Proxy signature is widely used in large-scale wireless industrial control Internet of things, the efficiency of signature master server can be greatly improved by using proxy signature. A new short proxy signature scheme based on bilinear mapping was proposed to adapt to the application environment with limited bandwidth and weak computing power. Firstly, the security of the proposed scheme was proved based on Computational Diffie-Hellman (CDH) problem and Collusion Attack Algorithm with k traitors (k-CAA) problem under the random oracle model. Then, the performance advantages of the proposed scheme were analyzed with other existing proxy signature and short proxy signature schemes, and the key codes of the proposed scheme were given. The experimental results show that, the proposed scheme performs one scalar multiplication operation and one hash operation in proxy signature generation; two bilinear pairing operation, one scalar multiplication operation and two hash operations in signature verification. Compared with other similar proxy signature schemes, the proposed scheme has advantages in computational performance and is suitable for application scenarios with weak computational power and limited transmission capacity.

The analysis of aggregate proxy signature scheme proposed by Yu et al. (YU X Y, HE D K. A certificate-based aggregate proxy signature scheme. Journal of Central South University (Science and Technology), 2015, 46(12): 4535-4541.) showed that a valid signatures could be forged for any messages while knowing a valid signature. Therefore, an improved certificate-based aggregate proxy signature scheme was proposed and a new attack model was given. The new scheme was proved to be existentially unforgeable for the new attacker in random oracle model. The results show that the proposed scheme can resist conspiracy attacks and forgery attacks, and it is more suitable for the computation-constrained and real-time tasks.