Linear Feedback Shift Registers Essay -- Computers, Cryptography

Abstract: Linear Feedback Shift Registers (LFSRs) are considered powerful methods for generating pseudo-random bits in cryptography algorithm applications. In this paper it is shown that the linear dependencies in the generated random bit sequences can be controlled by adding a chaotic logistic map to the LFSR’s systems. The structure of the LFSR’s output sequence in combination with a chaotic map is analyzed and proved to have at least as much uniformity than the corresponding set for the linear components individually. In order to understand that using the proposed PRBG is reliable in secure algorithms, the NIST suite test have been taken on the proposed method, finally to compare the proposed PRNG output sequence features with the two types of LFSRs (Fibonacci and Galois). Keywords: Linear Feedback Shift Register, Random Number, Chaotic Map, NIST. 1. Introduction In the modern world of computers, network security is the main concern which relies on the use of cryptography algorithms. high quality random number generation is a basic subject of cryptography algorithms and the importance of a secure random number generator design cannot be underestimated. Most common generation techniques about RNGs involve truly random and pseudorandom number generators. For a brief introduction in various types of RNGs: Truly Random Number Generators (RNGs) is a computer algorithm, which generates a sequence of statistically independent random numbers. Actually these generators require a naturally occurring source of randomness phenomena (i.e. as a non-deterministic system). Most practical implementations design a hardware device or a software program based on RNGs to produce a bit sequence which is statistically independent. Pseud... ...3245, 0.9966745]; so the p-values of our purposed method is in this interval and then the 15 tests of the NIST suite have been passed as shown In Fig. 6. Fig. 6. NIST test result (Red is the Proposed PRNG, Blue represents Galois and Green is Fibonacci) 6. Conclusion In this paper we presented a novel method to generate random bit sequence by combination of LFSR’s system and chaotic logistic map and it has been proved in a reliable theorem. At the end, we compared it with the same other methods such as Fibonacci LFSR and Galois LFSR, and the result was shown in table 1. Acknowledgments The author wish to thank the editor Professor G.Najafpour, Dr. H.Hassanpour and my teacher Mr. H.Rahimov for their valuable comments. In the end should be appreciated the efforts of Shahrood University of Technology’s ITC research center.