# Preprints

- Damien Robert,
*Fast pairings via biextensions and cubical arithmetic*. April 2024. (eprint.) - Sabrina Kunzweiler, Damien Robert,
*Computing modular polynomials by deformation*. January 2024. - Aurel Page, Damien Robert,
*Introducing Clapoti(s): Evaluating the isogeny class group action in polynomial time*. November 2023. (eprint.) - Pierrick Dartois, Luciano Maino, Giacomo Pope, Damien Robert,
*An Algorithmic Approach to $(2,2)$-isogenies in the Theta Model and Applications to Isogeny-based Cryptography*. November 2023. (eprint.) - Damien Robert,
*The geometric interpretation of the Tate pairing and its applications*. February 2023. (eprint, HAL.) - Damien Robert,
*Some applications of higher dimensional isogenies to elliptic curves (overview of results)*. December 2022. (eprint, HAL.) - Damien Robert,
*Evaluating isogenies in polylogarithmic time*. August 2022. (eprint, HAL.) - Abdoulaye Maiga, Damien Robert,
*Towards computing canonical lifts of ordinary elliptic curves in medium characteristic*. March 2022. (HAL.) - Abdoulaye Maiga, Damien Robert,
*Computing the canonical lift of genus 2 curves in odd characteristic*. December 2020. (HAL.) - David Lubicz, Damien Robert,
*Linear representation of endomorphisms of Kummer varieties*. December 2020. (HAL.) - Jean Kieffer, Aurel Page, Damien Robert,
*Computing isogenies from modular equations between Jacobians of genus 2 curves*. October 2020. (HAL, arxiv, Extended version.)

# Publications

- Damien Robert, Nicolas Sarkis,
*Computing 2-isogenies between Kummer lines*. IACR Communications in Cryptology (CiC), January 2024. (eprint.) - Pierrick Dartois, Antonin Leroux, Damien Robert, Benjamin Wesolowski,
*SQISignHD: New Dimensions in Cryptography*. Accepted for publication at Eurocrypt 2024, March 2023. (eprint, HAL.) Best paper award. - Damien Robert,
*Breaking SIDH in polynomial time*. Eurocrypt 2023, April 2023. (eprint, HAL, Slides (15 min, April 2023, Lyon, France), Video.) Best Paper Honorable Mention. - David Lubicz, Damien Robert,
*Fast change of level and applications to isogenies*. ANTS XV Conference — Proceedings, December 2022. (Published version, HAL.) - Alina Dudeanu, Dimitar Jetchev, Damien Robert, Marius Vuille,
*Cyclic Isogenies for Abelian Varieties with Real Multiplication*. Moscow Mathematical Journal, February 2022. (HAL.) - Markus Kirschmer, Fabien Narbonne, Christophe Ritzenthaler, Damien Robert,
*Spanning the isogeny class of a power of an elliptic curve*. Mathematics of Computation, September 2021. (Published version, HAL, arxiv.) - Abdoulaye Maiga, Damien Robert,
*Computing the 2-adic canonical lift of genus 2 curves*. Proceedings of the 7th International Conference on Mathematics and Computing (ICMC 2021), March 2022. (Published version, HAL.) - Enea Milio, Damien Robert,
*Modular polynomials on Hilbert surfaces*. Journal of Number Theory, November 2020. (Published version, HAL, Reproducible archive.) - David Lubicz, Damien Robert,
*Arithmetic on Abelian and Kummer Varieties*. Finite Fields and Their Applications, May 2016. (Published version, HAL, eprint.) - David Lubicz, Damien Robert,
*Computing separable isogenies in quasi-optimal time*. LMS Journal of Computation and Mathematics, February 2015. (Published version, HAL, arxiv.) - David Lubicz, Damien Robert,
*A generalisation of Miller’s algorithm and applications to pairing computations on abelian varieties*. Journal of Symbolic Computation, March 2015. (Published version, HAL, eprint.) - Romain Cosset, Damien Robert,
*An algorithm for computing (l,l)-isogenies in polynomial time on Jacobians of hyperelliptic curves of genus 2*. Mathematics of Computation, November 2014. (Published version, HAL, eprint.) - Kristin Lauter, Damien Robert,
*Improved CRT Algorithm for Class Polynomials in Genus 2*(long version). ANTS X Conference — Proceedings, November 2013. (Published version, Slides (30min, July 2012, San Diego, USA), HAL, eprint, Submitted short version, Updated short version.) - David Lubicz, Damien Robert,
*Computing isogenies between abelian varieties*. Compositio Mathematica, September 2012. (Published version, HAL, arxiv.) - Jean-Charles Faugère, David Lubicz, Damien Robert,
*Computing modular correspondences for abelian varieties*. Journal of algebra, October 2011. (Published version, HAL, arxiv.) - David Lubicz, Damien Robert,
*Efficient pairing computation with theta functions*. ANTS IX conference — Proceedings in LNCS, July 2010. (Published version, Slides (30min, July 2010, Nancy), HAL.)

# Books

- Damien Robert,
*General theory of abelian varieties and their moduli spaces*. March 2021. Draft version. *Guide to Pairing-Based Cryptography*. 2017. Chapter 3 on « Pairings » with Sorina Ionica, and Chapter 10 on « Choosing Parameters » with Sylvain Duquesne, Nadia El Mrabet, Safia Haloui and Franck Rondepierre

# Reports

- Andreas Enge, Damien Robert,
*Computing class polynomials in genus 2*. DGA Report, April 2013.

# HDR

*Efficient algorithms for abelian varieties and their moduli spaces*. Habilitation à diriger les recherches, June 2021, Université Bordeaux. (Slides (1h, Bordeaux), Detailed version.)

# PhD Thesis

*Theta functions and cryptographic applications*(in French). PhD thesis in Computer Sciences, July 2010, Université Henri-Poincarré, Nancy. (Slides (1h, Nancy), TEL.)- Received the second prize in Science for the Lorraine Region PhD awards, February 2012, Metz. (Inria announcement)
- Received the Lorraine University PhD awards in the domain of IAEM (Computer science, Mathematics, Electronic), October 2011, Nancy. (Photos of the ceremony)

# Invited Speaker

*Arithmetic and pairings on Kummer lines*(45min). Leuven isogeny days 4, October 2023, Leuven.*Efficient representation of isogenies*(1h). EWHA-KMS International Workshop on Cryptography, July 2023.*Applications of isogenies between abelian varieties to elliptic curves*(1h). Arithmétique en Plat Pays, March 2023.*Applications of isogenies between abelian varieties to elliptic curves cryptosystems*(1h). Vantage Seminar, December 2022.*Isogenies between abelian varieties – an algorithmic survey*(1h). Leuven isogeny days 3, September 2022, Leuven.*Isogenies, Polarisations and Real Multiplication*(1h). Journées C2 Codage et Cryptographie, October 2015, La Londe-Les-Maures.*Isogenies, Polarisations and Real Multiplication*(1h). Modular Forms and Curves of Low Genus: Computational Aspects, September 2015, ICERM, Providence, USA. (Long version.)*Optimal pairings on abelian varieties*(1h). Elliptic Curves Cryptography (ECC 2014), October 2014, Chennai, India.*Isogenies between abelian varieties*(Notes) (1h). ANR Peace conference Effective moduli spaces and applications to cryptography, June 2014, Rennes.*Pairings on abelian varieties and the Discrete Logarithm Problem*(1h). Discrete Logarithm Problem Conference DLP 2014, May 2014, Ascona, Suisse.*Computing optimal pairings on abelian varieties with theta functions*(1h). Geometry and Cryptography (Geocrypt 2011), June 2011, Bastia.*Generalizing Vélu’s formulas and some applications*(1h). Elliptic Curves Cryptography (ECC 2010), 25 year anniversary of elliptic curves computation, October 2010, Redmond, USA. (Video link.)*A Vélu’s like formula for computing isogenies on Abelian Varieties*(1h). Conférence Algorithmique et Arithmétique avec applications à la cryptographie, May 2010, Moscow, Russia.

# Talks

*Isogeny based cryptography: from the fall of SIKE to the rise of higher dimensional isogenies*(30 min). Workshop Inria, University of Waterloo, Université de Bordeaux, February 2024, Inria, Bordeaux.*Number theory for post-quantum cryptography*(20 min). Conseil Scientifique,, February 2024, IMB, Bordeaux.*Infinitesimal pairings and CSIDH*(1h). PEPR Isogeny meeting,, January 2024, Cybercampus, Paris.*Recent advances in isogeny based cryptography*(20min). 8th Franco-Japanese Cybersecurity Workshop, November 2023, ENSC, Bordeaux.*New applications of higher dimensional isogenies*(1h). September 2023, Loria, Nancy.*Breaking SIDH in polynomial time*(1h). April 2023, Institut Fourier, Grenoble.*Applications of isogenies between abelian varieties to elliptic curves*(1h). LFANT Seminar, March 2023, Bordeaux. On blackboard*The geometric interpretation of the Tate pairing*(1h). ANR Ciao Workshop, December 2022, Bordeaux. On blackboard*Evaluating isogenies in polylogarithmic time*(1h). LFANT Seminar, October 2022, Bordeaux. On blackboard*Breaking SIDH in polynomial time*(1h). LFANT Seminar, September 2022, Bordeaux.*Towards computing the canonical lift of an ordinary elliptic curve in medium characteristic*(1h). LFANT Seminar, April 2022, Bordeaux. On blackboard*Revisiter l’algorithme de Satoh de comptage de points en petite caractéristique par relèvement canonique*(1h). LFANT Seminar, October 2021, Bordeaux. On blackboard*Calcul d’isogénies sur des variétés abéliennes*(1h). CIAO Kickoff Meeting, February 2020, Bordeaux. On blackboard*Extending Elkies’ isogeny algorithm to genus~$2$*(1h). GAATI team, January 2020, Tahiti. On blackboard*An overview of isogenies computations*(1h). LFANT Seminar, September 2019, Bordeaux. On blackboard*Modular Polynomials*(1h). LIRIMA Team FAST kick-off conference, September 2017, Bordeaux. On blackboard*Arithmetic on Abelian and Kummer varieties*(2x1h). INRIA Team LFANT seminar, May 2015, Bordeaux. On blackboard, notes.*Arithmetic on Elliptic Curves, Abelian varieties and Kummer varieties*(45min). École Mathématique Africaine, March 2015, Université de Masuku, Franceville, Gabon.*Arithmetic on Abelian and Kummer varieties*(1h). Number Theory Seminar, December 2014, Caen. On blackboard, notes.*Isogeny graphs in dimension 2*(1h). Cryptography Seminar, December 2014, Caen.*Arithmetic on Abelian and Kummer varieties*(1h). Number Theory Seminar, April 2014, Institut Fourier, Grenoble. On blackboard, notes.*Arithmetic on abelian varieties and related topics*(1h). Seminar in Coding Theory and Cryptography of the University of Zurich and the University of Neuchâtel, March 2014, Neuchâtel, Suisse.*Computing optimal pairings on abelian varieties with theta functions*(1h). Industrial ANR Simpatic meeting, January 2014, Caen.*Arithmetic on Abelian and Kummer varieties*(30min). ANR Peace meeting, December 2013, Rennes.*On isogenies and polarisations*(1h). LFANT Seminar, November 2013, Bordeaux.*On isogenies and polarisations*(30min). Geometry and Cryptography (Geocrypt 2013), October 2013, Tahiti.*On isogenies between abelian varieties*(45min). Microsoft Research, August 2013, Redmond, USA.*Computing optimal pairings on abelian varieties with theta functions*(1h). Microsoft Research, August 2013, Redmond, USA.*Computing optimal pairings on abelian varieties with theta functions*(30min). Arithmetic Geometry Cryptography and Coding Theory (AGCT 14), June 2013, Luminy, Marseille.*Computing optimal pairings on abelian varieties with theta functions*(1h). Lacal, May 2013, Lausanne.*Computing optimal pairings on abelian varieties with theta functions*(1h). CCIS seminar, April 2013, Grenoble.*Computing cyclic isogenies using real multiplication*(Notes) (1h). ANR Peace meeting, April 2013, Paris.*Computing rational isogenies from the equations of the kernel*(30min). ANR Peace meeting, November 2012, Paris.*Improved CRT Algorithm for class polynomials in genus 2*(1h). Microsoft Research, August 2012, Redmond, USA.*About the CRT method to compute class polynomials in dimension 2*(1h). INRIA Team LFANT seminar, May 2012, Bordeaux.*Algorithms on abelian varieties for cryptography*(1h). Caen’s Cryptographic Seminar, March 2012, Caen.*Algorithms on abelian varieties for cryptography*(2h). INRIA Team Grace Seminar, January 2012, LIX, École Polytechnique, Paris.*Algorithms on abelian varieties for cryptography*(1h). "Butte aux cailles" Seminar, January 2012, Télécom ParisTech, Paris.*Public key cryptography with abelian varieties: results and challenges*(1h). ARITH Seminar, November 2011, Montpellier.*Computing optimal pairings on abelian varieties with theta functions*(1h). Séminaire de théorie des nombres, September 2011, Bordeaux.*About the CRT method to compute class polynomials in dimension~2*(1h). Journées C2 Codage et Cryptographie, April 2011, Oléron.*Cryptology, elliptic curves and number theory*(1h). Number Theory PhD Students’ seminar, March 2011, Bordeaux.*Computing optimal pairings on abelian varieties with theta functions*(1h). Séminaire Arithmétique et Théorie de l’Information, February 2011, Université Méditerranée, Marseille.*Abelian varieties, theta functions and cryptography*(1h30). PhD Students’ seminar, February 2011, Université Méditerranée, Marseille.*Computing isogenies and applications in cryptography*(1h). Cryptology seminar, January 2011, Université Versailles Saint-Quentin, Versailles.*Computing isogenies and applications in cryptography*(1h). Minalogic cryptology seminar, January 2011, Grenoble.*Abelian varieties, theta functions and cryptography*(40min+40min). Algorithmics of L-functions workshop, December 2010, Bordeaux. Part 1 on blackboard.*On the CRT method to compute class polynomials in genus~2*(30min). ANR Chic, December 2010, Paris.*Generalizing Vélu’s formulas and some applications*(1h). TANC Seminar, November 2010, LIX, École Polytechnique, Paris.*Speeding up the CRT method to compute class polynomials in genus 2*(1h). Microsoft Research, September 2010, Redmond, USA.*Abelian varieties, Theta functions and cryptography*(30min). Microsoft Research, July 2010, Redmond, USA.*Arithmétique rapide avec les fonctions thêta*(20min). ANR Chic, June 2010, Paris.*A Vélu’s like formula for computing isogenies on abelian varieties*(1h). Séminaire de théorie des nombres, February 2010, Bordeaux.*Calcul de pairing avec les fonctions thêta*(1h). LFANT Cryptographic Seminar, February 2010, Bordeaux.*A Vélu’s like formula for computing isogenies on abelian varieties*(1h). Séminaire Arithmétique et Théorie de l’Information, November 2009, Marseille.*An efficient computation of the commutator pairing*(20min). ANR Chic, October 2009, Paris.*A Vélu’s like formula for computing isogenies on abelian varieties*(40min). ANR Chic, October 2009, Paris.*Computing isogenies of small degrees on abelian varieties*(20min). Journées d’arithmétiques 2009, July 2009, Saint-Etienne.*Computing isogenies of small degrees on abelian varieties*(1h). Séminaire de cryptographie, April 2009, Rennes.*Abelian varieties and isogenies*(30min). Tsukuba Cryptographic Seminar, November 2008, Tsukuba, Japan.

# Rump Sessions

*Finding a supersingular isogeny path with only one isogeny computation*(4 min). Eurocrypt 2023, April 2023, Lyon, France. (Video.)*Sleeping in the volcano*. ECC 2011 conference, September 2011, Nancy.*AVIsogenies, a library for computing isogenies between abelian varieties*, with Gaëtan Bisson, Romain Cosset. ECC 2010, October 2010, Redmond, USA. (Video link (starts at 16m30s).)

# Notes

- Damien Robert,
*Some notes on algorithms for abelian varieties*. March 2024. A convenient compilation of my various notes on abelian varieties. - Damien Robert,
*Computing cyclic isogenies using real multiplication*. April 2013. - Damien Robert,
*On symmetric theta structures*. April 2013. - Damien Robert,
*Isogenies between abelian varieties*. June 2014. - Damien Robert,
*Arithmetic on Abelian and Kummer varieties*. December 2014. - Damien Robert,
*Polarisations, isogenies, and pairings on abelian varieties*. September 2022. Unfinished notes - Damien Robert,
*Reducible gluing of abelian varieties*. September 2022. Unfinished notes - Damien Robert,
*The arithmetic of theta groups and biextensions of abelian varieties*. August 2023. - Damien Robert,
*A note on optimising 2ⁿ-isogenies in higher dimension*. June 2023. - Damien Robert,
*Improving the arithmetic of Kummer lines*. August 2023.

# Other sources

All my scientific activities can be found in my cv (French version). The full bibliographic informations are available in this bibtex file (French version), whose output can ben seen in this pdf document (French version). My Academic work is available on my personnal site. I also keep a (partial) list of conferences I have attended. Finally, there is also the publication list generated from HAL (usually less up to date).

The most recent version of the papers are on this page, the links to HAL, eprint or Arxiv may reference older versions.