A new enhancement of elliptic curve digital signature algorithm

Elliptic Curve Digital Signature Algorithm (ECDSA) is a public key cryptographic algorithm based on the hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP), it is used to ensure users' authentication, data integrity and transactions non-repudiation. However, its weakness is to derive the signer's private key in case he uses the same random number for to generate two signatures for two different messages. Firstly, in this paper we present the ECDSA and analyse its variants proposed in the literature.Also, we propose a new improvement technique for ECDSA of Liao and Shen and ECDSA of Chande and Lee. We intend to do so by introducing the unknown parameters which are used in the verification of the signature. Our aim is to overcome the problem which has not been explained in ECDSA schemes of both Liao and Shen and Chande and Lee.