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

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

*Corresponding author for this work

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearch

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.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2022
EditorsYevgeniy Dodis, Thomas Shrimpton
Number of pages32
Place of publicationCham
PublisherSpringer
Publication date2022
Pages421-452
ISBN (Print)978-3-031-15984-8
DOIs
Publication statusPublished - 2022
Event42nd Annual International Cryptology Conference, CRYPTO 2022 - Santa Barbara, United States
Duration: 15 Aug 202218 Aug 2022

Conference

Conference42nd Annual International Cryptology Conference, CRYPTO 2022
Country/TerritoryUnited States
CitySanta Barbara
Period15/08/202218/08/2022
SeriesLecture Notes in Computer Science
Volume13510
ISSN0302-9743

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