### Simpler Statistically Sender Private Oblivious Transfer from Ideals of Cyclotomic Integers

Daniele Micciancio and Jessica Sorrell

##### Abstract

We present a two-message oblivious transfer protocol achieving statistical sender privacy and computational receiver privacy based on the RLWE assumption for cyclotomic number fields. This work improves upon prior lattice-based statistically sender-private oblivious transfer protocols by reducing the total communication between parties by a factor $O(n\log q)$ for transfer of length $O(n)$ messages. Prior work of Brakerski and Döttling uses transference theorems to show that either a lattice or its dual must have short vectors, the existence of which guarantees lossy encryption for encodings with respect to that lattice, and therefore statistical sender privacy. In the case of ideal lattices from embeddings of cyclotomic integers, the existence of one short vector implies the existence of many, and therefore encryption with respect to either a lattice or its dual is guaranteed to lose" more information about the message than can be ensured in the case of general lattices. This additional structure of ideals of cyclotomic integers allows for efficiency improvements beyond those that are typical when moving from the generic to ideal lattice setting, resulting in smaller message sizes for sender and receiver, as well as a protocol that is simpler to describe and analyze.

Available format(s)
Category
Cryptographic protocols
Publication info
Published elsewhere. Asiacrypt 2020
Keywords
oblivious transfer
Contact author(s)
jlsorrel @ eng ucsd edu
daniele @ cs ucsd edu
History
Short URL
https://ia.cr/2020/1413

CC BY

BibTeX

@misc{cryptoeprint:2020/1413,
author = {Daniele Micciancio and Jessica Sorrell},
title = {Simpler Statistically Sender Private Oblivious Transfer from Ideals of Cyclotomic Integers},
howpublished = {Cryptology ePrint Archive, Paper 2020/1413},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/1413}},
url = {https://eprint.iacr.org/2020/1413}
}

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