Concrete Security Characterizations of PRFs and PRPs: Reductions and Applications

We investigate, in a concrete security setting, several alternate characterizations of pseudorandom functions (PRFs) and pseudorandom permutations (PRPs). By analyzing the concrete complexity of the reductions between the standard notions and the alternate ones, we show that the latter, while equivalent under polynomial-time reductions, are weaker in the concrete security sense. With these alternate notions, we argue that it is possible to get better concrete security bounds for certain PRF/PRP-based schemes. As an example, we show how using an alternate characterization of a PRF could result in tighter security bounds for a certain class of message authentication codes. We also apply these techniques to give a simple concrete security analysis of the counter mode of encryption. In addition, our results provide some insight into how injectivity impacts pseudorandomness