A trustee-based and efficient divisible e-cash scheme

Divisible e-cash systems allow users to purchase a coin of value 2^l and spend it part by part. This system not only need to ensure the anonymity of users, but also can detect double-spending behavior from malicious user. In 2015, Canard presented the first efficient divisible e-cash system in both random oracle model and standard model. In the system, for the coin of value 2^l, the deposit protocol involves up to 2^l pairing operations. When the value of coin is big, the divisible e-cash system will face challenges. If the value is 2²⁰, the system will withstand huge computation pressure; if the value is 2³⁰, it will be a state of collapse. For these potential shortcomings, independent of the work of Canard, we propose a more efficient divisible system based on a trusted third-party, as an improved version of Canard's system. In the scheme, we make use of a trusted third-party, and reduce the number of public parameters and the number of zero-knowledge proof. Especially in the deposit operation, the complexity of deposit protocol is a linear correlation with l, which provides the possibility for solving the problem of large electronic cash.