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Title:
One-out-of-q OT Combiners
Authors: Oriol Farràs and Jordi Ribes-González
Abstract:In 1-out-of-q Oblivious Transfer (OT) protocols, a sender Alice is able to send one of q\ge 2 messages to a receiver Bob, all while being oblivious to which message was transferred. Moreover, the receiver learns only one of these messages. Oblivious Transfer combiners take n instances of OT protocols as input, and produce an OT protocol that is secure if sufficiently many of the n original OT instances are secure. We present new 1-out-of-q OT combiners that are perfectly secure against active adversaries. Our combiners arise from secret sharing techniques. We show that given an \mathbb{F}_q-linear secret sharing scheme on a set of n participants and adversary structure \mathcal{A}, we can construct n-server, 1-out-of-q OT combiners that are secure against an adversary corrupting either Alice and a set of servers in \mathcal{A}, or Bob and a set of servers B with \bar{B}\notin\mathcal{A}. If the normalized share size of the scheme is \ell, then the resulting OT combiner requires \ell calls to OT protocols, and the total amount of bits exchanged during the protocol is (q^2+q+1)\ell\log q. As a consequence of this result, for any prime power q\geq n we present n-server, 1-out-of-q OT combiners that are perfectly secure against active adversaries that corrupt either Alice or Bob, and also a minority of the OT candidates. The total amount of exchanged bits is (q^2+q+1)n\log q.
ePrint: https://eprint.iacr.org/2021/822
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