Paper 2026/1058

Efficient MPC-Based Modulus Conversion for Threshold FHE Decryption

Sebastian Kolby, Aarhus University

Claudio Orlandi, Aarhus University

Stanislas Pawlak, Aarhus University

Abstract

We present new techniques for converting secret-shared values between different moduli in arithmetic MPC, without relying on bit decomposition. More concretely, our protocols convert a sharing \([x]_q\) over a source modulus \(q\) into a sharing \([x]_t\) over a target modulus \(t\), under a mild bound on the size of \(x\). We give three variants: a particularly simple protocol for power-of-two moduli, a protocol for arbitrary source modulus and prime target modulus, and a general protocol for arbitrary target modulus via an intermediate prime modulus. All variants use only a constant number of openings and a small amount of preprocessing. We present them in the arithmetic black box model, so they can be instantiated on top of any MPC protocol supporting basic modular arithmetic. As a main application, we use these techniques to construct efficient threshold decryption protocols for lattice-based fully homomorphic encryption (FHE), including BFV, BGV, and related schemes. The resulting protocols are special-purpose MPC protocols with a small constant number of rounds. They avoid noise flooding, allowing the parameters of the underlying FHE scheme to be chosen without making room for additional decryption noise. The resulting protocols achieve statistical UC security against malicious adversaries. We improve substantially on previous work on MPC-based threshold FHE decryption: as a concrete example, the state-of-the-art protocol by Zyskind et al. (ACM CCS 2025) implements decryption of the BFV scheme (with ciphertext modulus $2^{64}$), using about 17.000 bits of preprocessed correlated randomness, while we need only 63.

@misc{cryptoeprint:2026/1058,
      author = {Ivan Damgård and Sebastian Kolby and Claudio Orlandi and Stanislas Pawlak},
      title = {Efficient {MPC}-Based Modulus Conversion for Threshold {FHE} Decryption},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1058},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1058}
}