Pseudo Random Binary Sequence Based on Cyclic Difference Set

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.

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On the stability of periodic binary sequences with zone restriction

Applicable Algebra in Engineering Communication and Computing ◽

10.1007/s00200-020-00467-3 ◽

2020 ◽

Author(s):

Ming Su ◽

Qiang Wang

Keyword(s):

Global Stability ◽

Local Stability ◽

Linear Complexity ◽

Binary Sequence ◽

Search Space ◽

Binary Sequences ◽

Zone Length ◽

Stability Measure ◽

Error Linear Complexity ◽

The Stability

Abstract Traditional global stability measure for sequences is hard to determine because of large search space. We propose the k-error linear complexity with a zone restriction for measuring the local stability of sequences. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods $$2^n$$ 2 n , or $$2^v r$$ 2 v r (r odd prime and 2 is primitive modulo r), or $$2^v p_1^{s_1} \cdots p_n^{s_n}$$ 2 v p 1 s 1 ⋯ p n s n ($$p_i$$ p i is an odd prime and 2 is primitive modulo $$p_i^2$$ p i 2 , where $$1\le i \le n$$ 1 ≤ i ≤ n ) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary $$2^n$$ 2 n -periodic binary sequence.

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IRREGULARLY DECIMATED CHAOTIC MAP(S) FOR BINARY DIGITS GENERATIONS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409023573 ◽

2009 ◽

Vol 19 (04) ◽

pp. 1169-1183 ◽

Cited By ~ 14

Author(s):

ALI KANSO ◽

NEJIB SMAOUI

Keyword(s):

Linear Complexity ◽

Statistical Tests ◽

Chaotic Map ◽

Dynamical Behavior ◽

Logistic Map ◽

Binary Sequences ◽

Threshold Function ◽

A New Technique ◽

High Level ◽

Parameter Values

This paper proposes a new technique for generating random-looking binary digits based on an irregularly decimated chaotic map. We present a class of irregularly decimated chaos-based keystream generators, related to the shrinking generator, for the generation of binary sequences. Each generator consists of two subsystems: a control subsystem and a generating subsystem, where each subsystem is based on a single chaotic map. This chaotic map is presented as a 1-D piecewise chaotic map related to the chaotic logistic map. We conduct an analysis of the dynamical behavior of the proposed map to integrate it as a component in the proposed generators subsystems. The output bits of these keystream generators are produced by applying a threshold function to convert the floating-point iterates of the irregularly decimated map into a binary form. The generated keystream bits are demonstrated to exhibit high level of security, long period length, high linear complexity measure and random-like properties at given certain parameter values. Standard statistical tests on the proposed generators, as well as other keystream generators, are performed and compared.

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On the k-Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields

Complexity ◽

10.1155/2019/8635209 ◽

2019 ◽

Vol 2019 ◽

pp. 1-7

Author(s):

Zhixiong Chen ◽

Qiuyan Wang

Keyword(s):

Lower Bound ◽

Finite Field ◽

Finite Fields ◽

Linear Complexity ◽

Discrete Logarithm ◽

Binary Sequence ◽

Binary Sequences ◽

Quadratic Character ◽

Legendre Sequence ◽

Error Linear Complexity

Let Fq be the finite field with q=pr elements, where p is an odd prime. For the ordered elements ξ0,ξ1,…,ξq-1∈Fq, the binary sequence σ=(σ0,σ1,…,σq-1) with period q is defined over the finite field F2={0,1} as follows: σn=0, if n=0, (1-χ(ξn))/2, if 1≤n<q, σn+q=σn, where χ is the quadratic character of Fq. Obviously, σ is the Legendre sequence if r=1. In this paper, our first contribution is to prove a lower bound on the linear complexity of σ for r≥2, which improves some results of Meidl and Winterhof. Our second contribution is to study the distribution of the k-error linear complexity of σ for r=2. Unfortunately, the method presented in this paper seems not suitable for the case r>2 and we leave it open.

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New algorithm for computing minerror linear complexity of pn-periodic binary sequences

Journal of Computer Applications ◽

10.3724/sp.j.1087.2013.00012 ◽

2013 ◽

Vol 33 (1) ◽

pp. 12-14

Author(s):

Zhihua NIU ◽

Danfeng GUO

Keyword(s):

Linear Complexity ◽

Binary Sequences

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Pseudorandom Bit Generator Based on Varying Time-Delayed Logistic Map

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.513-517.1727 ◽

2014 ◽

Vol 513-517 ◽

pp. 1727-1730 ◽

Cited By ~ 1

Author(s):

Ling Feng Liu ◽

Suo Xia Miao ◽

Han Ping Hu ◽

Ya Shuang Deng

Keyword(s):

Delay Time ◽

Statistical Tests ◽

Logistic Map ◽

Binary Sequences

In this paper, we propose a kind of pseudorandom bit generator based on varying time delayed logistic map. The variation of delay time is chaotic. The experiments show that the generated binary sequences have good cryptographic properties, and can pass all the well known statistical tests.

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