One-Out-of-q OT Combiners
Oriol Farràs, Jordi Ribes-González · IEEE Transactions on Information Theory · 2023
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 an$n$-server, 1-out-of-$q$OT combiner that is secure against an adversary corrupting either Alice and a set of servers in$\mathcal {A}$, or Bob and a set of servers$B$with$\bar {B} otin \mathcal {A}$. 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 \log q$. We also present a construction based on 1-out-of-2 OT combiners that uses the protocol of Crépeau, Brassard and Robert (FOCS 1986). This construction provides smaller communication costs for certain adversary structures, such as threshold ones: For any prime power$q\geq 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(qn\log q)$bits in total.