Security of public key encryption technique based on multiple chaotic systems

Recently, a new public key encryption technique based on multiple chaotic systems has been proposed [B. Ranjan, Phys. Rev. Lett. 95 (2005) 098702]. This scheme employs m-chaotic systems and a set of linear functions for key exchange over an insecure channel. Security of the proposed algorithm grows as (N P)^m, where N, P are the size of the key and the computational complexity of the linear functions respectively. In this Letter, the fundamental weakness of the cryptosystem is pointed out and a successful attack is described. Given the public keys and the initial vector, one can calculate the secret key based on Parseval's theorem. Both theoretical and experimental results show that the attacker can access to the secret key without difficulty. The lack of security discourages the use of such algorithm for practical applications.