Generating Boolean Beaver triples has always been an intriguing problem. On one hand, Overdrive-type FHE-based solutions offers asympototically-good solutions, and for suitable field size the concrete efficiency is also considered state-of-the-art. On the other hand, the current best practice for generating authenticated Boolean Beaver triples remains MASCOT-type COT-based protocols, which has communication of \(O(N^2 m)\) for generating \(m\) triples among \(N\) parties.

I guess this is a follow-up of Ring-LPN PCG.

There has been a number of works (Bombar et al. 2024, 2023; Boyle et al. 2022, 2020b, 2020a) trying to change the status quo, with the ultimate goal of creating a concretely efficient end-to-end MPC protocol. I made some slides about them.

References

Bombar, Maxime, Dung Bui, Geoffroy Couteau, Alain Couvreur, Clément Ducros, and Sacha Servan-Schreiber. 2024. “FOLEAGE: \$mathbb\\F\\\_4\$OLE-Based Multi-Party Computation for Boolean Circuits.”
Bombar, Maxime, Geoffroy Couteau, Alain Couvreur, and Clément Ducros. 2023. “Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding.”
Boyle, Elette, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Lisa Kohl, Nicolas Resch, and Peter Scholl. 2022. “Correlated Pseudorandomness from Expand-Accumulate Codes.” In Advances in Cryptology – CRYPTO 2022, edited by Yevgeniy Dodis and Thomas Shrimpton, 13508:603–33. Cham: Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-15979-4_21.
Boyle, Elette, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Lisa Kohl, and Peter Scholl. 2020a. “Efficient Pseudorandom Correlation Generators from Ring-LPN.” In Advances in Cryptology – CRYPTO 2020, edited by Daniele Micciancio and Thomas Ristenpart, 12171:387–416. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-56880-1_14.
———. 2020b. “Correlated Pseudorandom Functions from Variable-Density LPN.” In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), 1069–80. Durham, NC, USA: IEEE. https://doi.org/10.1109/FOCS46700.2020.00103.