Improving The Random Number Generator With Multiplicative Convolution Transform

Nikolai AndreevichAntonov

The creation of random number generators is an important issue in the field of mathematical modeling, applied mathematicsand modern cryptography. The ultimate goal of any generator is to obtain a sequence of numbers having the properties of random sample from given distribution.In addition, modern random number generators should satisfy the requirements of reproducibility of generated random sequence and the high speed of its production, as well as the generator’s resistance to algebraic attacks. The requirements above emphasize the importance of creating a class of algorithmic random number generators, andthe generator based on shift registers with linear feedback is an example of this class.The review of current researches shows that generators of this type can produce high-quality pseudo-random sequences but not all of these generators are resistant to various algebraic attacks. So, to determine the initial state of a single shift register, the Berlekamp-Massey algorithm is used, and for hacking a generator consisting of several registers, methods of correlation attacks are widely used. This paper proposes a method for enhancing the cryptographic strength of a single shift register with linear feedback while maintaining its statistical properties. The main feature of this method is a special transformation performed for the register elements, i.e. the multiplicative convolution transformation.Due to its structure, this kind of transformation makes difficult to determine the initial state of both one registerand a system of several registers.Thecharacteristicsof generated pseudorandom sequencesare comparable with properties of a sample from a uniform distribution, how it is proved by NIST and DieHarderstatistical tests results.

Volume 11 | 08-Special Issue

Pages: 2827-2833