How to perform mathematical operations in an electronic apparatus, a method for generating a pseudo-random number in an electronic apparatus, and a method for decoding and encrypting electronic data

摘要

A method of performing numerical computations in a mathematical system comprises expressing the mathematical system in discrete terms, using fixed-point variables in the computations, and extracting a sub-set of digits of a number. The sub-set of digits may represent a random or pseudo-random number. The mathematical system may be a system of non-linear differential equations, such as a chaotic system, for example a system with a positive Lyapunov exponent, or a discrete mapping, such as a logistic map, an Anosov or a Hénon map. The method is applicable to encryption and decryption algorithms, including stream ciphers and block ciphers, systems for generating a digital signature, Hash functions, and MAC (Message Authentication Code) functions. A test for periodical behaviour of a solution to the mathematical system is provided.