Paper 2021/822

One-out-of-$q$ OT Combiners

Oriol Farràs
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 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.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Minor revision. Transactions on Information Theory
DOI
10.1109/TIT.2023.3340294
Keywords
Oblivious transferOT combinersSecret sharing schemes
Contact author(s)
oriol farras @ urv cat
jordi ribes @ urv cat
History
2023-12-14: last of 4 revisions
2021-06-16: received
See all versions
Short URL
https://ia.cr/2021/822
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2021/822,
      author = {Oriol Farràs and Jordi Ribes-González},
      title = {One-out-of-$q$ OT Combiners},
      howpublished = {Cryptology ePrint Archive, Paper 2021/822},
      year = {2021},
      doi = {10.1109/TIT.2023.3340294},
      note = {\url{https://eprint.iacr.org/2021/822}},
      url = {https://eprint.iacr.org/2021/822}
}
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