We propose a distributed key generation protocol for pairing-based cryptosystems which is adaptively secure in the erasure-free and secure channel model, and at the same time completely avoids the use of interactive zero-knowledge proofs. Utilizing it as the threshold key generation protocol, we present a secure (t, n) threshold signature scheme based on the Waters' signature scheme. We prove that our scheme is unforgeable and robust against any adaptive adversary who can choose players for

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... uption at any time during the run of the protocols and make adaptive chosen-message attacks. And the security proof of ours is in the standard model (without random oracles). In addition our scheme achieves optimal resilience, that is, the adversary can corrupt any t < n/2 players. Keywords: threshold signature, distributed key generation, computational Diffie-Hellman problem, adaptively secure, provable security. Z. Wang et al.