Parisian Master of Research in Computer Science
Master Parisien de Recherche en Informatique (MPRI)

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cours:c-2-12-2 [2019/02/22 08:14]
bsmith [Planning, année/year 2018-2019]
cours:c-2-12-2 [2019/09/16 10:07] (current)
morain [Planning, année/year 2019-2020]
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 |[[http://www.lix.polytechnique.fr/Labo/Francois.Morain/|François Morain]]|PU|École polytechnique|LIX| |[[http://www.lix.polytechnique.fr/Labo/Francois.Morain/|François Morain]]|PU|École polytechnique|LIX|
 |[[http://www.lix.polytechnique.fr/~smith/|Benjamin Smith]]|CR|INRIA|LIX| |[[http://www.lix.polytechnique.fr/~smith/|Benjamin Smith]]|CR|INRIA|LIX|
-|[[http://www.loria.fr/~barbules/|Razvan Barbulescu]]|CR|CNRS|P6| 
  
  
  
-==== Planning, année/year 2018-2019 ====+ 
 +==== Planning, année/year 2019-2020 ====
  
 ** Taught in Period 1 and Period 2: see below ** ** Taught in Period 1 and Period 2: see below **
  
-Tuesday evenings from **17h45 to 19h15** in Bâtiment Sophie Germain (P7), salle 1003.+Tuesday evenings from **16h15 to 17h55** in Bâtiment Sophie Germain (P7), salle 1013.
  
-|18/09| François Morain  |Number theory and quantum factoring+|17/09| François Morain  | Generic groups; Z/NZ and applications
-|25/09| François Morain  |[[http://www.lix.polytechnique.fr/Labo/Francois.Morain/MPRI/2018/td180925.pdf|TD on number theory]]+|24/09| François Morain  | Elementary integer factorization| 
-|02/10| Razvan Barbulescu|Attacks on RSA+|01/10| François Morain  Continued fractions and applications; quantum integer factorization
-|09/10| Razvan Barbulescu|Attacks on pairings+|08/10| François Morain  L[1/2] factoring and discrete logarithms computations
-|16/10| Razvan Barbulescu|A quasi-polynomial discrete logarithm algorithm+|15/10| François Morain  Number field sieve
-|23/10| Razvan Barbulescu|** TD/Lab **| +|22/10| François Morain  Computing discrete logarithms in small characteristic
-|30/10| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/cheatsheet.pdf|Elliptic curves]]+|29/10| François Morain  |** TD/Lab **| 
-|06/11| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/2.pdf|Modern ECDH]]| +|05/11| Ben Smith        |ECM and basic ECC protocols
-|13/11| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/3.pdf|Elliptic curve signature schemes]]+|12/11| Ben Smith        |Real-world ECM and ECDH: Montgomery arithmetic
-|20/11| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/4-TD.pdf|Revision TD **18:00-19:00**]]| +|19/11 or 26/11|         |** Midterm exam **| 
-|27/11|                  |** Midterm exam **| +|03/12|                  (no class) 
-|04/12| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/5.pdf|Isogenies and endomorphisms]]+|10/12| Ben Smith        | | 
-|11/12| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/6.pdf|Isogenies, endomorphisms, and rational points]]+|17/12| Ben Smith        | |
-|18/12| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/7.pdf|Point counting]]|+
 |     |                  |Holidays| |     |                  |Holidays|
-|08/01| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/8.pdf|Commutative isogeny cryptosystems]]+|07/01| Ben Smith        | | 
-|15/01| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/9.pdf|Isogeny-based cryptography II]]+|14/01| Ben Smith        | | 
-|22/01| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/A.pdf|Divisors]]+|21/01| Ben Smith        | | 
-|29/01| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/B.pdf|Hyperelliptic curves]]+|28/01| Ben Smith        | | 
-|05/02|                  |** No class **| +|04/02| Ben Smith        | | 
-|12/02| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/C.pdf|Hyperelliptic curves, Weil descent, and Pairings]] **16:15-17:45**+|11/02| Ben Smith        | | 
-|19/02| Ben Smith        |[[https://www.lix.polytechnique.fr/~smith/MPRI/D.pdf|Pairings]], Conclusion/Revision **16:00->**+|18/02|                  | (no class
-|26/02|                  |** No class **+|25/02 or 06/03|         |** Final exam **|
-|05/03|                  |** Final exam **|+
  
-The Final Exam will take place on Tuesday, 5 March 2019, from 16h15 to 18h15 in the usual room. 
  
 ==== Course Objectives ==== ==== Course Objectives ====
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 ==== Plan ==== ==== Plan ====
  
-The course is split into three parts:+The course is split into two parts:
  
-== Cryptographic groups: 1.5 hours (François Morain) == +== Cryptographic groups, factorization, and discrete logarithmshours (François Morain) ==
-The first part of the course covers the use of groups in cryptography, including the concept of "generic groups" and associated algorithms.+
  
-== Factorization and discrete logarithms -- 4.5 hours (Razvan Barbulescu) == +== Modern and postmodern elliptic curve cryptography -- 15 hours (Ben Smith) == 
-In the second part, we consider the two fundamental algorithmic problems posed by the principal asymmetric cryptography primitives: +The second part of the course is an introduction to contemporary elliptic-curve cryptography (ECC), including hyperelliptic cryptosystems and pairings.
-integer factorization and discrete logarithms.  This analysis allows us to identify weak classes of keys, and to estimate security levels corresponding to a given keylength in view of the current state-of-the-art.  Our emphasis will be on recent advances in the field of discrete logarithms. +
- +
-== Modern and postmodern elliptic curve cryptography -- 18 hours (Ben Smith) == +
-The final part of the course is an introduction to contemporary elliptic-curve cryptography (ECC), including hyperelliptic cryptosystems and pairings.+
 It also describes a new generation of isogeny-based cryptosystems, which are designed to resist attacks by quantum algorithms. It also describes a new generation of isogeny-based cryptosystems, which are designed to resist attacks by quantum algorithms.
 After describing the basic properties and arithmetic of elliptic curves, we consider the current state-of-the-art in elliptic-curve cryptographic primitives. After describing the basic properties and arithmetic of elliptic curves, we consider the current state-of-the-art in elliptic-curve cryptographic primitives.
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 **F. Morain** donne sa partie du cours **en français ou en anglais** suivant la demande (english on request). **F. Morain** donne sa partie du cours **en français ou en anglais** suivant la demande (english on request).
- 
-**R. Barbulescu** will teach **in English**. 
  
 **B. Smith** will teach **in English**.  **B. Smith** will teach **in English**. 
 
Universités partenaires Université Paris-Diderot
Université Paris-Saclay
ENS Cachan École polytechnique Télécom ParisTech
ENS
Établissements associés Université Pierre-et-Marie-Curie CNRS INRIA CEA