[Resource Topic] 2023/1537: DEFEND: Verifiable Delay Functions from Endomorphism Rings

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DEFEND: Verifiable Delay Functions from Endomorphism Rings

Authors: Knud Ahrens, Jens Zumbrägel


We present a verifiable delay function based on isogenies of supersingular elliptic curves, using Deuring correspondence and computation of endomorphism rings for the delay. For each input x a verifiable delay function has a unique output y and takes a predefined time to evaluate, even with parallel computing. Additionally, it generates a proof by which the output can efficiently be verified. In our approach the input is a path in the 2-isogeny graph and the output is the maximal order isomorphic to the endomorphism ring of the curve at the end of that path. This approach is presumably quantum-secure, does not require a trusted setup or special primes and the verification is independent from the delay. It works completely within the isogeny setting and the computation of the proof causes no overhead.

ePrint: https://eprint.iacr.org/2023/1537

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