Security Analysis and Improvement of Elliptic Curve Digital Signature Scheme

Abstract

In digital signature, the digital signature based on elliptic curve cryptosystem has higher security. Elliptic curve cryptography (ECC) is the transfer of discrete logarithmic cryptography to elliptic curve. Compared with other cryptosystems, elliptic curve cryptography has the advantages of short key, small storage space, narrow bandwidth and high security. This paper focuses on the security of elliptic curve digital signature scheme. By analyzing the signature scheme of Zhang Qingsheng et al., we find that this scheme has the risk of replacing messages to forge the signature. In view of this risk, this paper proposes an improved scheme based on elliptic curve discrete logarithm problem. Furthermore, in this paper, we analyze the security of our improved scheme against the random number attack, the unknown plaintext and ciphertext attack and the replacement messages forged signature attack.