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.