Chaos-based public-key cryptography

Abstract

In this chapter we give an overview and the state of the art in the field of Chaos-based cryptography. The public key cryptosystems based on Chebyshev polynomials enjoy some nice chaotic properties, which makes them suitable for use in both encryption and digital signature. The cryptosystem can work either on real or integer numbers. The cryptosystem that works on real numbers is not secure and permits to recover the corresponding plaintext from a given ciphertext. In addition, it also allows forgeries if the cryptosystem is used for signing messages. On the other hand, ElGamal-like and RSA-like algorithms when using Chebyshev polynomials on integer numbers are secure as the aforementioned encryption algorithms. The chaos-based cryptography is discussed from a point of view which we believe is closer to the spirit of both cryptography and chaos theory than the way the subject has been treated recently by many researchers. © 2011 Springer-Verlag Berlin Heidelberg.