On Threshold Signatures from MPC-in-the-Head

We initiate the study of (n out of n) threshold signatures built from MPC-in-the-Head signatures. While recent impossibility results (Doerner, Kondi and Rosenbloom, CRYPTO'24) show that any such construction must have a signature size that grows with the number n of users (or else require a prohibitive non-black-box use of cryptography), we outline a general strategy to confine the dependency in the number of users to a term of the form λ 2 n + O ( 1 ) , where λ is a security parameter and O ( 1 ) a constant that depends on the signature scheme. We provide a concrete instantiation of our strategy by building a threshold signature on top of the scheme of (Carozza, Couteau, and Joux, EUROCRYPT'23).