Abstract. Threshold Fully Homomorphic Encryption (Th-FHE) is an extension of Fully Homomorphic Encryption (FHE) where the decryption capacity is splitted across multiple parties. As shown by Boneh et al [CRYPTO'18], Th-FHE may be used to thresholdize a cryptographic function CF, by publicly providing Th-FHE encryptions of CF's secrets, letting each party homomorphically evaluating CF and running the Th-FHE decryption protocol. In this presentation, we will show how to transform the CKKS FHE scheme of Cheon et al [ASIACRYPT'17] into an efficient Th-FHE, and use it to thresholdize several cryptographic functions. Concerning the Th-FHE version of CKKS, we will first highlight the performance of CryptoLab's HEaaN library, both for approximate and exact computations. We will then describe a distributed key generation algorithm to obtain a Th-FHE parametrization that is as efficient as the best FHE parametrizations, without relying on a trusted dealer. Finally, we will describe how to efficiently perform noise flooding in threshold decryption. In the second part of the talk, we will highlight applications of threshold CKKS: one-round threshold AES128 in < 0.1s, two-round threshold Dilithium in <1s and near real-time 1:N identification based on irises for millions of users.
Based on works with: Jung Hee Cheon, Hyeongmin Choe, Jincheol Ha, Guillaume Hanrot, Jaehyung Kim, Seonhong Min, Jai Hyun Park, Alain Passelègue, Damien Stehlé, Elias Suvanto. Made possible with CryptoLab's HEaaN library.
Suggested reading: Leveraging Discrete CKKS to Bootstrap in High Precision (ia.cr/2025/1786)
