Orient Express: Using Frobenius to Express Oriented Isogenies

2026
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Authors: Wouter Castryck; Riccardo Invernizzi; Gioella Lorenzon; Jonas Meers; Frederik Vercauteren
Published in: Progress in Cryptology – LATINCRYPT 2025
Publisher: Springer Nature Switzerland

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Abstract

The chapter delves into the cryptographic use of finite abelian group actions, with a focus on the efficiency and security of supersingular elliptic curves. It explores the concept of oriented isogenies, particularly the Frobenius orientation, which offers significant advantages in terms of efficiency and security. The text discusses the use of higher-dimensional isogeny representations and the evaluation of group actions, providing practical insights into parameter generation and implementation. Additionally, it compares the Frobenius orientation with other frameworks, highlighting its benefits and potential applications. The chapter concludes with a discussion on the security implications and potential threats, offering a comprehensive overview of the subject.

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Title: Orient Express: Using Frobenius to Express Oriented Isogenies
Authors: Wouter Castryck
Riccardo Invernizzi
Gioella Lorenzon
Jonas Meers
Frederik Vercauteren
Publisher: Springer Nature Switzerland
Book: Progress in Cryptology – LATINCRYPT 2025
Print ISBN: 978-3-032-06753-1

Electronic ISBN: 978-3-032-06754-8

Copyright Year: 2026
DOI: https://doi.org/10.1007/978-3-032-06754-8_6

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