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Description (résumé)

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 to the problem of key exchange. Mathematically speaking, public key cryptography considers the notion of one-way trapdoor function that is easy in one direction, hard in the reverse direction unless you have a special information called the trapdoor. The security of the most popular public key cryptosystems is based either on the hardness of factoring or the presumed intractability of the discrete log problem. Code-based cryptography is based on the following one-way trapdoor function. It is easy and fast to encode a message using linear transformations since it can be viewed as a matrix multiplication. It is hard to decode random linear code.  Recall that the general decoding problem was proven to be NP-complete in the late 1970s. And the trapdoor information is that there exists some families of codes that have efficient decoding algorithms. We have seen the generalized Reed-Solomon codes and the Goppa codes. McEliece presented, in 1978, the first public key cryptosystem based on error-correcting codes. The security of this scheme is based on two intractable problems: the hardness of decoding, or equivalently the problem of finding codewords of minimal support, and the problem of distinguishing a code with a prescribed structure from a random one.

"Domaine(s)" et indice(s) Dewey

• Analyse numérique (518)
• Théorie de l'information (003.54)
• données dans les systèmes informatiques (005.7)
• cryptographie (652.8)
• Mathématiques (510)

Thème(s)