Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation

Abstract

Abstract. We show that if a set of players hold shares of a value a ∈ Fp for some prime p (where the set of shares is written [a]p), it is possible to compute, in constant rounds and with unconditional security, sharings of the bits of a, i.e., compute sharingsOur protocol is secure against active adversaries and works for any linear secret sharing scheme with a multiplication protocol. The complexity of our protocol is O( log ) invocations of the multiplication protocol for the underlying secret sharing scheme, carried out in O(1) rounds.This result immediately implies solutions to other long-standing open problems such as constant-rounds and unconditionally secure protocols for deciding whether a shared number is zero, comparing shared numbers, raising a shared number to a shared exponent and reducing a shared number modulo a shared modulus.

Efficient, Oblivious Data Structures for MPC

“…For fields of characteristic two, EQZ can be implemented by computing the logical OR of the bit decomposition of a. Generally, a simple protocol requires O( ) invocations in O(log ) rounds, and PreMulC by Damgård et al [8] allows for constant rounds. However, the constant-round version turns out to be slower in our implementation.…”

“…Catrina and de Hoogh [6] presented an implementation that requires O( ) invocations in O(log ) rounds, while Damgård et al [8] showed that a constant-round implementation is feasible. Again, the constant-round implementation is slower in our implementation.…”

“…In GF(2 n ) this works as usual, and in GF(p) this can be done by a constant-round protocol by Damgård et al [8].…”

“…In GF(p), however, we can no longer use the efficient protocol of Catrina and de Hoogh [6], since this requires κ extra bits of room in the field element to achieve statistical security 2 −κ . We use the unconditionally secure protocol of Damgård et al [8] to do this to do this in a constant number of rounds.…”

Verifiable Computation in Multiparty Protocols with Honest Majority

“…While the generic construction is expensive in computation and communication, the result has sparked research activities in secure multiparty computation (SMC), with results that are impressive both performance-wise [9,11,17,20], as well as in the variety of concrete problems that have been tackled [10,14,16,21]. From the start, two kinds of adversaries -passive and active -have been considered in the construction of SMC protocols, with highest performance and the greatest variety achieved for protocol sets secure only against passive adversaries.…”