Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: Overall Objectives

Overall Objectives

Our research addresses the broad application domain of cryptography and cryptanalysis from the algorithmic perspective. We study all the algorithmic aspects, from the top-level mathematical background down to the optimized high-performance software implementations. Several kinds of mathematical objects are commonly encountered in our research. Some basic ones are truly ubiquitous: integers, finite fields, polynomials, real and complex numbers. We also work with more structured objects such as number fields, algebraic curves, or polynomial systems. In all cases, our work is geared towards making computations with these objects effective and fast.

The two facets of cryptology—cryptography and cryptanalysis—are central to our research. The key challenges are the assessment of the security of proposed cryptographic primitives (both public- and secret-key), as well as the introduction of new cryptographic primitives, or the performance improvement of existing ones.

Our research connects to both symmetric and asymmetric key cryptography. While the basic principles of these domains are rather different—indeed their names indicate different handlings of the key—research in both domains is led by the same objective of finding the best trade-offs between efficiency and security. In addition to this, both require to study design and analysis together as these two aspects nurture each other.

Our research topics can be listed either with broad applications domains in mind (a very coarse-grain view would have us list them under cryptography and cryptanalysis), or more thematically (see Figure 1). Either way, we also identify a set of tools that we sometimes develop per se, but most often as ingredients towards goals that are set in the context of other themes. Following the “vertical” reading direction in Figure 1, our research topics are as follows.

Figure 1. Visual representation of the thematic organization of CARAMBA. Solid dots: major interaction; clear dots: minor interaction.

As a complement to the last point, we consider that the impact of our research on cryptology in general owes a lot to the publication of concrete practical results. We are strongly committed to making our algorithms available as software implementations. We thus have several long-term software development projects that are, and will remain, part of our research activity.