A secure and efficient payment protocol based on ElGamal cryptographic algorithms

In this paper we present a secure and efficient transaction protocol that provides the anonymity and can detect the double spending. The proposed payment system is based on the ElGamal encryption scheme, the ElGamal signature scheme and the ElGamal blind signature protocol. We show that our transaction protocol is secure and efficient. We give the definitions of unlinkability and unforgeability of our security model and we prove that the proposed transaction protocol is unforgeable and satisfies the unlinkability property. We show that the proposed system is more efficient, in terms of the computation and communication cost, than the compared payment systems (Eslami et al. in Electron Commer Res Appl 10:59–66, 2011; Chen et al. in Electron Commer Res Appl 10:279–287, 2011; Liu et al. in Proceedings of second European PKI workshop: research and applications. Lecture notes in computer science, vol 3545, pp 206–214, 2005 and Chen et al. in Electron Commer Res Appl 10:673–682, 2011) for a customer who withdraws and spends an e-coin and for the merchant who verifies an electronic coin. Also, the proposed e-cash system is useful for the electronic transactions when the connection between the bank and the merchant is not available during the payment protocol. This means a less bandwidth of the payment protocol and then increases the speed of the electronic transaction.