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: 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

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 efficient additive homomorphism which can be used to protect important cryptographic tasks such as identification, signing and encryption. More precisely, we propose

efficient

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 security

of our encryption scheme under the DDH assumption.