In the recent 20 years, researches on NIZK proof system and related theory have improved gradually. Recent research focuses are mainly concentrated on the application and efficiency improvement of NIZK proof system, including the following aspects.
- Efficient NIZK proof and NIZK argument system that apply to specific application backgrounds: currently, the researches for NIZK efficiency are mainly concentrated on the computation in bilinear group, so it is worth deeply studying how to construct highly efficient NIZK protocol applicable to other mathematical backgrounds.
- Other cryptographic tools that cooperate with the existing proof systems: recently, Abe et al. [56] pro- pose structure-preserving commitments and signatures which apply perfectly to GS proof system so that it enables the modular design of the protocols and at the same time ensures the efficiency. At present, these researches are just beginning, and there are still a lot of problems in the efficiency and application of these schemes.
