Cryptocurrencies such as Bitcoin and Libra based on blockchain technology have set off a wave of digital economy, which can ensure the verifiability and integrity of transactions through digital signatures, in which the private key ensures the ownership of currency assets, if the private key was lost or stolen, the security of cryptocurrency assets will be significantly threatened. Compared with elliptic curve digital signature algorithm (ECDSA), Edwards curves digital signature algorithm (EdDSA) has the advantages of faster calculation speed, smaller key and signature space, and is widely used in the signature of Libra transactions. However, as a deterministic signature algorithm, it is vulnerable to differential fault attacks resulting in key loss and leakage. It is a challenge that how to resist this kind of attack and design a provably secure EdDSA signature. Therefore, we firstly define the security properties are firstly defined that the digital signature scheme against differential fault attacks that must be meet, and differential fault attack technology is utilized to cryptanalyze the EdDSA signature algorithm, and an EdDSA signature scheme that resists differential fault attacks is proposed, and it is proved that the scheme satisfies the existence of unforgeable under adaptive selection message attack (EUF-CMA) and resistance to differential fault attack. In order to reduce the risk of signature private key leakage, with the help of Paillier homomorphic encryption technology, we design a two-party cooperative EdDSA signature scheme against differential fault attack is designed, and prove the security of the scheme based on the universally composable (UC) security model is proved. Finally, we implement the two-party cooperative ECDSA signature algorithm and the two-party cooperative EdDSA signature algorithm against differential fault attack are implemented, and the implementation demonstrates that the effectiveness of the proposed scheme.