Cryptography Resilient to Continual Memory Leakage

In recent years, there has been a major efiort to design cryptographic schemes that remain secure even if part of the secret key is leaked. This is due to a recent proliferation of side channel attacks which, through various physical means, can recover part of the secret key. We explore the possibility of achieving security even with continual leakage, i.e., even if some information is leaked each time the key is used. We show how to securely update a secret key while information is leaked: We construct schemes that remain secure even if an attacker, at each time period, can probe the entire memory (containing a secret key) and \leak" up to a (1 ¡ o(1)) fraction of the secret key. The attacker may also probe the memory during the updates, and leak O(logk) bits, where k is the security parameter (relying on subexponential hardness allows k † bits of leakage during each update