Talks

2024

Material of all lectures on the Number Field Sieve

To prepare for Douala’s 2024 CIMPA school that I unfortunately could not join, I collected the source files of all the lectures I gave from 2019 to 2024 on the Number Field Sieve, here there are with CC-BY-NC-SA licence: Gitlab website: nfs-lectures.

Conference Talks

• Elliptic Curve Cryptography workshop (ECC), Taipei, Taiwan, October 30-November 1, Elliptic Curves for SNARK and Proof Systems. Slides.
• Elliptic Curve Cryptography workshop school, Taipei, Taiwan, October 28-29, Introduction on elliptic curves and pairings. Lecture 1 slides, Lecture 2 slides, group_law_short_weierstrass_affine.sage
• Elliptic Curve Cryptography workshop school, Taipei, Taiwan, October 28-29, Exercise session with SageMath. MontgomeryLadder.pdf, ladder_skeleton.py, ladder_tests.py, solutions: ladder.py.
• March 1st, 2024, Journées Numération, Arithmétique, Cryptographie, Jussieu, Paris. Elliptic curves for proof systems. Slides.

Seminars

• GRACE GT
• Crypto seminar, Rennes, September 20.

2023

Conference Talks

• July 2023, 12th, SIAM conference on applied algebraic geometry, Eindhoven, The Netherlands, MS53 Introduction: Elliptic Curves and Pairings in Cryptography. Slides.
  See also the page of the minisymposium for the other talks and slides.
• June 2023, 14th, WRACH workshop, Roscoff, Brittany, France, A short-list of pairing-friendly curves resistant to the Special TNFS algorithm at the 192-bit security level. Slides.

Seminars

• 15 décembre 2023, séminaire ALMASTY, Paris, Pairing-friendly elliptic curves, design, implementation, and discrete logarithm computations, slides.
• 30 novembre 2023, séminaire CAPSULE, Rennes, Pairing-friendly elliptic curves, design, implementation, and discrete logarithm computations, slides.
• 24 novembre 2023, séminaire F. Morain, Paris 7, Simulating the TNFS algorithm to deduce cryptographic key-sizes for field extensions GF(pⁿ), slides.
• 1er février 2023 séminaire GREYC, Caen, Factoring RSA of 240 decimal digits and computing discrete logarithms in a 240-decimal-digit prime field with the same software and hardware, slides, paper (open access), source code.

Médiation scientifique

Camp Cigognes, Ramonchamp, 24 octobre 2023

• 24 octobre 2023, Un algorithme pour détecter les nouvelles pollutions de l’air, slides, sac_a_dos.py.

Journée Maths en Jeans, Nancy, 2 mai 2023

• 2 mai 2023, centre de recherche Inria Nancy Grand Est, Un algorithme pour détecter les nouvelles pollutions de l’air, slides, sac_a_dos.py.

1 scientifique 1 classe chiche

• 2 février 2023, Saint Louis (68300), slides.
• 6 mars 2023, Saint Dié des Vosges, slides.

2022

Seminars

• September 14, 2022: Nancy Journées au vert, Co-factor Clearing and Subgroup Membership Testing on Pairing-Friendly Curves, Slides.
• July 4, 2022: Aarhus Crypto Day, Co-factor clearing and subgroup membership testing in pairing groups, Slides.
• June 24, 2022: Nancy, Caramba Seminar, A survey of elliptic curves for proof systems, Slides, preprint, SageMath source code.
• May 4, 2022: Aarhus, Crypto and Security Group Seminar, Pairings and pairing-friendly elliptic curves for Cryptography, an Introduction, Slides.

1 scientifique 1 classe chiche

• 22 novembre 2022, Verdun, slides.
• 1er et 2 décembre 2022, Longwy slides.

2021

Conference Talk

• March 26, 2021 Journées GDR-IM, online event, France, Factoring RSA of 240 decimal digits and computing discrete logarithms in a 240-decimal-digit prime field with the same software and hardware, Slides, paper (open access), source code.

Seminars

• April 20, 2021: Toulon, séminaire IMATH, Understanding the special tower number field sieve algorithm and applications to pairing-based cryptography, Slides, paper (open access), source code.
• May 18, 2021: Bordeaux, séminaire LFANT, Computing Murphy-alpha in the special tower number field sieve algorithm, and applications, Slides, paper (open access), source code.
• June 29, 2021: Nancy, The knapsack algorithm in analytical chemistry, Slides, preprint, source code (LGPL).
• July 2, 2021: Aarhus Crypto Summer Days, The knapsack algorithm in analytical chemistry, Slides, preprint, source code (LGPL).
• September 23, 2021: Computer Science seminar, Aarhus, The knapsack algorithm in analytical chemistry, Slides, toy example in Python, preprint, source code (LGPL).

2020

Invited Talk

• November 26, 2020, Diamant, online event, Utrecht, The Netherlands, Factoring RSA of 240 decimal digits and computing discrete logarithms in a 240-decimal-digit prime field with the same software and hardware, Slides, preprint, source code.

Conference Talk

• June 2020, 4th, PKC 2020, IACR International Conference on Practice and Theory of Public-Key Cryptography, online conference, Edinburgh, United Kingdom. A short-list of pairing-friendly curves resistant to Special TNFS at the 128-bit security level. slides, Video, preprint, DOI.

Seminar

• December 2020, 10th, Aarhus Crypto and Security Group Seminar, online event, Aarhus University, Denmark, Factoring RSA of 240 decimal digits and computing discrete logarithms in a 240-decimal-digit prime field with the same software and hardware, Slides, preprint, source code.

2019

Conference Talks

• July 2019, 10th, SIAM conference on applied algebraic geometry, Bern, Switzerland, MS134 part 4: coding theory and cryptography, Pairing-friendly curves in cryptography and the special tower number field sieve algorithm. Slides, preprint, source code in Magma and Sage.
• April 2019, 17th, WRAC’H workshop, Roscoff, Brittany, France, A comparison of pairing-friendly curve key-sizes at the 192-bit security level. Slides.

Seminars

• June 2019, 21st, Sorbonne Université, Jussieu, Paris, France, séminaire C2, A first step toward an implementation of the Tower Number Field Sieve: selecting polynomials. Slides, preprint, source code in Magma and Sage.
• March 2019, 1st, Université de Rennes 1, France, séminaire de cryptographie, Discrete logarithm computation in finite fields GF(pⁿ) with NFS variants and consequences in pairing-based cryptography. Slides
• February 2019, 28th, Loria – Inria Nancy, France, séminaire sécurité du Loria, Discrete logarithm computation in finite fields GF(pⁿ) with NFS variants and consequences in pairing-based cryptography. (see the Slides of Rennes)
• February 2019, 12th, Université de Franche-Comté, France, séminaire de théorie des nombres, Calculs de logarithmes discrets dans F_pⁿ avec le crible de corps de nombres. Slides

Others

• June 11 and 13, 2019, Inria Nancy. An introduction to NFS for discrete logarithm computation, with small examples in SageMath. Slides. SageMath code (.zip).
• December 2, 2019, ECC 2019, Bochum, Germany. Rump session: 1001 ways to fail record computations. Slides.

2017

Invited talk

• November 2017, ECC 2017, Neijmegen, Netherlands, Estimating size requirements for pairings: simulating the Tower-NFS algorithm in GF(pⁿ). slides.

2016

Invited talk

• August 2016, Mathematical structures for cryptography workshop, Lorentz Center, Leiden, Netherlands, Consequences for pairing-based cryptography of the recent improvements on discrete logarithm computation in GF(pⁿ). slides.

Conference Talks

• August 2016, SAC 2016 Selected Areas in Cryptography, St. John’s, Newfoundland, Memorial University, Canada, August 10-12, 2016, Solving discrete logarithms on a 170-bit MNT curve by pairing reduction. Slides, Preprint.
• June 2016, 2016 CMS Summer Meeting, Summer meeting of the Canadian Mathematical Society, Edmonton, University of Alberta, Canada, June 24-27, 2016, Faster Individual Discrete Logarithms in non-prime finite fields GF(pⁿ) with the NFS and FFS algorithms. Slides, Preprint.
• June 2016, CNTA XIV, 2016, 14th meeting of the Canadian Number Theory Asociation, Calgary, Alberta, Canada, June 20-24, 2016, Discrete Logarithm Record in a 508-bit finite field GF(p³) with the NFS algorithm. Slides, Preprint.

Seminars

• April 2016, 21th, Radboud University, Nijmegen, Netherlands, Discrete logarithm computation record in a finite field GF(p³) of 508 bits with the Number Field Sieve algorithm.
• April 2016, 13th, Université de Neuchâtel, Switzerland.
• March 23rd, Number Nosh Seminar, University of Calgary, Point counting on genus two curves: Schoof-Elkies-Atkin variant (feed-back from a workshop at IPAM, UCLA).
• February 10th, Number Nosh Seminar, University of Calgary, Computing discrete logarithms in finite fields with the Number Field Sieve algorithm.
• January 27th, Number Nosh Seminar, University of Calgary, Computing discrete logarithms in finite fields with the Number Field Sieve algorithm.

2015

Invited talks

• October 2015, CATREL Workshop, Palaiseau, France, Computing individual discrete logarithms faster in GF(pⁿ) with the Number Field Sieve algorithm. slides.
• September 2015, Elliptic Curve Cryptography (ECC) Conference, Bordeaux, France, Computing individual discrete logarithms faster in GF(pⁿ) with the Number Field Sieve algorithm. slides.

Conference Talks

• November 2015, ASIACRYPT 2015, Auckland, New Zealand, November 29-December 3, Computing Individual Discrete Logarithms Faster in GF(pⁿ) with the NFS-DL algorithm. Slides, Preprint.
• October 2015, Journées Codage et Cryptographie (JC2), La Londe Les Maures, France, Calculs de logarithmes discrets dans GF(p^k) à l’aide du crible de corps de nombres (NFS-DL), applications à k=2,3,4,6.
• May 2015, AGCT 2015, CIRM, Luminy, France Improving NFS for the discrete logarithm problem in non-prime finite fields, polynomial selection and individual logarithm. Slides.
• April 2015, EUROCRYPT 2015, Sofia, Bulgaria, Improving NFS for the discrete logarithm problem in non-prime finite fields. Slides, Preprint.

Seminars

• December 2015, 15th, GRACE Team GT, Christmas Special, Fin de post-doc
• November 2015, 26th Université de Versailles, Séminaire de cryptographie et sécurité informatique, Individual discrete logarithms in non-prime finite fields.
• November 2015, 13th, Université de Rennes, Séminaire de Cryptographie, Individual discrete logarithms in non-prime finite fields.
• October 2015, 10th, Université de Limoges, Séminaire Protection de l’Information, Codage, Cryptographie, Individual discrete logarithms in non-prime finite fields.
• March 2015, Université d’Aix Marseille, Séminaire Arithmétique et Théorie de l’Information, Polynomial selection for NFS-DL in non-prime finite fields.
• February 2015, Université de Toulon, séminaire d’Informatique et Algèbre Appliquée, IMATH, Polynomial selection for NFS-DL in non-prime finite fields.
• January 2015, Université de Caen, séminaire Cryptologie et Sécurité, GREYC, Polynomial selection for NFS-DL in non-prime finite fields.

2014

Seminar

• November 2014, Séminaire Codage, Cryptographie, Algorithmes (CCA), Paris, France, Polynomial selection for NFS-DL in non-prime finite fields.

2013

Invited talk

• September 2013, ECC Conference, Leuven, Belgium, Four dimensional GLV via the Weil restriction. slides.

Conference Talk

• June 2013, ACNS, Banff, Alberta, Canada, Comparing the Pairing Efficiency over Composite-Order and Prime-Order Elliptic Curves. Preprint

2012

Conference Talks

• October 2012, Journées Codage et Cryptographie, Dinard, France, Comparing the Pairing Efficiency over Composite-Order and Prime-Order Elliptic Curves.
• September 2012, YACC, Porquerolles, France, Comparing the Pairing Efficiency over Composite-Order and Prime-Order Elliptic Curves.
• May 2012, Pairing 2012, Cologne, Germany, Improved Broadcast Encryption Scheme with Constant-Size Ciphertext.Preprint
• May 2012, Pairing 2012, Cologne, Germany, Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions.Preprint