A review of mathematical and computational aspects of CSIDH algorithms

Cryptography (94A60) Elliptic curves over global fields (11G05) Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52) Isogeny (14K02) Quantum cryptography (quantum-theoretic aspects) (81P94)

Cites Work

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Binary quadratic forms. An algorithmic approach
On Lovász' lattice reduction and the nearest lattice point problem
Sieving for closest lattice vectors (with preprocessing)
A simple and compact algorithm for SIDH with arbitrary degree isogenies
Towards practical key exchange from ordinary isogeny graphs
CSIDH: an efficient post-quantum commutative group action
A faster way to the CSIDH
On collisions related to an ideal class of order 3 in CSIDH
Lossy CSI-fish: efficient signature scheme with tight reduction to decisional CSIDH-512
Optimal strategies for CSIDH
He gives C-sieves on the CSIDH
Rational isogenies from irrational endomorphisms
CSI-FiSh: efficient isogeny based signatures through class group computations
Further optimizations of CSIDH: a systematic approach to efficient strategies, permutations, and bound vectors
Stronger and faster side-channel protections for CSIDH
SeaSign: compact isogeny signatures from class group actions
Quantum circuits for the CSIDH: optimizing quantum evaluation of isogenies
Finding closest lattice vectors using approximate Voronoi cells
On Lions and elligators: an efficient constant-time implementation of CSIDH
Endomorphisms of Abelian varieties over finite fields
\( L_1\)-norm ball for CSIDH: optimal strategy for choosing the secret key space
Radical isogenies
Analogues of Vélu’s formulas for isogenies on alternate models of elliptic curves
Elliptic Curves and Their Applications to Cryptography
Modern Computer Algebra
Isogeny volcanoes
Another Subexponential-time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
Fast heuristic algorithms for computing relations in the class group of a quadratic order, with applications to isogeny evaluation
Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies
Twisted Edwards Curves
The Arithmetic of Elliptic Curves
How To Prove Yourself: Practical Solutions to Identification and Signature Problems
CSIDH on the Surface
Polynomial Multiplication over Finite Fields in Time \( O(n \log n \)
Constructing elliptic curve isogenies in quantum subexponential time
Abelian varieties over finite fields
A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
Faster computation of isogenies of large prime degree
Computing isogenies between supersingular elliptic curves over \(\mathbb {F}_p\)
SCALLOP: scaling the CSI-FiSh
A lower bound on the length of signatures based on group actions and generic isogenies
Horizontal racewalking using radical isogenies
Full quantum equivalence of group action DLog and CDH, and more

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