zkDaily - 2026-06-02

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ZKP Frontier Tracker 🎯

Tue

06.02

2026

Toward zkSNARK-assisted Isogeny-based Cryptography

Paper

https://eprint.iacr.org/2026/1096

Yi-Fu Lai Isogeny-based Cryptography

Lai and Maino, in their paper, propose efficient zkSNARK for isogeny-based cryptography using optimized Vélu formulas and theta model to encode various isogeny relations in R1CS, with applications to DeuringVRF signatures, SQISign, and POKÉ key validation, removing extra assumptions.

Notes Notes 要点

Existing ZKP for isogenies limited to small-degree chains, inefficient.
Provide efficient R1CS for - and -isogenies and masked evaluations via optimized Vélu formulas.
Design R1CS for non-smooth isogenies of special degrees using theta model.
Compiler removes 'one-more' evaluation assumption in DeuringVRF signatures.
Eliminate hint-based assumption in SQISign; conceptual key validation for POKÉ.
Experimental proof sizes around 400 KB under NIST-1 primes.

Collected by @icerdesign

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Q&A Deep Dive 💬

Tue

06.02

2026

What problem does this paper address?

The paper studies how to apply zkSNARKs to isogeny-based cryptography. Many isogeny relations are difficult to express in generic proof systems, so the authors introduce new R1CS encodings to make proofs more practical.

What is the main technical contribution of the paper?

Using optimized Vélu-style formulas, the authors develop efficient R1CS encodings for several classes of isogenies and their evaluations, enabling zkSNARKs to support a broader range of isogeny relations.

What is the significance of this work for SQISign and DeuringVRF?

The paper shows how zkSNARKs can remove the one-more evaluation assumption in DeuringVRF and discusses reducing reliance on hint-based assumptions in SQISign.

Prompted by @icerdesign