Paper 2026/1627

Adaptively CCA-Secure Threshold Decryption from Lattices with Polynomial Modulus

Abstract

Threshold Decryption (TD) enables a set of decryptors, each holding a secret key share, to collaboratively decrypt ciphertexts. In this paper, we resolve the open problem raised by Devevey et al. [PKC 2021] of constructing an adaptively secure TD with polynomial modulus from lattices. As identified by Hwang et.al. [ePrint 2026/1585], solving this open problem is a particularly challenging task. The most challenging part is how to limit the leakage of secret key shares from decryption queries while keeping the modulus a polynomial. In this paper, we resolve the above open problem with two TD schemes TD1, TD2 from lattices in the random oracle model. -- TD1 is a non-interactive TD scheme achieving adaptive CCA-security with polynomial modulus for a small number of decryptors and bounded decryption queries. It can be extended to achieve robustness and works well in the asynchronous settings. -- TD2 is a non-interactive TD scheme achieving adaptive CCA-security with polynomial modulus for bounded decryption queries. Compared with TD1, it supports any polynomial number of decryptors and works well in the synchronous settings. To our best knowledge, our TD1 and TD2 are the first non-interactive TD schemes achieving adaptive security and polynomial modulus from lattices. The core techniques behind our schemes include the polynomial noise flooding technique and the coupled refined Leftover Hash Lemma (LHL) working for adaptive noisy linear leakage, which may be of independent interest.