| Summary: | The classic Elliptic curve digital Signature Algorithm (ECDSA) uses one inversion operation in the process of signature and verification, which greatly reduces the efficiency of digital signatures. Up to now, most research schemes improve efficiency by reducing reverse operations, but they fail to attach importance to such issues as forgery signature attack. At the same time, in the blockchain, the weak randomness of ECDSA will lead to the attack of forging random numbers, which is a potential problem of digital currency transactions. In consideration of this reason, in this article, an improved provably secure elliptic curve digital signature scheme is constructed. First, the new scheme introduces double parameters in the signature process, that can effectively resist the weak randomness attack of ECDSA in Bitcoin, and can be applied to blockchain digital currency trading systems. Second, in the random oracle model, it is provably indistinguishable against Elliptic Curve Discrete Logarithm Problem (ECDLP) under the super type I and type II adversary. Third, the new scheme avoids the inverse operation in the signature and verification phase. Compared with the ECDSA, the running speed is optimized by 50.1%. Similarly, the proposed scheme has higher computational efficiency than other existing algorithms.
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