### An Algebraic Framework for Silent Preprocessing with Trustless Setup and Active Security

##### Abstract

Recently, number-theoretic assumptions including DDH, DCR and QR have been used to build powerful tools for secure computation, in the form of homomorphic secret-sharing (HSS), which leads to secure two-party computation protocols with succinct communication, and pseudorandom correlation functions (PCFs), which allow non-interactive generation of a large quantity of correlated randomness. In this work, we present a group-theoretic framework for these classes of constructions, which unifies their approach to computing distributed discrete logarithms in various groups. We cast existing constructions in our framework, and also present new constructions, including one based on class groups of imaginary quadratic fields. This leads to the first construction of two-party homomorphic secret sharing for branching programs from class group assumptions. Using our framework, we also obtain pseudorandom correlation functions for generating oblivious transfer and vector-OLE correlations from number-theoretic assumptions. These have a trustless, public-key setup when instantiating our framework using class groups. Previously, such constructions either needed a trusted setup in the form of an RSA modulus with unknown factorisation, or relied on multi-key fully homomorphic encryption from the learning with errors assumption. We also show how to upgrade our constructions to achieve active security using appropriate zero-knowledge proofs. In the random oracle model, this leads to a one-round, actively secure protocol for setting up the PCF, as well as a 3-round, actively secure HSS-based protocol for secure two-party computation of branching programs with succinct communication.

Note: Updated DXDH assumption

Available format(s)
Category
Cryptographic protocols
Publication info
A major revision of an IACR publication in CRYPTO 2022
Keywords
silent preprocessing MPC HSS PCF OT VOLE class groups
Contact author(s)
damiano abram @ cs au dk
ivan @ cs au dk
orlandi @ cs au dk
peter scholl @ cs au dk
History
2022-06-14: revised
See all versions
Short URL
https://ia.cr/2022/363

CC BY

BibTeX

@misc{cryptoeprint:2022/363,
author = {Damiano Abram and Ivan Damgård and Claudio Orlandi and Peter Scholl},
title = {An Algebraic Framework for Silent Preprocessing with Trustless Setup and Active Security},
howpublished = {Cryptology ePrint Archive, Paper 2022/363},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/363}},
url = {https://eprint.iacr.org/2022/363}
}

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