TY - GEN
T1 - An Algebraic Framework for Silent Preprocessing with Trustless Setup and Active Security
AU - Abram, Damiano
AU - Damgård, Ivan
AU - Orlandi, Claudio
AU - Scholl, Peter
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85141672418&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-15985-5_15
DO - 10.1007/978-3-031-15985-5_15
M3 - Article in proceedings
AN - SCOPUS:85141672418
SN - 978-3-031-15984-8
T3 - Lecture Notes in Computer Science
SP - 421
EP - 452
BT - Advances in Cryptology – CRYPTO 2022
A2 - Dodis, Yevgeniy
A2 - Shrimpton, Thomas
PB - Springer
CY - Cham
T2 - 42nd Annual International Cryptology Conference, CRYPTO 2022
Y2 - 15 August 2022 through 18 August 2022
ER -