Séminaire de Cryptographie

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elise barelli

Short McEliece key from algebraic geometry codes with automorphism

In 1978, McEliece introduced a public key encryption scheme based on linear codes and suggested to use classical Goppa codes, ie: subfield subcodes of algebraic geometric (AG) codes built on a curve of genus 0. This proposition remains secure and in order to have a generalization of classical Goppa codes, in 1996, H. Janwa and O. Moreno suggested to use subfield subcode of AG codes, which we call alternant AG codes. This proposition give a bigger choice of code because we can vary the curve, the genus, and the rational points of the divisor which generate the code. The principal limitation is the very large public keys of these codes compared to other public-key cryptosystems. To overcome this limitation, we decrease the key size by choosing codes which admit very compact public matrix. A way to obtained short key is to use codes having a non-trivial automorphisme group, for instance here we deal with quasi-cyclic alternant AG codes.