  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 with public feedback for authenticated ARQ
(Automatic Repeat reQuest). The code design relies on puncturing nonsystematic
low-density parity-check codes with the intent of inflicting an eavesdropper
with stopping sets in the decoder. Furthermore, the design amplifies errors
when stopping sets occur such that a receiver must guess all the channel-erased
bits correctly to avoid an expected error rate of one half in the ciphertext.
We extend previous results on the coding scheme by giving design criteria that
reduces the effectiveness of a maximum-likelihood attack to that of a
message-passing attack. We further extend security analysis to models with
multiple receivers and collaborative attackers. Cryptographic security is
enhanced in all these cases by exploiting properties of the physical-layer. The
enhancement is accurately presented as a function of the degrees of freedom in
the eavesdropper's knowledge of the ciphertext, and is even shown to be present
when eavesdroppers have better channel quality than legitimate receivers.
