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Multi-clients Verifiable Computation via Conditional Disclosure of Secrets

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Security and Cryptography for Networks (SCN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12238))

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Abstract

In this paper, we explore the connection between two-party conditional disclosure of secrets (CDS) and verifiable computation. Here, the integrity mechanism underlying CDS is leveraged to ensure two-clients verifiable computation, where the computation is outsourced to an external server by two clients that share the input to the function. Basing integrity on CDS enjoys several significant advantages such as non-interactivity, constant rate communication complexity, a simple verification procedure, easily batched, and more.

In this work, we extend the definition of plain CDS, considering two additional security properties of privacy and obliviousness that respectively capture input and output privacy. We then show that these extended notions of CDS are useful for designing secure two-party protocols in the presence of an untrusted third party.

We complement the above with a sequence of new CDS constructions for a class of predicates of interest, including private set-intersection (PSI) and set-union cardinality, comparison, range predicate, and more. Based on these constructions we design new non-interactive constant-rate protocols for comparing two strings based on symmetric-key cryptography, and without requiring bit-decomposition. We additionally design new protocols for PSI cardinality and PSI based on recent work by Le, Ranellucci, and Gordon (CCS 2019) with similar advantages.

C. Hazay—This work is supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, and by ISF grant No. 1316/18.

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Notes

  1. 1.

    We measure the upload rate as the ratio between the size of the encoded messages and the inputs. We further define the download rate by the ratio between the size of \(f(x_1,x_2)\) and s.

  2. 2.

    Loosely speaking, a \(\varSigma \)-protocol is a 3-round public-coin interactive proof for an \(\textsf {NP}\) relation, for which there exists an extractor that extracts the witness upon rewinding the prover. We require an additional transcript verifiability property that is leveraged for achieving correctness against malicious input encoding of Alice and Bob, going beyond semi-honest security.

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Authors and Affiliations

  1. Bar-Ilan University, Ramat-Gan, Israel

    Rishabh Bhadauria & Carmit Hazay

Authors
  1. Rishabh Bhadauria
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  2. Carmit Hazay
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Correspondence to Rishabh Bhadauria or Carmit Hazay .

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Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

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Bhadauria, R., Hazay, C. (2020). Multi-clients Verifiable Computation via Conditional Disclosure of Secrets. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_8

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  • DOI: https://doi.org/10.1007/978-3-030-57990-6_8

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