An Improved Non-Interactive Zero-Knowledge Range Proof for Decentralized Applications

Abstract

Blockchain is the core technology underlying the first decentralized cryptocurrency, Bitcoin, introduced by Nakamoto in 2008. Since then, blockchain technology has many more advancements that are being developed and experimented. In particular, recent blockchain platforms such as Ethereum offer general and executable scripts, namely smart contracts, that can be employed to develop decentralized applications (DApps) in many domains beyond payment. However, the transparency of blockchain data raises concerns for many applications that require high privacy level. Therefore, many privacy enhancing technologies have been applied to DApp development, including zero knowledge proof (ZKP). This paper focuses on a particular kind of ZKP, called zero knowledge range proof (ZKRP), that has been applied in blockchain-based payments for banks. ZKRP allows a user to convince other people that a secret value actually lies within an interval without revealing any information about the secret. Here we introduce a new ZKRP which has the following remarkable features: (1) Non-interactive: No communication is required between a user and a verifier during the proof. (2) Range-flexibility: There is no limitation on the lower bound and the upper bound of the range except that they are natural numbers. (3) Efficiency: Our scheme is modified from that of Pang et al. (2010), yet achieves better security and is more efficient than their scheme. We believe our new ZKRP can be beneficial to the development of DApps and can extend the application scope to more scenarios.