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Low Communication Threshold FHE from Standard (Module-)LWE

by Hiroki Okada - 2026.02.05

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Meetup 083

Abstract

Threshold fully homomorphic encryption (ThFHE) is a multi-party extension of FHE; any subset of at least T out of N parties can decrypt the ciphertexts by combining their decryption shares. Recently, Passelègue and Stehlé (Asiacrypt 2024) presented a ThFHE scheme with polynomially short decryption shares from the “known-norm” variant of learning with errors (LWE) assumption, in which the norm of the secret key is leaked to the adversary. While known-norm LWE is reduced from standard LWE, its module extension, known-covariance module-LWE (MLWE), lacks a known reduction from standard MLWE. Hence, extending their ThFHE scheme to the MLWE-based construction remains an open question.

​In this paper, we address this open problem: We construct a ThFHE scheme with polynomially small decryption shares from standard LWE/MLWE. Our core technique, which we call noise padding, eliminates the need of known-norm variants of LWE. We distribute shares of a padding noise and use them to adjust the distribution of decryption noise so that no information about the secret key is leaked. Furthermore, our ThFHE efficiently realizes arbitrary T-out-of-N threshold decryption via simple Shamir secret sharing instead of {0,1}-linear secret sharing. Hence, the sizes of the keys, ciphertexts and decryption shares in our scheme are compact: they are O(1) w.r.t. the number of parties N.

About the speaker

Hiroki Okada is a researcher at KDDI Research.

​His research interests include lattice-based cryptography and especially FHE.

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