Blockchain systems face increasing security threats, particularly the risk of side-channel attacks. In blockchain payment channels, the signing process of transactions often leaks a lot of sensitive information, making the system an easy target for attackers to launch side-channel attacks. Attackers can infer private data such as private key information by capturing physical information such as time during the signing process, which in turn compromises the security of the entire payment system. To effectively address this challenge, this paper proposes a novel signature algorithm specifically designed to defend against side-channel attacks. Specifically, a random delay is introduced into the signature algorithm as a random noise, which disturbs the side-channel information of the signature process, making it impossible for the attacker to infer the private data from the side-channel information in the channel. Through experimental verification, the signature algorithm proposed in this paper has a significant advantage in resisting side-channel attacks, with an improvement of 89.52% compared to the current payment channel system scheme.