Efficient Arbitrarily Divisible E-Cash Applicable to Secure Massive Transactions

Abstract

A conventional divisible E-cash (DEC) system allows each user to withdraw a coin of value 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , then spend it in several times by dividing it into small ones of value 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sup> , for some l ∈ {0, 1, ⋯, n}. Observing that the price of many commodities is not just 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sup> , it requires to pay more than one coin in a transaction. In order to improve the efficiency of spend protocol, we propose a new construction called arbitrarily DEC (ADEC) which can divide a large coin into several small ones with arbitrarily integer values. We propose a new construction of ADEC based on a public linked list. Using bilinear pairings, we instantiate two ADEC systems: one holds its useful properties in the standard model and the other one in the random oracle model. These two systems allow users to pay for transactions in constant time. Moreover, our construction can be applied to secure the E-commerce of merchant with high volumes of transactions, a merchant can get a result in constant time for depositing a coin and can complete the deposit procedure in a reasonable time, even if he/she deposits massive coins. Our schemes are quite practical for users/merchants using resource-constrained mobile devices.