Combined Pseudo-Random Sequence Generator for Cybersecurity

Abstract

Random and pseudo-random number and bit sequence generators with a uniform distribution law are the most widespread and in demand in the market of pseudo-random generators. Depending on the specific field of application, the requirements for their implementation and the quality of the generator's output sequence change. In this article, we have optimized the structures of the classical additive Fibonacci generator and the modified additive Fibonacci generator when they work together. The ranges of initial settings of structural elements (seed) of these generators have been determined, which guarantee acceptable statistical characteristics of the output pseudo-random sequence, significantly expanding the scope of their possible application, including cybersecurity. When studying the statistical characteristics of the modified additive Fibonacci generator, it was found that they significantly depend on the signal from the output of the logic circuit entering the structure. It is proved that acceptable statistical characteristics of the modified additive Fibonacci generator, and the combined generator realized on its basis, are provided at odd values of the module of the recurrent equation describing the work of such generator. The output signal of the combined generator has acceptable characteristics for a wide range of values of the initial settings for the modified additive Fibonacci generator and the classic additive Fibonacci generator. Regarding the use of information security, it is worth noting the fact that for modern encryption and security programs, generators of random numbers and bit sequences and approaches to their construction are crucial and critical.

Keywords: authentication; encryption of information; pseudo-random number; pseudo-random sequence generators.

Figure 1

Generalized scheme of the joint work of AFG and MAFG.

Figure 2

Structure scheme of the joint work of AFG and MAFG.

Figure 3

Statistical portrait of the AFG output sequence.

Figure 4

Dependencies of repetition periods for $X\_0$, $h=2$ and $a=0$.

Figure 5

Dependencies of repetition periods for $X\_0$, $h=3$ and $a=0$.

Figure 6

Statistical portrait of the MAFG output sequence: (a) with an odd value $h=9$, (b) at an even value $h=10$.

Figure 7

Statistical portrait of the MAFG output sequence for $h=8$, $a=a_0\oplus a_1$ with initial values: (a) $Y\_0=7$, (b) $Y\_0=32$, (c) $Y\_0=100$.

Figure 8

Statistical portrait of the MAFG output sequence for $h=8$, $a=a_0\oplus a_2$ with initial values: (a) $Y\_0=7$, (b) $Y\_0=32$, (c) $Y\_0=100$.

Figure 8

Statistical portrait of the MAFG output sequence for $h=8$, $a=a_0\oplus a_2$ with initial values: (a) $Y\_0=7$, (b) $Y\_0=32$, (c) $Y\_0=100$.

Figure 9

Statistical portrait of the combined generator output sequence for h = 10, $a=a_0\oplus a_3$ with initial values: (a) $Y\_0=7$, (b) $Y\_0=32$, (c) $Y\_0=100$.

Figure 10

Results of passing the NIST tests with the combined generator.

Figure 11

Statistical portrait of the combined generator for h = 9, $a=a_0\oplus a_3$ with initial values: (a) $X\_0=7,Y\_0=36$; (b) $X\_0=32,Y\_0=36$; (c) $X\_0=7,Y\_0=64$; (d) $X\_0=32,Y\_0=64$; (e) $X\_0=7,Y\_0=71$; (f) $X\_0=32,Y\_0=71$; (g) $X\_0=7,Y\_0=100$; (h) $X\_0=32,Y\_0=100$; (i) $X\_0=7,Y\_0=1004$; (j) $X\_0=32,Y\_0=1004$.

Figure 11

Statistical portrait of the combined generator for h = 9, $a=a_0\oplus a_3$ with initial values: (a) $X\_0=7,Y\_0=36$; (b) $X\_0=32,Y\_0=36$; (c) $X\_0=7,Y\_0=64$; (d) $X\_0=32,Y\_0=64$; (e) $X\_0=7,Y\_0=71$; (f) $X\_0=32,Y\_0=71$; (g) $X\_0=7,Y\_0=100$; (h) $X\_0=32,Y\_0=100$; (i) $X\_0=7,Y\_0=1004$; (j) $X\_0=32,Y\_0=1004$.