Towards a Quantum-Resistant Weak Verifiable Delay Function

Abstract

In this paper, we present a new quantum-resistant weak Verifiable Delay Function based on a purely algebraic construction. Its delay depends on computing a large-degree isogeny between elliptic curves, whereas its verification relies on the computation of isogenies between products of two elliptic curves. One of its major advantages is its expected fast verification time. However, it is important to note that the practical implementation of our theoretical framework poses significant challenges. We examine the strengths and weaknesses of our construction, analyze its security and provide a proof-of-concept implementation.

On the Parallelization of Square-Root Vélu’s Formulas

“…Therefore, optimizing the computation of large prime-degree isogenies is of great interest for constructive purposes as well as for cryptanalysis. Interestingly, a new generation has also risen of isogeny-based protocols which utilize the techniques of the attack constructively, such as FESTA [14], QFESTA [15], IS-CUBE [16] and constructions for VDFs [17] and VRFs [18], of which the last two also involve large-degree isogenies.…”