DID-based Distributed Verifiable Random Function with Successor Rule-based de Bruijn Sequence in Blockchain

This paper focuses on addressing the prevalent issues related to established Verifiable Random Function (VRF) schemes and presents our novel VRF scheme. Our proposed distributed VRF scheme employs multi-party computation (MPC) where each participant is identified by their own decentralized identifiers (DID) on a blockchain network, making the collective randomness by preventing any single participant from determining the output of the VRF. We further aim to enhance the randomness of our VRF scheme by utilizing a successor rule-based de Bruijn sequence to generate pseudo-random numbers with a strong balanced property, ensuring both numbers of 1s and 0s are equal. For generic VRF construction, we adapt the approach of selective-secure VRF scheme using verifiable functional encryption (VFE), which is a more generalized version of homomorphic encryption plus verifiability. Moreover, we estimate the security aspects of our VRF scheme and the entropy approximation based on the information-Theoretic perfect secrecy model. Also, using the NIST SP800-22 test suite for randomness, we demonstrate the randomness performance with a 98.29% overall pass rate on the total 176 tests of 11 standard tests and 0.6765 of the average p-value for statistical randomness. We provide technical details on implementing our VRF MPC model in the Solidity smart contract.