One-Out-of-<i>q</i> OT Combiners

Identifier:  imarina:9366242

Handle: https://hdl.handle.net/20.500.11797/imarina9366242

Authors:  Farras, Oriol; Ribes-Gonzalez, Jordi

Abstract:
In 1-out-of- q Oblivious Transfer (OT) protocols, a sender Alice is able to send one of q >= 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 Fq -linear secret sharing scheme on a set of n participants and adversary structure A , we can construct an n -server, 1-out-of- q OT combiner that is secure against an adversary corrupting either Alice and a set of servers in A , or Bob and a set of servers B with B is not an element of A . If the normalized total 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; logq . We also present a construction based on 1-out-of-2 OT combiners that uses the protocol of Cr & eacute;peau, Brassard and Robert (FOCS 1986). This construction provides smaller communication costs for certain adversary structures, such as threshold ones: For any prime power q >= n , there are n -server, 1-out-of- q OT combiners that are perfectly secure against active adversaries corrupting either Alice or Bob, and a minority of the OT candidates, exchanging O(qnlogq) bits in total.