Secure Arithmetic Computation with Constant Computational Overhead

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

  • Benny Applebaum
  • ,
  • Ivan Damgård
  • Yuval Ishai
  • ,
  • Michael Nielsen
  • ,
  • Lior Zichron

We study the complexity of securely evaluating an arithmetic circuit over a finite field ð�”½ in the setting of secure two-party computation with semi-honest adversaries. In all existing protocols, the number of arithmetic operations per multiplication gate grows either linearly with log |ð�”½| or polylogarithmically with the security parameter. We present the first protocol that only makes a constant (amortized) number of field operations per gate. The protocol uses the underlying field ð�”½ as a black box, and its security is based on arithmetic analogues of well-studied cryptographic assumptions. Our protocol is particularly appealing in the special case of securely evaluating a “vector-OLE” function of the form ax+b, where x ∈ ð�”½ is the input of one party and a, b ∈ ð�”½ w are the inputs of the other party. In this case, which is motivated by natural applications, our protocol can achieve an asymptotic rate of 1/3 (i.e., the communication is dominated by sending roughly 3w elements of ð�”½). Our implementation of this protocol suggests that it outperforms competing approaches even for relatively small fields ð�”½ and over fast networks. Our technical approach employs two new ingredients that may be of independent interest. First, we present a general way to combine any linear code that has a fast encoder and a cryptographic (“LPN-style”) pseudorandomness property with another linear code that supports fast encoding and erasure-decoding, obtaining a code that inherits both the pseudorandomness feature of the former code and the efficiency features of the latter code. Second, we employ local arithmetic pseudo-random generators, proposing arithmetic generalizations of boolean candidates that resist all known attacks.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2017 - 37th Annual International Cryptology Conference, Proceedings
EditorsHovav Shacham, Jonathan Katz
Number of pages32
Volume10401
PublisherSpringer VS
Publication year1 Jan 2017
Pages223-254
ISBN (print)9783319636870
DOIs
Publication statusPublished - 1 Jan 2017
Event37th Annual International Cryptology Conference, CRYPTO 2017 - Santa Barbara, United States
Duration: 20 Aug 201724 Aug 2017

Conference

Conference37th Annual International Cryptology Conference, CRYPTO 2017
LandUnited States
BySanta Barbara
Periode20/08/201724/08/2017
SeriesLecture Notes in Computer Science
Volume10401
ISSN0302-9743

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