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The only known construction of certificateless signature sche-mes that can be proven secure against a malicious Key Generation Center (KGC) requires the random oracle model to prove the security. In this paper, we present a certificateless signa ure scheme which is secure against malicious-but-passive KGC attack without random oracle. The security of our scheme based on our proposed complexity assumptions we call the Augmented Computational Diffie-Hellman (ACDH) assumption and 2-Many Diffie-Hellman (2-Many-DH) assumption. At the same time, we discuss the relationship between the new assumptions and some related problems. [ABSTRACT FROM AUTHOR]