Leakage-resilient cryptography from the inner-product extractor

Abstract. We present a generic method to secure various widely-used cryptosystems against arbitrary side-channel leakage, as long as the leak-age adheres three restrictions: first, 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 hid-den, 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 efficient additive homomorphism which can be used to protect important cryptographic tasks such as identification, signing and encryption. More precisely, we propose effi-cient implementations of the Okamoto identification 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 se-curity of our encryption scheme under the DDH assumption.