International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Efficient Perfectly Secure Computation with Optimal Resilience

Ittai Abraham
Gilad Asharov
Avishay Yanai
DOI: 10.1007/s00145-022-09434-2
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Abstract: Secure computation enables n mutually distrustful parties to compute a function over their private inputs jointly. In 1988, Ben-Or, Goldwasser, and Wigderson (BGW) proved that any function can be computed with perfect security in the presence of a malicious adversary corrupting at most $$t< n/3$$ t < n / 3 parties. After more than 30 years, protocols with perfect malicious security, and round complexity proportional to the circuit’s depth, still require (verifiably) sharing a total of $$O(n^2)$$ O ( n 2 ) values per multiplication. In contrast, only O ( n ) values need to be shared per multiplication to achieve semi-honest security. Sharing $$\Omega (n)$$ Ω ( n ) values for a single multiplication seems to be the natural barrier for polynomial secret-sharing-based multiplication. In this paper, we construct a new secure computation protocol with perfect, optimal resilience and malicious security that incurs (verifiably) sharing O ( n ) values per multiplication. Our protocol requires a constant number of rounds per multiplication. Like BGW, it has an overall round complexity that is proportional only to the multiplicative depth of the circuit. Our improvement is obtained by a novel construction for weak VSS for polynomials of degree 2t , which incurs the same communication and round complexities as the state-of-the-art constructions for VSS for polynomials of degree t . Our second contribution is a method for reducing the communication complexity for any depth 1 sub-circuit to be proportional only to the size of the input and output (rather than the size of the circuit). This implies protocols with sub-linear communication complexity (in the size of the circuit) for perfectly secure computation for important functions like matrix multiplication.
  title={Efficient Perfectly Secure Computation with Optimal Resilience},
  journal={Journal of Cryptology},
  author={Ittai Abraham and Gilad Asharov and Avishay Yanai},