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Abstract. We initiate the formal study on authenticated key exchange (AKE) under bad randomness. This could happen when (1) an adversary compromises the randomness source and hence directly controls the randomness of each AKE session; and (2) the randomness repeats in different AKE sessions due to reset attacks. We construct two formal security models, Reset-1 and Reset-2, to capture these two bad randomness situations respectively, and investigate the security of some widely used AKE protocols in these models by showing that they become insecure when the adversary is able to manipulate the randomness. On the positive side, we propose simple but generic methods to make AKE protocols secure in Reset-1 and Reset-2 models. The methods work in a modular way: first, we strengthen a widely used AKE protocol to achieve Reset-2 security, then we show how to transform any Reset-2 secure AKE protocol to a new one which also satisfies Reset-1 security.

Recently bilinear pairings on elliptic curves have raised great interest in cryptographic comnmnity. BaKed oi, their good properties, many excellent ID-based cryptographic schemes have been proposed. However, in these proposed schemes, the private key generator should be assumed trusted, while in real environment, this assumption does not always hold. To overcome this weakness, in this paper, we will use the threshold technology to devise a secure ID-based signcryption scheme. Since tile threshold technology ks adopted not Olfly in the master key management but also in the group signature, our schelne can achieve high security and resist solne malicious attacks under a certain threshold.

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