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This paper proposes an efficient key-evolving paradigm to deal with the key exposure problem of digital signature schemes. In the paradigm the secret key evolves with time and it is computationally infeasible for an adversary to forge a signature for the periods before the time of the key exposure. The scheme we propose is based on pairing (bilinear maps) and is efficiently constructed. We associate time with all nodes of a binary tree rather than the leaves only for the first time in a signature scheme. The complexity is a log magnitude in terms of the number of the total time periods. Compared with other previous key-evolving signature schemes, the signing and key update algorithm are very efficient. Finally, we give a detailed security analysis for the scheme. The security proof is based on the computational Diffie-Hellman assumption.