Welcome to the resource topic for 2017/617
Title:
Secure Arithmetic Computation with Constant Computational Overhead
Authors: Benny Applebaum, Ivan Damgård, Yuval Ishai, Michael Nielsen, Lior Zichron
Abstract:We study the complexity of securely evaluating an arithmetic circuit over a finite field F 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 |F| 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 F 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 $\vec{a}x+\vec{b}$, where $x\in F$ is the input of one party and $\vec{a},\vec{b}\in F^w$ 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 $F$). Our implementation of this protocol suggests that it outperforms competing approaches even for relatively small fields $F$ 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.
ePrint: https://eprint.iacr.org/2017/617
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