Towards practical key exchange from ordinary isogeny graphs

DOI10.1007/978-3-030-03332-3_14zbMath1447.94029arXiv1809.07543OpenAlexW4289542210MaRDI QIDQ1710681

Peng Zhang

Publication date: 23 January 2019

Full work available at URL: https://arxiv.org/abs/1809.07543

zbMATH Keywords

elliptic curvesisogenieskey exchangepost-quantum cryptography

Mathematics Subject Classification ID

Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50) Quantum cryptography (quantum-theoretic aspects) (81P94)

Related Items

SoK: how (not) to design and implement post-quantum cryptography ⋮ Explicit Connections Between Supersingular Isogeny Graphs and Bruhat–Tits Trees ⋮ On the hardness of the computational ring-LWR problem and its applications ⋮ An isogeny-based ID protocol using structured public keys ⋮ An efficient post-quantum KEM from CSIDH ⋮ Hilbert modular polynomials ⋮ Breaking the decisional Diffie-Hellman problem for class group actions using genus theory: extended version ⋮ Supersingular curves you can trust ⋮ Proving knowledge of isogenies: a survey ⋮ Multiparty non-interactive key exchange and more from isogenies on elliptic curves ⋮ A subexponential-time, polynomial quantum space algorithm for inverting the CM group action ⋮ Orienteering with one endomorphism ⋮ Cryptographic group actions and applications ⋮ Radical isogenies ⋮ CSIDH: an efficient post-quantum commutative group action ⋮ On oriented supersingular elliptic curves ⋮ Hash functions from superspecial genus-2 curves using Richelot isogenies ⋮ Orienting supersingular isogeny graphs ⋮ Lossy CSI-fish: efficient signature scheme with tight reduction to decisional CSIDH-512 ⋮ Threshold schemes from isogeny assumptions ⋮ CSURF-TWO: CSIDH for the ratio \((2:1)\) ⋮ Optimal strategies for CSIDH ⋮ Breaking the decisional Diffie-Hellman problem for class group actions using genus theory

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Improved algorithm for the isogeny problem for ordinary elliptic curves
• Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves
• Class polynomials for nonholomorphic modular functions
• Expander graphs based on GRH with an application to elliptic curve cryptography
• A key-exchange system based on imaginary quadratic fields
• Computing isogenies between Montgomery curves using the action of \((0,0)\)
• A modular analysis of the Fujisaki-Okamoto transformation
• A simple and compact algorithm for SIDH with arbitrary degree isogenies
• CSIDH: an efficient post-quantum commutative group action
• Counting points on elliptic curves over finite fields
• Computing the number of points on an elliptic curve over a finite field: algorithmic aspects
• Public key cryptography based on semigroup actions
• Elliptic curve cryptosystems in the presence of permanent and transient faults
• An algorithm to compute volcanoes of 2-isogenies of elliptic curves over finite fields
• An elliptic curve trapdoor system
• Mathematics of Public Key Cryptography
• On the Security of Supersingular Isogeny Cryptosystems
• Another Subexponential-time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
• Explicit isogenies in quadratic time in any characteristic
• Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies
• Elliptic Curves and Primality Proving
• Fast algorithms for computing isogenies between elliptic curves
• The Arithmetic of Elliptic Curves
• Speeding the Pollard and Elliptic Curve Methods of Factorization
• Constructing Isogenies between Elliptic Curves Over Finite Fields
• Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack
• Pairing the volcano
• A Subexponential Algorithm for Evaluating Large Degree Isogenies
• Nemo/Hecke
• Accelerating the CM method
• Constructing elliptic curves over finite fields with prescribed torsion
• Modular polynomials via isogeny volcanoes
• Constructing elliptic curve isogenies in quantum subexponential time
• A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
• Algorithmic Number Theory
• Computing isogenies between supersingular elliptic curves over \(\mathbb {F}_p\)