Notice
1.9. McEliece Cryptosystem
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Descriptif
This is the last session ofthe first week of this MOOC. We have already all the ingredientsto talk about code-based cryptography. Recall that in 1976 Diffieand Hellman published their famous paper "New Directionsin Cryptography", where they introduced public keycryptography providing a solution to the problem of key exchange. Mathematically speaking,public key cryptography considers the notion ofone-way trapdoor function that is easy in one direction,hard in the reverse direction unless you have a specialinformation called the trapdoor. The security of the mostpopular public key cryptosystems is based either on thehardness of factoring or the presumed intractability ofthe discrete log problem. Code-based cryptography is based onthe following one-way trapdoor function. It is easy and fast toencode a message using linear transformations since it can beviewed as a matrix multiplication. It is hard to decoderandom linear code. Recall that the generaldecoding problem was proven to be NP-complete in the late 1970s. And the trapdoorinformation is that there exists some families of codes that haveefficient decoding algorithms. We have seen thegeneralized Reed-Solomon codes and the Goppa codes.McEliece presented, in 1978, the first public key cryptosystembased on error-correcting codes. The security of this schemeis based on two intractable problems: the hardness ofdecoding, or equivalently the problem of finding codewordsof minimal support, and the problem of distinguishinga code with a prescribed structure from a random one.
Intervention
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