Abstract: Linear feedback shift registers (LFSRs) are considered powerful methods for generating pseudo-random bits in cryptographic algorithm applications. In this paper we show that linear dependencies in the generated random bit sequences can be controlled by adding a chaotic logistic map to LFSR systems. The structure of the LFSR output sequence in combination with a chaotic map is analyzed and shown to have at least the same uniformity as the corresponding ensemble for the linear components taken individually. To understand that using the proposed PRBG is reliable in secure algorithms, NIST suite tests were carried out on the proposed method, finally to compare the characteristics of the proposed PRNG output sequence with the two types of LFSR (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 primary concern which is based on the use of encryption algorithms. High-quality random number generation is a fundamental topic of cryptographic algorithms, and the importance of secure random number generator design cannot be underestimated. The most common generation techniques on RNGs involve truly random and pseudorandom number generators. For a brief introduction on the various types of RNG: Truly Random Number Generators (RNG) is a computer algorithm that generates a sequence of statistically independent random numbers. In reality these generators require a natural source of randomness phenomena (i.e. as a non-deterministic system). Most practical implementations design an RNG-based hardware device or software program to produce a statistically independent sequence of bits. Pseud...... middle of document ......3245, 0.9966745]; so the p-values ​​of our proposed method fall within this range and thus the 15 NIST suite tests passed as shown in Fig. 6.Fig. 6. NIST test result (red is the proposed PRNG, blue represents Galois, and green is Fibonacci)6. ConclusionIn this paper we presented a new method to generate random bit sequences by combining LFSR system and chaotic logistic map and it was proved in a reliable theorem. Finally, 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 would like to thank the editor Professor G.Najafpour, Dr. H.Hassanpour and the my teacher Mr. .H.Rahimov for their valuable comments. Ultimately, the efforts of the ITC research center of Shahrood University of Technology must be appreciated.