{"id":340979,"date":"2016-12-24T12:38:28","date_gmt":"2016-12-24T20:38:28","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=340979"},"modified":"2018-10-16T20:49:33","modified_gmt":"2018-10-17T03:49:33","slug":"interactive-proofs-continual-memory-leakage","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/interactive-proofs-continual-memory-leakage\/","title":{"rendered":"Interactive Proofs under Continual Memory Leakage"},"content":{"rendered":"

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<\/em>. 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\u201911) 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.<\/p>\n

Towards that end, we define the notion of non-transferable proofs for all languages in N<\/em> P<\/em>. In such proofs, instead of receiving w<\/em> as input, the prover will receive an \u201cencoding\u201d of the witness w<\/em> such that the encoding is sufficient to prove the validity of x<\/em>; further, this encoding can be \u201cupdated\u201d to a fresh new encoding for the next execution. We then require that if (x<\/em>,w<\/em>) are sampled from a \u201chard\u201d distribution, then no PPT adversary A<\/em>*<\/sup> can gain the ability to prove x<\/em> (on its own) to an honest verifier, even if A<\/em>*<\/sup> has participated in polynomially many interactive proof executions (with leakage) with an honest prover whose input is (x<\/em>,w<\/em>). Non-transferability is a strong security guarantee which suffices for many cryptographic applications (and in particular, implies witness hiding).<\/p>\n

We show how to construct non-transferable proofs for all languages in N<\/em> P<\/em> which can tolerate leaking a constant fraction of prover\u2019s secret-state during each execution. Our construction is in the common reference string<\/em> (CRS) model. To obtain our results, we build a witness-encoding scheme which satisfies the following continual-leakage-resilient (CLR) properties:<\/p>\n
\n
    \n
  • \n

    The encodings can be randomized to yield a fresh new encoding,<\/p>\n<\/li>\n

  • \n

    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<\/em>, can output a valid encoding provided that the witness w<\/em> along with its corresponding input instance x<\/em> were sampled from a hard distribution.<\/p>\n<\/li>\n<\/ul>\n<\/div>\n

    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.<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

    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 […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Springer Berlin Heidelberg","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"34th Annual Cryptology Conference","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"164-182","msr_page_range_start":"164","msr_page_range_end":"182","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"34th Annual Cryptology 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