Multi-party computation with conversion of secret sharing

Abstract

Abstract. Classical results in unconditionally secure multi-party computation (MPC) protocols with a passive adversary indicate that every n-variate function can be computed by n participants, such that no set of size t < n/2 participants learns any additional information other than what they could derive from their private inputs and the output of the protocol. We study unconditionally secure MPC protocols in the presence of a passive adversary in the trusted setup ('semi-ideal') model, in which the participants are supplied with some auxiliary information (which is random and independent from the participant inputs) ahead of the protocol execution (such information can be purchased as a "commodity" well before a run of the protocol). We present a new MPC protocol in the trusted setup model, which allows the adversary to corrupt an arbitrary number t < n of participants. Our protocol makes use of a novel subprotocol for converting an additive secret sharing over a field to a multiplicative secret sharing, and can be used to securely evaluate any n-variate polynomial G over a field F , with inputs restricted to non-zero elements of F . The communication complexity of our protocol is O(ℓ · n 2 ) field elements, where ℓ is the number of non-linear monomials in G. Previous protocols in the trusted setup model require communication proportional to the number of multiplications in an arithmetic circuit for G; thus, our protocol may offer savings over previous protocols for functions with a small number of monomials but a large number of multiplications.

Secure multi-party computation with a quantum manner

“…While the computation of linear function is straightforward, evaluating non-linear terms like x i × x j is subtler. To compute the monomials, each participant needs to receive additional multiplicative shares from other participants using a multiplicative (n, n) secret sharing, so that they could convert multiplicative shares to additive shares [30]. Such a procedure is given in algorithm 1.…”

Secure joint Bitcoin trading with partially blind fuzzy signatures

“…Specifically, in addition to the participant threshold to be satisfied, a transaction can be successful only if r (< t − 1) privileged participants agree the transaction. In the following, we investigate the joint Bitcoin trading in this scenario and present a variant to cater for the privileged participants included in the threshold (Ghodosi et al 2012;Tang 2007). We first describe the "key generation" procedure.…”

FPGA Implementations of SPRING

“…For this purpose, we use the technique suggested by Ghodosi et al in [13]. 4 This procedure is applied for each entry independently.…”

“…The side-channel literature usually refers to[12] for such a task, but the algorithms in this reference are quite sequential. We focus on the approach suggested in[13] which seems easier to parallelize and simpler in our hardware context.…”