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

Damiano Abram*, Ivan Damgård, Claudio Orlandi, Peter Scholl

*Corresponding author af dette arbejde

Publikation: Bidrag til bog/antologi/rapport/proceedingKonferencebidrag i proceedingsForskning

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.

OriginalsprogEngelsk
TitelAdvances in Cryptology – CRYPTO 2022
RedaktørerYevgeniy Dodis, Thomas Shrimpton
Antal sider32
UdgivelsesstedCham
ForlagSpringer
Publikationsdato2022
Sider421-452
ISBN (Trykt)978-3-031-15984-8
DOI
StatusUdgivet - 2022
Begivenhed42nd Annual International Cryptology Conference, CRYPTO 2022 - Santa Barbara, USA
Varighed: 15 aug. 202218 aug. 2022

Konference

Konference42nd Annual International Cryptology Conference, CRYPTO 2022
Land/OmrådeUSA
BySanta Barbara
Periode15/08/202218/08/2022
NavnLecture Notes in Computer Science
Vol/bind13510
ISSN0302-9743

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