Fully Leakage-Resilient Codes

Leakage resilient codes (LRCs) are probabilistic encoding schemes that guarantee message hiding even under some bounded leakage on the codeword. We introduce the notion of fully leakage resilient codes (FLRCs), where the adversary can leak lambda(0) bits from the encoding process, namely, the message and the randomness involved during the encoding process. In addition the adversary can as usual leak from the codeword. We give a simulation-based definition requiring that the adversary's leakage from the encoding process and the codeword can be simulated given just lambda(0) bits of leakage from the message. We give a fairly general impossibility result for FLRCs in the popular split-state model, where the codeword is broken into independent parts and where the leakage occurs independently on the parts. We then give two feasibility results for weaker models. First, we show that for NC0-bounded leakage from the randomness and arbitrary poly-time leakage from the parts of the codeword the inner-product construction proposed by Davi et al. (SCN'10) and successively improved by Dziembowski and Faust (ASIACRYPT'11) is a FLRC for the split-state model. Second, we provide a compiler from any LRC to a FLRC in the common reference string model where the leakage on the encoding comes from a fixed leakage family of small cardinality. In particular, this compiler applies to the split-state model but also to other models.