Notice
4.1. Introduction
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Descriptif
Welcome to the fourth week of the MOOC Code-based Cryptography. Recall that we have mainlytwo ways of cryptanalyzing in the McEliece cryptosystem.We have Message Attacks, which address the problem ofdecoding a random linear code; these attacks has alreadybeen studied in the third week, by Nicolas Sendrier. Notice that efficientgeneric attack just makes the use of larger code in theMcEliece scheme necessary. And we also have Key Attacks. These attacks try toretrieve the code structure, rather than attempting to use anspecific decoding algorithm. These attacks will bestudied during this week. First, let us give asmall introduction. The principle of theMcEliece cryptosystem is as follows: consider a large familyof codes, with an efficient decoding algorithm, whichis indistinguishable from a random family of linear codesof the same length and dimension. Then, the public key is agenerator matrix of a code of the chosen family and thenumber of errors that we can correct. And the secret key is anefficient decoding algorithm specific for such code. The encryption algorithm:we take a plaintext and the public key, and we generatean error-vector of weight at most t, which is theerror-correcting capacity. We encode the messageusing the public key, then, the ciphertext is just theresulting codeword, and the error. How to decrypt? We justapply the secret key that is an efficient decoding algorithm,to retrieve the original message. McEliece proposed to usebinary Goppa code, but the parameters that heproposed are not enough nowadays. But there exist other familiessuitable for the McEliece scheme? On the following slides, we give asummary of these different proposals.
Intervention
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