Théorie de l'information

In this session, we will talk about the easy map of the  - one-way trapdoor functions based on error-correcting codes. We suppose that the set of all messages that we wish to transmit is the set

Welcome to the third week of the MOOC on code-based cryptography. This week, we will learn about message attacks. Among the ten sessions of this week, the first six will present the most essential

In this session, we will introduce an attack against binary Reed-Muller codes. Reed-Muller codes were introduced by Muller in 1954 and, later, Reed provided the first efficient decoding algorithm

 There are two standard ways to describe a subspace, explicitly by giving a basis, or implicitly, by the solution space of the set of homogeneous linear equations. Therefore, there are two ways of

In this session, I will detail two combinatorial solutions to the decoding problem. The first one is the Exhaustive Search. To find our w columns, we will simply enumerate all the tuples j1 to jw

In this session, we will present an attack against Algebraic Geometry codes (AG codes). Algebraic Geometry codes is determined by a triple. First of all, an algebraic curve of genus g, then a n

This sequence will be about the error-correcting capacity of a linear code. We describe the way of considering the space Fq^n as a metric space. This metric is necessary to justify the principle of

In this third session, we will present the most important concept of the week: Information Set Decoding. The problem of decoding is not only a combinatorial problem. Because we are dealing with

All the results that we have seen this week doesn't mean that code based cryptography is broken. So in this session we will see that Goppa code still resists to all these attacks. So recall that

The process of correcting errors and obtaining back the message is called decoding. In this sequence, we will focus on this process, the decoding. We would like that the decoder of the received

In this session, I will present the main technique to make the analysis of the various algorithms presented in this course. So, Information Set Decoding refers to a family of algorithms which is

Welcome to the last week of this MOOC on code-based cryptography. This week, we will be discussing other cryptographic constructions relying on coding theory. We have seen how to do public key