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International Symposium on Cyber Security, Cryptology, and Machine Learning

CSCML 2022: Cyber Security, Cryptology, and Machine Learning pp 408–427Cite as

A Linear-Time 2-Party Secure Merge Protocol

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13301))

Abstract

We present a linear-time, space and communication data-oblivious algorithm for securely merging two private, sorted lists into a single sorted, secret-shared list in the two party setting. Although merging two sorted lists can be done insecurely in linear time, previous secure merge algorithms all require super-linear time and communication. A key feature of our construction is a novel method to obliviously traverse permuted lists in sorted order. Our algorithm only requires black-box use of the underlying Additively Homomorphic cryptosystem and generic secure computation schemes for comparison and equality testing.

B. H. Falk, R. Nema and R. Ostrovsky—Work done while consulting for Stealth Software Technologies, Inc.

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Notes

  1. 1.

    Since \(b_0 = \lnot b_1\) at every iteration after the first, we could increase efficiency by storing only a single bit, but the exposition is simpler if we forego this minor optimization.

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Authors and Affiliations

  1. University of Pennsylvania, Philadelphia, USA

    Brett Hemenway Falk

  2. UCLA, Los Angeles, USA

    Rohit Nema & Rafail Ostrovsky

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  1. Brett Hemenway Falk
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  2. Rohit Nema
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  3. Rafail Ostrovsky
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Correspondence to Rohit Nema .

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Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Shlomi Dolev

  2. University of Maryland, College Park, MD, USA

    Jonathan Katz

  3. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Amnon Meisels

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Falk, B.H., Nema, R., Ostrovsky, R. (2022). A Linear-Time 2-Party Secure Merge Protocol. In: Dolev, S., Katz, J., Meisels, A. (eds) Cyber Security, Cryptology, and Machine Learning. CSCML 2022. Lecture Notes in Computer Science, vol 13301. Springer, Cham. https://doi.org/10.1007/978-3-031-07689-3_30

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