Thesis in cryptography (M/F): Linear algebra for Gröbner bases
- FTC PhD student / Offer for thesis
- 36 month
- Doctorate
This offer is available in English version
This offer is open to people with a document recognizing their status as a disabled worker.
Offer at a glance
The Unit
Laboratoire de mathématiques de Versailles
Contract Type
FTC PhD student / Offer for thesis
Working hHours
Full Time
Workplace
78035 VERSAILLES
Contract Duration
36 month
Date of Hire
01/10/2026
Remuneration
2300 € gross monthly
Apply Application Deadline : 03 July 2026 23:59
Job Description
Thesis Subject
In cryptanalysis, some attacks are modeled as polynomial systems in several variables, defined over finite fields. To solve these systems, the most efficient methods rely on the computation of Gröbner bases, using algorithms based on linear algebra applied to certain matrices, called Macaulay matrices. For the parameters used in cryptography, these matrices are very large, and their manipulation becomes costly in terms of both computation time and memory.
In some cases, structured polynomial systems are obtained, such as bi-homogeneous systems. The doctoral student's task will be to develop and implement an algorithm dedicated to solving bilinear polynomial systems, which constitute a particular class of bi-homogeneous systems of degree 2. Indeed, it is well known that, to solve such systems, the computation of a Gröbner basis amounts to manipulating smaller Macaulay matrices, corresponding to blocks of degree two. However, no efficient software implementation of such an algorithm is currently available, and comparing its performance with that of classical algorithms, such as F4 and F5, remains an open question.
The thesis will then focus on solving bilinear systems arising from the modeling of index calculation attacks applied to elliptic curves.
This work will be part of the "Linear Algebra" Work Package of the ANR PEPR Cryptanalysis project.
Your Work Environment
The doctoral student will be integrated into the 'Cryptology and Information Security' team of the LMV laboratory (UMR CNRS 8100). He/She will be supervised by Sorina Ionica (LMV) and Charles Bouillaguet (LIP6), with very regular progress meetings, and the training will be monitored within the framework of the ED STIC, also relying on the individual thesis monitoring committee.
Constraints and risks
The position is located in a sector related to the protection of scientific and technical potential (PPST), and therefore requires, in accordance with regulations, that your arrival be authorized by the competent authority of the MESR.
Compensation and benefits
Compensation
2300 € gross monthly
Annual leave and RTT
44 jours
Remote Working practice and compensation
Pratique et indemnisation du TT
Transport
Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€
About the offer
| Offer reference | UMR8100-LOUGOU-004 |
|---|---|
| CN Section(s) / Research Area | Information sciences: bases of information technology, calculations, algorithms, representations, uses |
About the CNRS
The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.
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