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44 résultats
section 1 sur 4
résultats 1 à 12
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1.1. Introduction I - Cryptography  Droits d'accès : non autorisé
Description : 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 cry ...
Date : 05-05-2015
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1.1. Introduction I - Cryptography
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1.2. Introduction II - Coding Theory  Droits d'accès : non autorisé
Description : 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 informat ...
Date : 05-05-2015
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1.2. Introduction II - Coding Theory
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1.3. Encoding (Linear Transformation)  Droits d'accès : non autorisé
Description : 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 ...
Date : 05-05-2015
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1.3. Encoding (Linear Transformation)
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1.4. Parity Checking  Droits d'accès : non autorisé
Description :  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, ...
Date : 05-05-2015
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1.4. Parity Checking
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1.5. Error Correcting Capacity  Droits d'accès : non autorisé
Description : 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 ...
Date : 05-05-2015
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1.5. Error Correcting Capacity
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1.6. Decoding (A Difficult Problem)  Droits d'accès : non autorisé
Description : 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 ...
Date : 05-05-2015
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1.6. Decoding (A Difficult Problem)
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1.7. Reed-Solomon Codes  Droits d'accès : non autorisé
Description : Reed-Solomon codes were introduced by Reed and Solomon in the 1960s. These codes are still used in storage device, from compact-disc player to deep-space application. And they are widely used mainly because of two features: first of all, because they are MDS code, that is, they attain the maximum er ...
Date : 05-05-2015
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1.7. Reed-Solomon Codes
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1.8. Goppa Codes  Droits d'accès : non autorisé
Description : In this session, we will talk about another family of codes that have an efficient decoding algorithm: the Goppa codes. One limitation of the generalized Reed-Solomon codes is the fact that the length is bounded by the size of the field over which it is defined. This implies that these codes are use ...
Date : 05-05-2015
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1.8. Goppa Codes
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1.9. McEliece Cryptosystem  Droits d'accès : non autorisé
Description : This is the last session of the first week of this MOOC. We have already all the ingredients to talk about code-based cryptography. Recall that in 1976 Diffie and Hellman published their famous paper "New Directions in Cryptography", where they introduced public key cryptography providing a solution ...
Date : 05-05-2015
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1.9. McEliece Cryptosystem
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2.1. Formal Definition  Droits d'accès : non autorisé
Description : Welcome to the second week of this MOOC entitled Code-Based Cryptography. This week, we will talk in detail about the McEliece cryptosystem. First, in this session, we will describe formally the McEliece and the Niederreiter systems, which are the principal public-key schemes, based on error-correct ...
Date : 05-05-2015
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2.1. Formal Definition
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2.2. Security-Reduction Proof  Droits d'accès : non autorisé
Description : Welcome to the second session. We will talk about the security-reduction proof. The security of a given cryptographic algorithm is reduced to the security of a known hard problem. To prove that a cryptosystem is secure, we select a problem which we know is hard to solve, and we reduce the problem to ...
Date : 05-05-2015
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2.2. Security-Reduction Proof
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2.3. McEliece Assumptions  Droits d'accès : non autorisé
Description : In this session, we will talk about McEliece assumptions. The security of the McEliece scheme is based on two assumptions as we have already seen: the hardness of decoding a random linear code and the problem of distinguishing a code with a prescribed structure from a random one. In this sequence, w ...
Date : 05-05-2015
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2.3. McEliece Assumptions
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