Fully leakage-resilient signatures revisited: Graceful degradation, noisy leakage, and construction in the bounded-retrieval model

Our main constructions have leakage rate 1−o(1), and are proven secure in the standard model. We additionally give a construction in the BRM, relying on a random oracle. All of our schemes are described in terms of generic building blocks, but also admit efficient instantiations under fairly standard number-theoretic assumptions. Finally, we explain how to extend some of our schemes to the setting of noisy leakage, where the only restriction on the leakage functions is that the output does not decrease the min-entropy of the secret key by too much.