Blind signatures are a versatile cryptographic primitive with many applications, especially in privacy-preserving technologies. Threshold blind signature schemes (TBS) enhance blind signatures with a signing procedure distributed among up to n signers to reduce the risk attached to the compromise of the secret key. So far, TBS constructions over groups rely on strong assumptions, e.g., the algebraic group model (AGM) or interactive assumptions. In this work, we propose two TBS based on the computational Diffie-Hellman assumption ( \(\textsf{CDH} \) ) in the ROM: The starting point for both constructions is the pairing-based signature scheme derived from Boneh-Boyen IBE (Eurocrypt’04), and their recent blind signature variants by Katsumata et al. (Asiacrypt’23) and Klooß et al. (Asiacrypt’24) based on the decisional Diffie-Hellman assumption ( \(\textsf{DDH} \) ). We first remove the reliance on \(\textsf{DDH} \) in their schemes, then provide careful adaptations to the threshold setting.