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Gradual GRAM and Secure Computation for RAM Programs

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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

Despite the fact that the majority of applications encountered in practice today are captured more efficiently by RAM programs, the area of secure two-party computation (2PC) has seen tremendous improvement mostly when the function is represented by Boolean circuits. One of the most studied objects in this domain is garbled circuits. Analogously, garbled RAM (GRAM) provide similar security guarantees for RAM programs with applications to constant round 2PC. In this work we consider the notion of gradual GRAM which requires no memory garbling algorithm. Our approach provides several qualitative advantages over prior works due to the conceptual similarity to the analogue garbling mechanism for Boolean circuits. We next revisit the GRAM construction from [11] and improve it in two orthogonal aspects: match it directly with tree-based ORAMs and explore its consistency with gradual ORAM.

C. Hazay—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.

    While some of the computation of these garbled memory algorithms can be carried out offline, it requires storing a large state that grows with the memory size.

  2. 2.

    Informally, the transformation encrypts the memory elements and apply an ORAM construction to hide the access pattern.

  3. 3.

    Note that this construction suffers from a circularity issue in its security analysis; see [13] for a detailed discussion.

  4. 4.

    This is because the translation mapping in [11] involves a PRF evaluation per stored bit.

  5. 5.

    We note that our description is informal. Specifically, the keys are encrypted bit-by-bit implying \(2\kappa \) ciphertexts, as each key is of size \(\kappa \).

  6. 6.

    We use the variable \(\mathsf {mode}\) to interchange between \(\mathsf{{Read/Write}}\) and \(\mathsf {Eviction}\). We abuse notation and denote by \(1-\mathsf {mode}\) the “opposite” (namely, the other) value of \(\mathsf {mode}\).

  7. 7.

    The syntax \(\overline{\mathsf {type}}\) refers to the opposite of the variable \(\mathsf {type}\). For example, if \(\mathsf {type}=\mathsf {left}\) then \(\overline{\mathsf {type}}=\mathsf {right}\).

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Authors and Affiliations

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

    Carmit Hazay & Mor Lilintal

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  1. Carmit Hazay
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  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

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

    Vladimir Kolesnikov

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Hazay, C., Lilintal, M. (2020). Gradual GRAM and Secure Computation for RAM Programs. 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_12

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