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Research

Papers

Parametrizing maximal orders along supersingular l-isogeny paths
Laia Amoros, James Clements, and Chloe Martindale		 preprint code
A Direct Key Recovery Attack on SIDH
Luciano Maino, Chloe Martindale, Lorenz Panny, Giacomo Pope, and Benjamin Wesolowski		 eprint published version code
On homomorphic encryption using abelian groups: Classical security analysis
Eleni Agathocleous, Vishnupriya Anupindi, Annette Bachmayr, Chloe Martindale, Rahinatou Yuh Njah Nchiwo, and Mima Stanojkovski		 eprint
An attack on SIDH with arbitrary starting curve
Luciano Maino and Chloe Martindale		 eprint
Explicit connections between supersingular isogeny graphs and Bruhat-Tits trees
Laia Amorós, Annamaria Iezzi, Kristin Lauter, Chloe Martindale, and Jana Sotáková		 eprint published version code
Improved torsion point attacks on SIDH variants
Victoria de Quehen, Péter Kutas, Chris Leonardi, Chloe Martindale, Lorenz Panny, Christophe Petit, and Katherine E. Stange		 arxiv
eprint 		published version code
How to not break SIDH (presented at CFAIL2019)
Chloe Martindale and Lorenz Panny		 eprint
Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
Georgios Fotiadis and Chloe Martindale		 eprint
Tiny Wireguard Tweak
Jacob Appelbaum, Chloe Martindale, and Peter Wu		 eprint published version
Quantum circuits for the CSIDH: optimizing quantum evaluation of isogenies
Daniel J. Bernstein, Tanja Lange, Chloe Martindale, and Lorenz Panny		 preprint published version website
Pairing-Friendly Twisted Hessian Curves
Chitchanok Chuengsatiansup and Chloe Martindale		 eprint published version
Optimal TNFS-secure pairings on elliptic curves with even embedding degree
Georgios Fotiadis and Chloe Martindale		 eprint code
Hilbert Modular Polynomials
Chloe Martindale		 preprint published version code
CSIDH: An Efficient Post-Quantum Commutative Group Action
Wouter Castryck, Tanja Lange, Chloe Martindale, Lorenz Panny, and Joost Renes		 eprint published version website
PhD thesis: Isogeny Graphs, Modular Polynomials, and Applications
Supervised by Marco Streng		 thesis
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
Sean Ballentine, Aurore Guillevic, Elisa Lorenzo Garcia, Chloe Martindale, Maike Massierer, Benjamin Smith, and Jaap Top		 arxiv published version

Past students

Isabel Bromfield; Master's thesis (Bristol, 2022): Error-Corrected Quantum Cryptanalysis of CSIDH
Co-supervised with Ryan Mann and Romy Minko 		thesis
Samuel Gregg; Bachelor's thesis (Bristol, 2021): Introduction to Elliptic-curve Cryptography
Co-supervised with Matthew Bisatt
Georgie Hammond; Bachelor's thesis (Bristol, 2021): Elliptic curves and their applications
Harry Hedges; Bachelor's thesis (Bristol, 2021): Properties of CSI-FiSh: An analysis of the CSI-FiSh digital signature scheme
Cameron Low; Bachelor's thesis (Bristol, 2021): An overview and optimization of CSIDH-related key agreements
Chao Yang; MSc thesis (Bristol, 2021): An efficient algorithm for updating a key known to multiple parties
Dimitrij Ray; Master's thesis (Eindhoven, 2018): Constructing the Deuring Correspondence with Applications to Supersingular Isogeny-Based Cryptography
Co-supervised with Tanja Lange and Lorenz Panny. 		presentation code thesis
Ivo Kok; Bachelor's thesis (Leiden, 2014): Rings in which every ideal has two generators
Co-supervised with Marco Streng. 		thesis

Modular Polynomials

Here is a growing list of Hilbert modular polynomials. The theory behind this and the algorithm to compute them is in Chapter 2 of my PhD thesis. The code to compute these polynomials is here.