Informatica

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 corruption 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.

In this paper, we propose a new ID-based threshold signature scheme from the bilinear pairings, which is provably secure in the random oracle model under the bilinear Diffie–Hellman assumption. Our scheme adopts the approach that the private key associated with an identity rather than the master key of PKG is shared. Comparing to the-state-of-art work by Baek and Zheng, our scheme has the following advantages. (1) The round-complexity of the threshold signing protocol is optimal. Namely, during the signing procedure, each party broadcasts only one message. (2) The communication channel is optimal. Namely, during the threshold signing procedure, the broadcast channel among signers is enough. No private channel between any two signing parties is needed. (3) Our scheme is much more efficient than the Baek and Zheng scheme in term of computation, since we try our best to avoid using bilinear pairings. Indeed, the private key of an identity is indirectly distributed by sharing a number xID∈ $\mathbb{Z}^{*}_{q}$, which is much more efficient than directly sharing the element in the bilinear group. And the major computationally expensive operation called distributed key generation protocol based on the bilinear map is avoided. (4) At last, the proactive security can be easily added to our scheme.