We construct a stream-cipher SC whose implementation is secure even if a bounded amount of arbitrary (adaptively, adversarially chosen) information about the internal state of SC is leaked during computation of each output block. This captures all possible side-channel attacks on SC where (1) the amount of information leaked in a given period is bounded, but overall can be arbitrary large and (2) “only computation leaks information”. The construction is based on alternating extraction (used in the intrusion-resilient secret-sharing scheme from FOCS’07). We move this concept to the computational setting by proving a lemma that states that the output of any pseudorandom generator (PRG) has high HILL pseudoentropy (i.e. is indistinguishable from some distribution with high min-entropy) even if arbitrary information about the seed is leaked. The amount of leakage λ that we can tolerate in each step depends on the strength of the underlying PRG, it is at least logarithmic, but can b...