Paper 2024/429

FOLEAGE: $\mathbb{F}_4$OLE-Based Multi-Party Computation for Boolean Circuits

Maxime Bombar, Centrum Wiskunde & Informatica
Dung Bui, IRIF, Université Paris Cité
Geoffroy Couteau, CNRS, IRIF, Université Paris Cité
Alain Couvreur, French Institute for Research in Computer Science and Automation, Computer Science Laboratory of the École Polytechnique, Institut Polytechnique de Paris
Clément Ducros, IRIF, Université Paris Cité
Sacha Servan-Schreiber, Massachusetts Institute of Technology
Abstract

Secure Multi-party Computation (MPC) allows two or more parties to compute any public function over their privately-held inputs, without revealing any information beyond the result of the computation. Modern protocols for MPC generate a large amount of input-independent preprocessing material called multiplication triples, in an offline phase. This preprocessing can later be used by the parties to efficiently instantiate an input-dependent online phase computing the function. To date, the state-of-the-art secure multi-party computation protocols in the preprocessing model are tailored to secure computation of arithmetic circuits over large fields and require little communication in the preprocessing phase, typically O(N · m) to generate m triples among N parties. In contrast, when it comes to computing preprocessing for computations that are naturally represented as Boolean circuits, the state-of-the-art techniques have not evolved since the 1980s, and in particular, require every pair of parties to execute a large number of oblivious transfers before interacting to convert them to N-party triples, which induces an Ω(N^2 · m) communication overhead. In this paper, we introduce FOLEAGE, which addresses this gap by introducing an efficient preprocessing protocol tailored to Boolean circuits. FOLEAGE exhibits excellent performance: It generates m multiplication triples over F2 using only N · m + O(N^2 · log m) bits of communication for N-parties, and can concretely produce over 12 million triples per second in the 2-party setting on one core of a commodity machine. Our result builds upon an efficient Pseudorandom Correlation Generator (PCG) for multiplication triples over the field F4. Roughly speaking, a PCG enables parties to stretch a short seed into a large number of pseudorandom correlations non-interactively, which greatly improves the efficiency of the offline phase in MPC protocols. Our construction significantly outperforms the state-of-the-art, which we demonstrate via a prototype implementation. This is achieved by introducing a number of protocol-level, algorithmic-level, and implementation-level optimizations on the recent PCG construction of Bombar et al. (Crypto 2023) from the Quasi-Abelian Syndrome Decoding assumption.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
Preprint.
Keywords
Secure ComputationMPCPseudorandom Correlation GeneratorsPCGOblivious Linear EvaluationOLE
Contact author(s)
maxime bombar @ cwi nl
bui @ irif fr
couteau @ irif fr
alain couvreur @ inria fr
cducros @ irif fr
3s @ mit edu
History
2024-05-29: revised
2024-03-12: received
See all versions
Short URL
https://ia.cr/2024/429
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/429,
      author = {Maxime Bombar and Dung Bui and Geoffroy Couteau and Alain Couvreur and Clément Ducros and Sacha Servan-Schreiber},
      title = {{FOLEAGE}: $\mathbb{F}_4${OLE}-Based Multi-Party Computation for Boolean Circuits},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/429},
      year = {2024},
      url = {https://eprint.iacr.org/2024/429}
}
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