Leakage tolerance refers to allowing the scheme to leak some secret information to enhance the robustness of the signature scheme, which is suitable for most occasions where the equipment and communication lines cannot be perfectly protected. The length of the short signature is generally only half that of the ordinary signature, which can greatly reduce the communication data volume of the narrowband real-time interactive system. This study proposes a short signature scheme for the signature key associated with the information to be signed, and the scheme is tolerant to partial leakage. The efficiency and security of the scheme are analyzed, and the security of the scheme is proved under the tolerant leak oracle. The experimental results show that the scheme has good performance and is suitable for applications with limited transmission bandwidth.