International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Paper: Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography

Authors:
Ivan Damgård
Mikkel Krøigaard
Yuval Ishai
Download:
URL: http://eprint.iacr.org/2010/106
Search ePrint
Search Google
Abstract: We study the following two related questions: - What are the minimal computational resources required for general secure multiparty computation in the presence of an honest majority? - What are the minimal resources required for two-party primitives such as zero-knowledge proofs and general secure two-party computation? We obtain a nearly tight answer to the first question by presenting a perfectly secure protocol which allows $n$ players to evaluate an arithmetic circuit of size $s$ by performing a total of $\O(s\log s\log^2 n)$ arithmetic operations, plus an additive term which depends (polynomially) on $n$ and the circuit depth, but only logarithmically on $s$. Thus, for typical large-scale computations whose circuit width is much bigger than their depth and the number of players, the amortized overhead is just polylogarithmic in $n$ and $s$. The protocol provides perfect security with guaranteed output delivery in the presence of an active, adaptive adversary corrupting a $(1/3-\epsilon)$ fraction of the players, for an arbitrary constant $\epsilon>0$ and sufficiently large $n$. The best previous protocols in this setting could only offer computational security with a computational overhead of $\poly(k,\log n,\log s)$, where $k$ is a computational security parameter, or perfect security with a computational overhead of $\O(n\log n)$. We then apply the above result towards making progress on the second question. Concretely, under standard cryptographic assumptions, we obtain zero-knowledge proofs for circuit satisfiability with $2^{-k}$ soundness error in which the amortized computational overhead per gate is only {\em polylogarithmic} in $k$, improving over the $\omega(k)$ overhead of the best previous protocols. Under stronger cryptographic assumptions, we obtain similar results for general secure two-party computation.
BibTeX
@misc{eprint-2010-23007,
  title={Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / multiparty computation},
  url={http://eprint.iacr.org/2010/106},
  note={Full version of Eurocrypt 2010 paper mk@cs.au.dk 14666 received 26 Feb 2010, last revised 26 Feb 2010},
  author={Ivan Damgård and Mikkel Krøigaard and Yuval Ishai},
  year=2010
}