A Novel Multicast Key Exchange Algorithm Based on Extended Chebyshev Map

The Chebyshev map is a typical chaotic map which has been widely investigated for cryptography. However, researchers argue that almost all the encryption algorithms based on some chaotic maps are not as secure as they are announced. In this paper, the limitations of some multicast key agreement schemes are discussed. To eliminate those false and remain novelty, we consider how the chaotic maps can be improved to fulfill the cryptographic demands. To achieve this, we extend the domain of Chebyshev maps from real number set to finite field. Based on this extension, this paper proposes a novel multicast key exchange algorithm. By detailed experiments and analysis, we show that this algorithm is secure and efficient. As far as we know, such a multicast key exchange algorithm has not been reported. The results given here, to the best of our knowledge, are novel.