InfinityRand: Blockchain Non-Interactive Randomness Beacon Protocol Based on Trapdoor Verifiable Delay Function

Due to the prosperity of Decentralized Finance (DeFi) ecosystems and the rise of Decentralized Autonomous Organization (DAO) groups, blockchain as the underlying revolutionary theory has been attracted a lot of attention. How to achieve cryptographically unpredictable randomness in the publicly verifiable blockchain network, one of the typical collaborative systems, is a critical issue. Since Ethereum finished merging its mainnet with beacon chain, the research on randomness beacon in the blockchain field has become a hotspot. Most of the current distributed randomness beacon schemes are interactive protocols. They are constructed with Public Verifiable Secret Sharing (PVSS), leading high communication complexity O(n ² ). In contrast, randomness beacons constructed based on Verifiable Delay Functions (VDFs) rely on the sequentiality and uniqueness of VDFs could solve this problem. This paper proposes a blockchain non-interactive randomness beacon protocol: InfinityRand (IR), which decoupled from the underlying message distribution mechanism. It could generate publicly verifiable, strongly bias-resistant, and fair random numbers. In designing InfinityRand, we also design a new trapdoor VDF scheme, which is constructed using negative wrapped convolution (NWC) based number theoretic transform (NTT) on polynomial ring. We conduct security analysis and evaluation experiments. Experiments show that InfinityRand could provide well unpredictability, leader election fairness and scalability guarantees.