Proving knowledge of isogenies: a survey

Proceedings Paper Computer Science, Information Systems

SIDH Proof of Knowledge

Luca De Feo et al.

Summary: This paper identifies an invalid assumption in the soundness proof of the De Feo-Jao-Pl<^>ut identification scheme, which is the basis for SIDH signatures. The authors provide a counterexample for this assumption and propose two sigma protocols to address the issue. The paper also avoids the soundness issue raised by Ghantous, Pintore, and Veroni in the SIDH identification scheme.

ADVANCES IN CRYPTOLOGY- ASIACRYPT 2022, PT II (2022)

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Proceedings Paper Computer Science, Theory & Methods

The supersingular isogeny path and endomorphism ring problems are equivalent

Benjamin Wesolowski

Summary: The paper proved that the path-finding problem in isogeny graphs and the endomorphism ring problem for supersingular elliptic curves are equivalent under reductions of polynomial expected time, assuming the generalised Riemann hypothesis. The algorithm developed for the quaternion analog of the path-finding problem is a powerful cryptanalytic tool and building-block for cryptosystems.

2021 IEEE 62ND ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2021) (2022)

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Proceedings Paper Computer Science, Interdisciplinary Applications

Verifiable Isogeny Walks: Towards an Isogeny-Based Postquantum VDF

Jorge Chavez-Saab et al.

Summary: This paper investigates the problem of constructing postquantum-secure verifiable delay functions (VDFs) based on supersingular isogenies. It proposes a different approach using succinct non-interactive arguments (SNARGs) tailored to the arithmetic structure of the isogeny setting to achieve good asymptotic efficiency. As a result, an isogeny-based VDF construction with postquantum security, quasi-logarithmic verification, and requiring no trusted setup is obtained. Additionally, non-interactive arguments for isogeny walks in the supersingular graph over F-p2 are constructed, which may have independent interest.

SELECTED AREAS IN CRYPTOGRAPHY (2022)

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Proceedings Paper Computer Science, Information Systems

A New Adaptive Attack on SIDH

Tako Boris Fouotsa et al.

Summary: The SIDH key exchange scheme is vulnerable to various attacks, such as adaptive attacks and passive attacks, which exploit torsion point information to recover secret isogenies.

TOPICS IN CRYPTOLOGY, CT-RSA 2022 (2022)

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Article Computer Science, Theory & Methods