Mind Your Coins: Fully Leakage-Resilient Signatures with Graceful Degradation

We construct new leakage-resilient signature schemes. Our schemes remain unforgeable against an adversary leaking arbitrary (yet bounded) information on the entire state of the signer (sometimes known as fully leakage resilience). The main feature of our constructions, is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible. This property was recently put forward by Nielsen et al. (PKC 2014) to deal with settings in which the secret key is much larger than the size of a signature. One remarkable such case is the so-called Bounded Retrieval Model (BRM), where one intentionally inflates the size of the secret key while keeping constant the signature size and the computational complexity of the scheme. 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. ∗Part of the work done while at Aarhus University. †Partially supported by Danish Council for Independent Research via DFF Starting Grant 10-081612. Partially supported by the European Research Commission Starting Grant 279447.