What a lovely hat

Paper 2014/660

Interactive Proofs under Continual Memory Leakage

Prabhanjan Ananth, Vipul Goyal, and Omkant Pandey

Abstract

We consider the task of constructing interactive proofs for NP which can provide meaningful security for a prover even in the presence of continual memory leakage. We imagine a setting where an adversarial verifier participates in multiple sequential interactive proof executions for a fixed NP statement x. In every execution, the adversarial verifier is additionally allowed to leak a fraction of the (secret) memory of the prover. This is in contrast to the recently introduced notion of leakage-resilient zero-knowledge (Garg-Jain-Sahai'11) where there is only a single execution. Under multiple executions, in fact the entire prover witness might end up getting leaked thus leading to a complete compromise of prover security. Towards that end, we define the notion of non-transferable proofs for all languages in NP. In such proofs, instead of receiving w as input, the prover will receive an "encoding'' of the witness w such that the encoding is sufficient to prove the validity of x; further, this encoding can be "updated'' to a fresh new encoding for the next execution. We then require that if (x,w) are sampled from a "hard'' distribution, then no PPT adversary A* can gain the ability to prove x (on its own) to an honest verifier, even if A* has participated in polynomially many interactive proof executions (with leakage) with an honest prover whose input is (x,w). Non-transferability is a strong security guarantee which suffices for many cryptographic applications (and in particular, implies witness hiding). We show how to construct non-transferable proofs for all languages in NP which can tolerate leaking a constant fraction of prover's secret-state during each execution. Our construction is in the common reference string (CRS) model. To obtain our results, we build a witness-encoding scheme which satisfies the following continual-leakage-resilient (CLR) properties: - The encodings can be randomized to yield a fresh new encoding, - There does not exist any efficient adversary, who receiving only a constant fraction of leakage on polynomially many fresh encodings of the same witness w, can output a valid encoding provided that the witness w along with its corresponding input instance x were sampled from a hard distribution. Our encoding schemes are essentially re-randomizable non-interactive zero-knowledge (NIZK) proofs for circuit satisfiability, with the aforementioned CLR properties. We believe that our CLR-encodings, as well as our techniques to build them, may be of independent interest.