To increase the interoperability and privacy of digital asset transactions in multiparty cross-chain scenarios, Chen et al. proposed a cross-chain protocol based on multi-signatures and adaptor signatures that does not rely on smart contracts but instead depends on underlying scripts and signatures. However, since the protocol was designed without considering concurrent execution scenarios, it may still be vulnerable to certain types of attacks, posing potential security risks in practical applications. Therefore, this paper first presents an ROS attack against Chen et al.’s scheme, in which ROS attack was originally proposed by Benhamouda et al. in 2022 against the Schnorr-type threshold and multi-signatures and our attack exploits the random numbers generated by users in the offline-tolerant mechanism. By using a system of equations construction method, it is possible to forge valid signatures for arbitrary messages. Subsequently, the existing Chen et al.’s scheme is improved by establishing a nonlinear dependency between the random number and the message, without introducing additional interaction rounds or random parameters. This improvement eliminates the solvability of the linear system of equations in the ROS attack, thereby defending against this type of attack. Furthermore, security definitions and proofs are provided, detailing the complete properties of the improved adaptor signature scheme. Therefore, the proposed scheme in this paper enhances the theoretical security strength while maintaining the functionality and efficiency of Chen et al.’s scheme, and hence has more effective practicality.