Turbo Codes Can Be Asymptotically Information-Theoretically Secure

This paper shows that a turbo-coded communication system can be made secure with a little bit of complexity cost. The classical permutation ciphers are revisited and analyzed. Firstly, the ideal stream permutation ciphers are shown to be asymptotically information-theoretically secure in the sense that the channel from plaintext to ciphertext has a vanished capacity, while the practical stream permutation ciphers are shown to be more secure than the classical stream ciphers in terms of protecting keys. Secondly, a necessary condition to break down a block permutation cipher is derived, which is then utilized to guarantee the computational security of a modified block permutation cipher. Thirdly, turbo ciphers (turbo-like codes with private interleavers) are proposed and analyzed.