Till now, the types of attacks for cryptographic device are usually distinguished as leakage and tampering attacks respectively.The former, also known as side-channel attacks, is described that when running a cryptographic device, the adversary can observe the physical characteristics of the execution of this cryptographic device.These physical characteristics will leak information about the secret key used in the whole system.The latter, called tampering attacks, tampers the secret information proactively and observes the output behavior of the system.In this paper, we primarily explore how to construct a signature scheme which resists chosen message attack and meets requirements of leakage-resilience and tamper-resilience.At this moment, we take both of the two attacks described above into consideration rather than consider only one of them.Firstly in the case of no leakage on randomness, we give a signature scheme and its security proof.In our scheme, we use an extractor to randomize the value of correlated input hash function which will help to handle leakage about secret key.Then we consider the case when there exists leakage on randomness and improve the scheme described before.In such case we prove the security of our fully leakage signature scheme following the idea of [4].