Fully leakage-resilient signatures with auxiliary inputs

The auxiliary input model for leakage-resilient encryption considers the leakage of a computationally hard-to-invert function, which can capture a wide class of possible side channel attacks. To avoid the trivial attack that the leakage function simply outputs the forged signature, we propose a new selective auxiliary input model for signatures. This model captures side channel attacks that are based on the physical implementation of the cryptosystem regardless of the underlying public parameters chosen. We provide the first generic construction of fully leakage-resilient signatures, allowing polynomial leakage of the signing key and all intermediate randomness used, under this selective auxiliary input model. We then demonstrate an efficient instantiation of it, thus solving an open problem mentioned by Boyle et al. (Eurocrypt 2011).