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Nombre de programmes trouvés : 48
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le (7m19s)

1.1. Introduction I - Cryptography

Welcome to this MOOC which is entitled: code-based cryptography. This MOOC is divided in five weeks. The first week, we will talk about error-correcting codes and cryptography, this is an introduction week.Then, we will introduce the McEliece cryptosystem, and the security proof for the McEliece cryptosystem. We will talk about generic attack, message attack, in other words. This course will be given by Nicolas Sendrier. Then, we'll give structural attacks or key attacks, and at the end, we will talk about othercryptographic constructions relying on coding theory. This last week will be given by Matthieu Finiasz.  Today is the first ...
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le (5m51s)

1.2. Introduction II - Coding Theory

In this session, we will give a brief introduction to Coding Theory. Claude Shannon's paper from 1948 entitled "A Mathematical Theory of Communication" gave birth to the disciplines of Information Theory and Coding Theory. The main goal of these disciplines is efficient transfer of reliable information. To be efficient, the transfer of information must not require a big amount of time and effort.  To be reliable, the transmitted and received data must resemble. However, during the transmission over a noisy channel, the information will be damaged. So, it has become necessary to develop ways of detecting when an error has ...
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le (8m14s)

1.6. Decoding (A Difficult Problem)

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 vector, which is the encoding of the original message plus a certain vector, is again the original message, for every message and every reasonable noisy pattern. The basis of decoding is the following principle, called Minimum Distance Decoding. Given a received vector, we look for a codeword that minimizes the Hamming distance with the received vector One of ...
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le (6m21s)

4.2. Support Splitting Algorithm

This session will be about the support splitting algorithm. For the q-ary case, there are three different notions of equivalence. The general one: two codes of length n are semi-linear equivalent if they are equal up to a fixed linear map. Each linear map is the composition of a permutation, a scalar multiplication, which could vary for each coordinate, and a field automorphism. But for this session, we consider a more restrictive definition, which coincides with the general case for binary linear code. Two codes are permutation-equivalent if they are ...
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le (4m22s)

5.2. The Courtois-Finiasz-Sendrier (CFS) Construction

In this session, I am going to present the Courtois-Finiasz-Sendrier Construction of a code-based digital signature. In the previous session, we have seen that it is impossible to hash a document into decodable syndromes. But it is possible to hash onto the space of all syndromes. The document is not always decodable. And we are going to see two techniques to work around this problem. The first technique is to add a counter to the document. This way, we hash both the counter and the document and obtain a hash which is tied to both the document and the ...
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le (4m52s)

5.3. Attacks against the CFS Scheme

In this session, we will have a look at the attacks against the CFS signature scheme. As for public-key encryption, there are two kinds of attacks against signature schemes. First kind of attack is key recovery attacks where an attacker tries to recover the secret key from the knowledge of the public key. These attacks are exactly the same as against the McEliece cryptosystem that you have seen last week. The only difference is the parameters. Here in the signature, we have a small t and a large n but the algorithm ...
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le (4m15s)

1.3. Encoding (Linear Transformation)

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 of k-tuples having elements from the field Fq. There are qk possible messages and we referred to it as the message space.  In order to detect and possibly correct errors, we add some redundancy, thus the k tuples will be embedded into n-tuples with n greater than k. In this MOOC, we will focus on linear ...
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le (4m47s)

1.4. Parity Checking

 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 describing a linear code, explicitly, as we have seen in the previous sequence, by a generator matrix, or implicitly, by the null space of a matrix. This is what we will see in this sequence. This leads to the following definition: H is a parity check matrix of a linear code, if the code is the null space ...
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le (8m26s)

1.5. Error Correcting Capacity

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 decoding that is returning the nearest codeword to the received vector. The metric principle is based on the following concept: the Hamming distance between two vectors is the number of coordinates in which they differ. The Hamming weight of a vector is the number of non-zero coordinates. Here we give some examples. So, the Hamming distance ...
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