Overcoming the Hole in the Bucket: Public-Key Cryptography Resilient to Continual Memory Leakage

In recent years, there has been a major effort to design cryptographic schemes that remain secure even when arbitrary information about the secret key is leaked (e.g., via side-channel attacks). We explore the possibility of achieving security under \emph{continual} leakage from the \emph{entire} secret key by designing schemes in which the secret key is updated over time. In this model, we construct public-key encryption schemes, digital signatures, and identity-based encryption schemes that remain secure even if an attacker can leak a constant fraction of the secret memory (including the secret key) in each time period between key updates. We also consider attackers who may probe the secret memory during the updates themselves. We stress that we allow unrestricted leakage, without the assumption that ``only computation leaks information''. Prior to this work, constructions of public-key encryption schemes secure under continual leakage were not known even under this assumption.