Secure arithmetic computation with constant computational overhead

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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�”½w 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
PublisherSpringer Verlag
Number of pages32
ISBN (Print)9783319636870
StatePublished - 2017
Event37th Annual International Cryptology Conference, CRYPTO 2017 - Santa Barbara, United States
Duration: 20 Aug 201724 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10401 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference37th Annual International Cryptology Conference, CRYPTO 2017
Country/TerritoryUnited States
CitySanta Barbara


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