An efficient rejection-free threshold ring signature from lattices and its application in receipt-free cloud e-voting

The threshold ring signature is a generalization of the ring signature. It confirms that $t$-out-of-$N$ members are signing anonymously in a set of $N$ users, and thus it can be well applied to e-voting. In this paper, we present a more efficient lattice-based threshold ring signature, using Lagrange polynomial interpolation to express the threshold. The scheme eliminates the dependence on Stern-like identification protocols with large soundness error, and achieves much shorter signature sizes. It also uses the technique of Gaussian convolution (G+G) proposed by Devevey et al. in Asiacrypt 2023 to remove the rejection sampling in BLISS signature. Compared with previous distributed FSwA (Fiat-Shamir with Aborts) signatures where the number of repetitions increases exponentially with that of signers, our scheme has much higher computation efficiency. We prove the unforgeability and strong anonymity, i.e., fellow-signer anonymity, unclaimability and anonymity against the untrusted leader of our proposed threshold ring signature scheme. Leveraging the security and efficiency advantages of our signature scheme, we propose a post-quantum receipt-free and verifiable e-voting protocol for large-scale elections with untrusted cloud servers.