In ubiquitous computing environment, how to implement security and trust among the users that connected to a network is a big problem. Digital signature provides authenticity, integrity and nonrepudiation to many kinds of applications in ubiquitous computing environment. In this paper, we present a very efficient certificateless signature scheme from bilinear maps. In our scheme, only one paring operation is needed in the signing and verification processes. The security of the new scheme is

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... d on the intractability of the q-Strong Diffie-Hellman (q-SDH) Problem and the Discrete Logarithm Problem. We prove the existential unforgeability of our scheme under adaptively chosen message attack against both types of adversaries in the random oracle model [3] .