Using nonlinear discrete mappings to construct pseudo-chaotic cryptosystems

Abstract

Cryptographic methods are used to solve the problem of unauthorized access to information. Analysis has shown that stream encryption schemes, which can be considered from the perspective of nonlinear dynamics, are promising. A distinctive feature of such schemes is their generation by a deterministic generator from a short key (seed) using a discrete dynamic system. However, the chaotic nature of dynamic systems is inherently contradictory: on the one hand, it provides the properties of obfuscation and dispersion (by text and key) essential for cryptography; on the other, it causes inconveniences due to their strong sensitivity to fluctuations and rounding. It has been shown that the main problem with using pseudo-chaotic dynamic systems is related to the specifics of computer computations, namely, the fact that the number of different states in a computer is finite, meaning that any constructed trajectory is periodic with a short period. Furthermore, different platforms (hardware and software) use different algorithms for calculating mathematical functions and store intermediate results with varying accuracy, so the results obtained on different platforms can differ significantly. To overcome these problems, we propose using a new dynamic system, namely, a generalized Tent mapping with control, which stabilizes cycles of a given duration. These cycles depend on the system parameters and the initial value; these values represent a short key for generating a long pseudo-chaotic sequence. Research into the proposed approach has shown that the resulting cycle will depend on the initial point and the key parameters. This allows for a number of possible sequence variants greater than (3 ) 10  p m . This complex dependence makes the cycle virtually uncomputable for cyberattacks.