Paper 2026/1125

Threshold Signatures in the Head

Abstract

Threshold cryptography distributes trust among multiple parties by enabling joint cryptographic operations without reconstructing secret keys. While post-quantum signature schemes based on the MPC-in-the-Head (MPCitH) paradigm are highly generic, recent impossibility results show that their thresholdization either incurs prohibitive distributed symmetric computations or leads to signature sizes growing with the number of signers. Achieving practical tradeoffs in this setting remains challenging. In this paper, we propose a generic framework for threshold MPCitH signatures based on Merkle-tree commitments. Our approach adapts the PIOP+PCS paradigm to the distributed setting by introducing and instantiating the notion of threshold polynomial commitment schemes (TPCS). We present a generic compiler combining a PIOP, a TPCS, and an arithmetic black box into a threshold signature scheme, and prove its unforgeability from the security of its components. We further provide a concrete Merkle-tree-based TPCS achieving moderate signature-size overhead, as low as 200 bytes per signer at the 128-bit security level. This is to be compared with an overhead of roughly 2 kB per signer for the previously suggested approach to thresholdize MPC-in-the-Head based on GGM trees. By compiling this TPCS with a standard PIOP, we obtain a generic threshold signature scheme from any hard problem or one-way function, which we showcase MQ-based and AES-based instantiations.