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<title><string language="fre"><![CDATA[1.9. McEliece Cryptosystem]]></string></title>
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<string language="fre"><![CDATA[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.]]></string></description>
<keyword><string language="fre"><![CDATA[algèbre linéaire]]></string></keyword><keyword><string language="fre"><![CDATA[chiffrement à clé publique]]></string></keyword><keyword><string language="fre"><![CDATA[cryptage des données]]></string></keyword><keyword><string language="fre"><![CDATA[cryptographie]]></string></keyword>
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