Cryptanalysis of chaotic convolutional coder

In this paper, we evaluate the security of a recently proposed joint error correction and encryption approach called chaotic convolutional coder, which integrates the chaotic encryption into the convolutional coding. We show that the probability of recovering the key vector controlling the chaotic switch is at least 0.289 under known-plaintext attack, if the number of available plaintext/ciphertext pairs p is equal to the constraint length k of the chaotic convolutional coder. In the case that p = k + e, where e > 0, we prove that the probability to recover the key vector is lower bounded by 1-2^-e. We also consider the security of the chaotic con-volutional coder under chosen-plaintext attack. We propose two approaches to efficiently derive the key vector without leaving tractable pattern to the register. In particular, one of these two methods based on an efficient erasure code is capable of recovering the key vector with complexity of order O(k log k).