PQC CSIKE algorithm on non-cyclic Edwards curves

DOI10.1007/s10559-023-00622-xMaRDI QIDQ6198087

S. V. Abramov, A. V. Bessalov

Publication date: 20 February 2024

Published in: Cybernetics and Systems Analysis (Search for Journal in Brave)

zbMATH Keywords

isogenyisomorphismquadratic residuequadratic nonresiduetwisted Edwards curvecomplete Edwards curvequadratic Edwards curvecurve orderpoint order\(w\)-coordinatescurve in generalized Edwards form

Mathematics Subject Classification ID

Cryptography (94A60) Curves over finite and local fields (11G20) Quantum cryptography (quantum-theoretic aspects) (81P94)

Cites Work

• Unnamed Item
• How to construct CSIDH on Edwards curves
• CSIDH: an efficient post-quantum commutative group action
• Number of curves in the generalized Edwards form with minimal even cofactor of the curve order
• Differential addition on twisted Edwards curves
• Optimized method for computing odd-degree isogenies on Edwards curves
• Supersingular twisted Edwards curves over prime fields. II: Supersingular twisted Edwards curves with the \(j\)-invariant equal to \(66^3\)
• Supersingular twisted Edwards curves over prime fields. I: Supersingular twisted Edwards curves with \(j\)-invariants equal to zero and \(12^3\)
• Analogues of Vélu’s formulas for isogenies on alternate models of elliptic curves
• Twisted Edwards Curves
• Faster Addition and Doubling on Elliptic Curves
• Towards optimized and constant-time CSIDH on embedded devices

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