In practice, adversaries may be able to acquire a part of private state of cryptographic system via side-channel attacks, on account of unexpected physical defects of cryptosystem, which is a serious threat to traditional cryptosystem that does not consider physical issues. Leakage-resilient cryptography was proposed to prevent adversaries from doing so. Unfortunately, there are few literatures in leakage-resilient signature. In this paper, we extend the framework of Dual-Form Signatures (DFSs) proposed by Gerbush et al. to the leakage setting, which provides a new path towards obtaining proofs under weaker assumptions. Applying this framework, we present a DFS scheme based on static assumptions with leakage bound (n - 1 - 2c) log p2 where n is a positive integer greater than or equal to 2 and c is a fixed positive constant, which can be easily extended to the continual leakage model as well. Combining this result and the framework proposed by Huang et al., we can obtain identity-based signature schemes and certificateless signature schemes sharing the same leakage bound (n - 1 - 2c) log p2.