Fair Offline Payment Using Verifiable Encryption

Abstract

Verifiable encryption allows a receiver, who cannot decrypt the ciphertext, to verify what has been encrypted. This technique is widely used in fair exchange to convince a receiver that he/she can later obtain the requested item by presenting the item in an encrypted form to a TTP (Trusted Third Party). In this paper, we apply verifiable encryption to offline payment systems based on the representation problem to provide the payment atomicity. Our verifiable encryption uses the Naccache-Stern cryptosystem and a proof of equality of discrete logarithms from different groups. Although additional cost is required during payments, we show that the cost is reasonable. Furthermore, we have improved the efficiency of dispute settlement significantly. In our method, the TTP does not have to interact with any other party other than the one who filed a complaint to resolve disputes.