Compared with public key cryptography such as RSA, elliptic curve cryptosystem owns features like high security, low computation overload, short key size and less bandwidth and therefore this system has been recognized by the world and has been applied into digital signature field. However, the current elliptical curve signature scheme has the shortage of low defense of birth defects. Accordingly, this study introduces a new scheme based on two random numbers to decrease the possibility of the same random number used in two signatures. After the analysis of security and complexity, it is proved that the scheme can defend birth defects better and thus improves the security of signature. Besides, the signature scheme has the features of automatically recovery, low computational complexity and easy operation.
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