| Cours |
Date |
Cours / Lecture |
Enseignant |
Support de cours/Slides |
| 1 |
17/9/2013 |
General Introduction. Polynomial System Solving. Applications in Robotics and Cryptology. |
JC Faugère |
 |
| 2 |
24/9/2013 |
Ideal, Varietes definition of Gröbner Bases. Buchberger's Algorithm. Gröbner bases properties. |
JC Faugère |
|
| 3 |
1/10/2013 |
Characterizations of Gröbner Bases. |
JC Faugère |
|
| 4 |
8/10/2013 |
Elimination. Buchberger's Criteria. Strategies. |
JC Faugère |
|
| 5 |
15/10/2013 |
Quotient Space - FGLM |
JC Faugère |
|
| 6 |
22/10/2013 |
Sparse FGLM - Matrix Representation - Macaulay Matrices- Regular Sequences |
JC Faugère |
|
| 7 |
29/10/2013 |
F4 Algorithm - Linear Algebra - F5 Criterion . Matrix-F5 algorithm. |
JC Faugère |
|
| 8 |
5/11/2013 |
Complexity results.
Hilbert function.
Overdetermined systems. Semi-Regular systems. |
JC Faugère |
|
| 9 |
12/11/2013 |
Minrank
Bilinear Systems
Solving systems over finite fields Hybrid Method. The binary case. |
JC Faugère |
|
| 10 |
19/11/2013 |
Alegraic Attacks against ECDLP (Discrete Logarithm Problem for Elliptic Curves) -- Semaev's Equations |
L Perret |
|
| 11 |
26/11/2013 |
MinRank and Applications to Multivariate Schemes (HFE, ....) |
L Perret |
|
| Partiel |
3/12/2013 |
Examen (Partiel/Oral Examen 14h15-15h45) |
|
|
| 12 |
10/12/2013 |
Functional Decomposition and Applications in Cryptography |
L Perret |
|
| 13 |
17/12/2013 |
Algebraic Cryptanalysis of McEliece Schemes (I) |
L Perret |
|
| 14 |
|
Algebraic Cryptanalysis of McEliece Schemes (II) |
L Perret |
|
| 15 |
|
Polynomials With Errors -- Fully-Homomorphic Variant of
Polly-Cracker |
L Perret |
|
| 16 |
|
Polynomials With Errors -- Fully-Homomorphic Variant of
Polly-Cracker |
L Perret |
|
| E |
|
Final Exam: questions asked on an article handled to students four weeks before the exam  |
|
Exemple de sujets  et |