Finite-Length Analysis of Wiretap Codes using Universal Hash Functions

This paper investigates the relation between the second-order coding rate, where the second-order turns out to be strictly larger than √n, and the mutual information as the leaked information for a fixed error probability by using wiretap codes constructed by universal₂ hash functions. We first generalize the upper bound on ε-smooth max information in {tyagi} and use it in our analysis where we adopt the method in {hayashi-tan}, which uses universal hashing for compressing a source and making it secure from another correlated source, and apply it to the wiretap channel. We prove first- and second-order achievability results by assuming that the conjecture we state holds true.