficulty of predicting bit in that sequence whether it is physical or statistical analysis Such ideal random sequences can be produced from natural resources, for example, atmospheric noises, radioactive decay and other natural phenomena. Sequences having long cycle length, high linear complexity and uniform bit pattern are considered to be ideal for security applications. Linear complexity of these sequences is low, unsuitable in security based applications. Linear complexity and uniformity of bit pattern distribution properties of MK sequence are investigated and numerical results are demonstrated theoretically for different length of sequences.
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