Leakage-Resilient Cryptography from the Inner-Product Extractor

We present a generic method to secure various widely-used cryptosystems against arbitrary side-channel leakage, as long as the leakage adheres three restrictions: rst, it is bounded per observation but in total can be arbitrary large. Second, memory parts leak independently, and, third, the randomness that is used for certain operations comes from a simple (non-uniform) distribution. As a fundamental building block, we construct a scheme to store a cryptographic secret such that it remains information theoretically hidden, even given arbitrary continuous leakage from the storage. To this end, we use a randomized encoding and develop a method to securely refresh these encodings even in the presence of leakage. We then show that our encoding scheme exhibits an e cient additive homomorphism which can be used to protect important cryptographic tasks such as identi cation, signing and encryption. More precisely, we propose e cient implementations of the Okamoto identi cation scheme, and of an ElGamal-based cryptosystem with security against continuous leakage, as long as the leakage adheres the above mentioned restrictions. We prove security of the Okamoto scheme under the DL assumption and CCA2 security of our encryption scheme under the DDH assumption.