Permutation and Complementary Algorithm to Generate Random Sequences for Binary Logic

Jie Wan, Jeffrey Z. J. Zheng

School of Software, Yunnan University Kunming, China.

DOI: 10.4236/ijcns.2011.45039                

Abstract

Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion operations to extend n-variable Logic function space from 2²ⁿ functions to 2²ⁿ * 2ⁿ! configurations for variant logic framework. Each configuration contains ²ⁿ functions can be shown in a 2^2n-1*2^2n-1 matrix. A set of visual results can be represented by their symmetric properties in W, F and C codes respec-tively to provide the essential support on the variant logic framework.

Keywords

Logic Function, Permutation and Complementary, Variant Logic, Symmetric Distribution, Random Sequence

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	W. Stallings, “Cryptography and Network Security: Principles and Practice,” Prentice Hall, 2005.
[2]	J. Soto and L. Bassham, “Randomness Testing of the Advanced Encryption Standard Finalist Candidates,” National Institute of Standards and Technology (NIST), 2000.
[3]	National Institute of Standards and Technology (NIST), “Random number generation,” 2008. Internet Avail- able: http://csrc.nist.gov/groups/ST/toolkit/rng/index.html
[4]	J. Zhi, J. Zheng and C. H. Zheng, “A framework to express variant and invariant functional spaces for binary logic,” Frontiers of Electrical and Electronic Engineering in China, Vol. 5, No. 2, 2010, pp. 163-172.
[5]	S. Wolfram, “Theory and Applications of Cellular Auto- mata,” Singapore: Word Scientific, 1986.
[6]	S. Wolfram, “Cellular automata as models of complexity,” Nature, Vol. 311, 1984, pp. 419-424.
[7]	J. Wan and J. Zheng, “Showing Exhaustive Number Sequences of Two Logic Variables for Variant Logic Functional Space,” Proceedings of Asia-Pacific Youth Conference on Communication (APYCC), October 2010, p. 4.