Provable security theory generally adopts the method of reduction, which makes use of the unsolvable mathematical problems in number theory to reduce the scheme to be safe. The idea of proof is a method of proof by contradiction: First, it is assumed that it is not difficult to solve the scheme presented in this paper, then the process of proving it, and finally, it is deduced that it is not difficult to calculate a certain difficult problem, which contradicts the difficulty of the mathematical problem. Then, it means that the assumption is not valid, and the scheme is proved to be safe. In this paper, the security of the scheme proposed in our previous paper is proved in detail.the scheme is proved to be secure against existential forgery under selective attributes and adaptive chosen-message attack. Its security can be reduced to the hardness of the computational Diffie-Hellman problem.
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