Efficient Pseudo-chaotic Number Generator for Cryptographic Applications

Abstract

A secure and efficient pseudo-random number generator is crucial for the security of a stream cipher or block cipher in a cryptosystem. This paper is devoted to the design and analysis of a new robust Pseudo-Chaotic Number Generator (PCNG) based on discrete chaotic maps over a finite field, and a multiplexing mechanism. The proposed PCNG contains three discrete chaotic maps: Piece-Wise Linear Chaotic Map (PWLCM), skew tent and logistic map. XOR operators are applied on these maps to form three optional intermediate outputs that are selected by the multiplexing mechanism to produce the final pseudo-chaotic sequence. The XOR operators and multiplexing mechanism can increase the dynamic pseudo-chaotic properties significantly. The PCNG is designed over a finite 2 32 field, has a simple structure and can be easily implemented. It has been implemented on a new stream cipher. Security analyses and statistical experiments have been carried out and the results have proven that the proposed PCNG can generate effective pseudorandom numbers and the stream cipher exhibits good security properties with large secret key space and high key sensitivity. Therefore, the proposed PCNG can be successfully applied in cryptosystems.

Fractional Chaotic System Solutions and Their Impact on Chaotic Behaviour

“…This sensitivity can be measured by Lyapunov Exponent(LE) which calculates the rate of exponential divergence of trajectories starting from two close initial conditions. This characteristics also contributes to the application of chaotic systems in many domains of science and engineering, such as biology [3], economics [4], finance [5], cryptography [6] [7] and etc. In the meantime, fractional calculus is considered as the generalization of classical integer-order integration and differentiation operators to real, or complex orders [8].…”

A Stream Cipher Based on Fractional Pseudo Chaotic Random Number Generator

“…Nonlinear systems with chaotic behavior have been vastly investigated and applied in the design of cryptosystem [1] [2]. The pseudo-random generators are designed based on chaotic system due to its numerous merits such as random-like behavior and the sensitivity to the initial conditions and to parameters [3].…”