Exact Equivocation Expressions for Wiretap Coding Over Erasure Channel Models

Traditional security analysis of wiretap codes requires evaluation of equivocation in the asymptote as the code blocklength tends to infinity. Finite blocklength codes, however, require exact expressions for equivocation so as to allow for comparison of parameterized codes across different code constructions or within the same construction. In this letter, we present two exact equivocation expressions for coset coding over the wiretap channel model with binary erasure channels (BECs) for both the main channel and the eavesdropper's channel. The expressions are functions of the algebraic structure of the binary wiretap codes, and they also hold for the special case when the main channel is noiseless.