Implementation and Performance Analysis of Verifiable Random Functions with Additional Data on Various Twisted Edwards Curves

Verifiable Random Functions (VRFs) are cryptographic primitives that generate outputs with publicly verifiable proofs to confirm their correctness. This paper presents an implementation of Verifiable Random Functions with Additional Data (VRF-AD) on various Twisted Edwards curves: Bandersnatch, Jubjub, Ed25519, and Baby Jubjub. We adhere to the IETF VRF standard, extending it to incorporate a Pedersen VRF, which serves as the foundation for a Ring VRF with ring proof capabilities. Our implementation offers two different encode-to-curve methods: the Elligator2 approach for Bandersnatch, and a generic try-and-increment approach for the other curves. We introduce performance optimizations through the Gallant-Lambert-Vanstone (GLV) method for scalar multiplication and conduct a comparative analysis across all four curves. Our findings indicate that the Bandersnatch curve provides optimal performance in both proof generation and verification compared to other Twisted Edwards curves. This work contributes to the expanding landscape of verifiable randomness, offering solutions for applications in blockchain technology, privacy-preserving cryptographic protocols, and distributed systems that require provable fairness.