Coding for Cryptographic Security Enhancement Using Stopping Sets

In this paper, we discuss the ability of channel codes to enhance cryptographic secrecy. Toward that end, we present the secrecy metric of degrees of freedom in an attacker's knowledge of the cryptogram, which is similar to equivocation. Using this notion of secrecy, we show how a specific practical channel coding system can be used to hide information about the ciphertext, thus increasing the difficulty of cryptographic attacks. The system setup is the wiretap channel model where transmitted data traverse through independent packet erasure channels (PECs) with public feedback for authenticated automatic repeat-request (ARQ). The code design relies on puncturing nonsystematic low-density parity-check (LDPC) codes with the intent of inflicting an eavesdropper with stopping sets in the decoder. The design amplifies errors when stopping sets occur such that a receiver must guess all the channel-erased bits correctly to avoid an error rate of one half in the ciphertext. We extend previous results on the coding scheme by giving design criteria that reduce the effectiveness of a maximum-likelihood (ML) attack to that of a message-passing (MP) attack. We further extend security analysis to models with multiple receivers and collaborative attackers. Cryptographic security is even enhanced by the system when eavesdroppers have better channel quality than legitimate receivers.