Paper 2021/822

One-out-of-$q$ OT Combiners

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 $$-out-of-$$ OT combiners that are perfectly secure against active adversaries. Our combiners arise from secret sharing techniques. We show that given an $$-linear secret sharing scheme on a set of $$ participants and adversary structure $$, we can construct $$-server, $$-out-of-$$ OT combiners that are secure against an adversary corrupting either Alice and a set of servers in $$, or Bob and a set of servers $$ with $$. If the normalized total share size of the scheme is $$, then the resulting OT combiner requires $$ calls to OT protocols, and the total amount of bits exchanged during the protocol is $$. We also present a construction based on $$-out-of-$$ OT combiners that uses the protocol of Crépeau, Brassard and Robert (FOCS 1986). This construction provides smaller communication costs for certain adversary structures, such as threshold ones: For any prime power $$, there are $$-server, $$-out-of-$$ OT combiners that are perfectly secure against active adversaries corrupting either Alice or Bob, and a minority of the OT candidates, exchanging $$ bits in total.