Abstract. A cryptographic primitive is leakage-resilient, if it remains secure even if an adversary can learn a bounded amount of arbitrary information about the computation with every invocation. As a consequence, the physical implementation of a leakage-resilient primitive is secure against every side-channel as long as the amount of information leaked per invocation is bounded. In this paper we prove positive and negative results about the feasibility of constructing leakage-resilient pseudorandom functions and permutations (i.e. block-ciphers). Our results are three fold: