"Preview Talk" (by Team PANTHERIA) @ MPTS 2026, in reply to the NIST Threshold Call
Abstract. In this talk, we first describe the conventional (non-threshold) FHE cryptosystems already implemented in OpenFHE, Lattigo, and Poulpy, which serve as the basis for thresholdization. The following conventional FHE schemes are included: BFV, BGV, CGGI/TFHE, CKKS, DM/FHEW, and LMK+. All of these schemes are based on the hardness of (Ring) Learning With Errors and support various native homomorphic operations. Next, we summarize the thresholdized variants of BFV, BGV, and CKKS implemented in OpenFHE and Lattigo, which use homomorphic addition for distributed key generation and noise flooding for distributed decryption, in the passively secure model for the small and medium categories and dishonest majority. Then, we propose Th-(d)BFV, Th-FHEW, and Th-BGV as thresholdized extensions of (decomposed) BFV, LMK+, and BGV, respectively, that use a Multi-Party Computation (MPC)-based protocol for distributed decryption to support small lattice parameters and achieve active security in the small and medium categories for both dishonest and honest majority settings. We also propose an improved distributed key generation protocol for Th-FHEW, which minimizes the key generation noise. Moreover, we will consider the Laminate verifiable computation method to achieve active security for homomorphic evaluation in the Th-(d)BFV and Th-BGV
Joint work: Andreea Alexandru, Ahmad Al Badawi, Daniel Apon, Jean-Philippe Bossuat, Sylvain Chatel, Ben Fisch, Nicholas Genise, Shai Halevi, Loïs Huguenin, Guy Itzhaki, Andrey Kim, Yongwoo Lee, Zeyu Liu, Janmajaya Mall, Christian Mouchet, Carlo Pascoe, Chris Peikert, Kabir Peshawaria, Yuriy Polyakov, Saraswathy R.V., Sarabjeet Singh, Yongsoo Song, Eran Tromer, Vinod Vaikuntanathan, Vincent Zucca, Guy Zyskind.
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