International Association
for Cryptologic Research

In FSE 2010, Nandi proved a sufficient condition of pseudo random function (PRF) for affine domain extensions (ADE), wide class of block cipher based domain extensions. This sufficient condition is satisfied by all known blockcipher based ADE constructions, however, it is not a characterization of PRF. In this paper we completely characterize the ADE and show that {\\em message authentication code (MAC) and weakly collision resistant (WCR) are indeed equivalent to PRF}. Note that a PRF is trivially a MAC and WCR, however, the converse need not be true in general. So our result suggests that it would be sufficient to ensure resisting against weakly collision attack or the forging attack to construct a pseudo random function ADE. Unlike FSE 2010 paper, here we consider the {\\em forced collisions of inputs of underlying blockciphers by incorporating the final outputs of a domain extension queried by an adaptive adversary}. This is the main reason why we are able to obtain a characterization of PRF. Our

approach is a more general and hence might have other theoretical interest.