Verifiable delay functions and delay encryptions from hyperelliptic curves

Abstract

Verifiable delay functions (VDFs) and delay encryptions (DEs) are two important primitives in decentralized systems, while existing constructions are mainly based on time-lock puzzles. A disparate framework has been established by applying isogenies and pairings on elliptic curves. Following this line, we first employ Richelot isogenies and non-degenerate pairings from hyperelliptic curves for a new verifiable delay function, such that no auxiliary proof and interaction are needed for the verification. Then, we demonstrate that our scheme satisfies all security requirements, in particular, our VDF can resist several attacks, including the latest attacks for SIDH. Besides, resorting to the same techniques, a secure delay encryption from hyperelliptic curves is constructed by modifying Boneh and Frankiln’s IBE scheme, which shares the identical setup with our VDF scheme. As far as we know, these schemes are the first cryptographic applications from high-genus isogenies apart from basic protocols, i.e., hash functions and key exchange protocols.