TY - GEN
T1 - Multi-party Homomorphic Secret Sharing and Sublinear MPC from Sparse LPN
AU - Dao, Quang
AU - Ishai, Yuval
AU - Jain, Aayush
AU - Lin, Huijia
N1 - Publisher Copyright:
© 2023, International Association for Cryptologic Research.
PY - 2023
Y1 - 2023
N2 - Over the past few years, homomorphic secret sharing (HSS) emerged as a compelling alternative to fully homomorphic encryption (FHE), due to its feasibility from an array of standard assumptions and its potential efficiency benefits. However, all known HSS schemes, with the exception of schemes built from FHE or indistinguishability obfuscation (iO), can only support two parties. In this work, we give the first construction of a multi-party HSS scheme for a non-trivial function class, from an assumption not known to imply FHE. In particular, we construct an HSS scheme for an arbitrary number of parties with an arbitrary corruption threshold, supporting evaluations of multivariate polynomials of degree log / log log over arbitrary finite fields. As a consequence, we obtain a secure multiparty computation (MPC) protocol for any number of parties, with (slightly) sub-linear per-party communication of roughly O(S/ log log S) bits when evaluating a layered Boolean circuit of size S. Our HSS scheme relies on the sparse Learning Parity with Noise (LPN) assumption, a standard variant of LPN with a sparse public matrix that has been studied and used in prior works. Thanks to this assumption, our construction enjoys several unique benefits. In particular, it can be built on top of any linear secret sharing scheme, producing noisy output shares that can be error-corrected by the decoder. This yields HSS for low-degree polynomials with optimal download rate. Unlike prior works, our scheme also has a low computation overhead in that the per-party computation of a constant degree polynomial takes O(M) work, where M is the number of monomials.
AB - Over the past few years, homomorphic secret sharing (HSS) emerged as a compelling alternative to fully homomorphic encryption (FHE), due to its feasibility from an array of standard assumptions and its potential efficiency benefits. However, all known HSS schemes, with the exception of schemes built from FHE or indistinguishability obfuscation (iO), can only support two parties. In this work, we give the first construction of a multi-party HSS scheme for a non-trivial function class, from an assumption not known to imply FHE. In particular, we construct an HSS scheme for an arbitrary number of parties with an arbitrary corruption threshold, supporting evaluations of multivariate polynomials of degree log / log log over arbitrary finite fields. As a consequence, we obtain a secure multiparty computation (MPC) protocol for any number of parties, with (slightly) sub-linear per-party communication of roughly O(S/ log log S) bits when evaluating a layered Boolean circuit of size S. Our HSS scheme relies on the sparse Learning Parity with Noise (LPN) assumption, a standard variant of LPN with a sparse public matrix that has been studied and used in prior works. Thanks to this assumption, our construction enjoys several unique benefits. In particular, it can be built on top of any linear secret sharing scheme, producing noisy output shares that can be error-corrected by the decoder. This yields HSS for low-degree polynomials with optimal download rate. Unlike prior works, our scheme also has a low computation overhead in that the per-party computation of a constant degree polynomial takes O(M) work, where M is the number of monomials.
UR - http://www.scopus.com/inward/record.url?scp=85173062582&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-38545-2_11
DO - 10.1007/978-3-031-38545-2_11
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AN - SCOPUS:85173062582
SN - 9783031385445
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 315
EP - 348
BT - Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings, Part II
A2 - Handschuh, Helena
A2 - Lysyanskaya, Anna
T2 - Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings
Y2 - 20 August 2023 through 24 August 2023
ER -