Luby-Rackoff Backwards: Increasing Security by Making Block Ciphers Non-invertible

We argue that the invertibility of a block cipher can reduce the security of schemes that use it, and a better starting point for scheme design is the non-invertible analog of a block cipher, that is, a pseudorandom function (PRF). Since a block cipher may be viewed as a pseudorandom permutation, we are led to investigate the reverse of the problem studied by Luby and Rackoff, and ask: “how can one transform a PRP into a PRF in as security-preserving a way as possible?” The solution we propose is data-dependent re-keying. As an illustrative special case, let E : {0, 1}n×{0, 1}n → {0, 1}n be the block cipher. Then we can construct the PRF F from the PRP E by setting F (k, x) = E(E(k, x), x). We generalize this to allow for arbitrary block and key lengths, and to improve efficiency. We prove strong quantitative bounds on the value of data-dependent re-keying in the Shannon model of an ideal cipher, and take some initial steps towards an analysis in the standard model.