Pseudo-random number generator based on fuzzy logic

Abstract

We investigate the parameters of pseudo-random number generator based on fuzzy logic (FRNG) and select the best one. The first parameter is the "size of buffer", the second parameter is the "number of membership functions for fuzzy variables in FRNG". These parameters play essential role for the FRNG and directly influence to the randomness of the output binary sequence. We investigate FRNG's parameters by generating pseudo-random binary sequences and testing them with using NIST test suite. We compare final FRNG with Matlab random generator and 16 random generators form Diehard bundle.

Secure Gamma Generation For Stream Cipher based on Fuzzy Logic

“…Table 1 contains the selected polynomials briefly described using the parameters (b 1 , b 2 , …, b m , n) of (1). 131-258 (1,5,7,15,29,129,191) 7 259-514 (1,2,4,8,16,33,193,419) 8 515-1026 (1,2,5,9,18,36,72,298,929) 9 1027-2050 (1,2,4,8,16,32,64,129,807,1163) To remove confusion, we write one these polynomials in its expanded form (2):…”

“…It is worth mentioning, that all functions of table 2 should practically follow the normal distribution (Gaussian). ' Figure 2' illustrates a practical example, where we generated 1 Mbits using LFSR with the characteristic polynomial (1,5,7,15,29,129,191), and the chosen size of buffer equals 64 bits. Then we built the corresponding histogram to the third function of table 2 (f 11 ).…”

“…It is worth mentioning that the obtained results are very worthy from the cryptanalysis point of view because it makes the developed generator more secure. (1,6,11,22,43) 48-64 5 67-130 (1,5,9,21,41,89) 40-64 6 131-258 (1,5,7,15,29,129,191) 40-64 7 259-514 (1,2,4,8,16,33,193,419) 32-64 8 515-1026 (1,2,5,9,18,36,72,298,929) 32-64 9…”

“…Most of the good pseudo-random number generators use non-linear functions to combine the output of several LFSRs [7]. In the work [1] we developed a pseudo-random number generator based on fuzzy logic [8] [9] (FPRNG) which gives us a lot of benefits to achieving non-linearity. ' Figure 1' depicts the general structure of FPRNG.…”

“…Previous versions of FPRNG have the same size for all buffers of used LFSRs. In [1], we studied FPRNG's parameters to pick up the best values for them. We found that the best value of the size of the buffer regarding the statistical properties of the generated stream is equal to 32 bits.…”