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2016

Folding Alternant and Goppa Codes With Non-Trivial Automorphism Groups

3 years 6 months ago
Folding Alternant and Goppa Codes With Non-Trivial Automorphism Groups
The main practical limitation of the McEliece public-key encryption scheme is probably the size of its key. A famous trend to overcome this issue is to focus on subclasses of alternant/Goppa codes with a non trivial automorphism group. Such codes display then symmetries allowing compact parity-check or generator matrices. For instance, a key-reduction is obtained by taking quasi-cyclic (QC) or quasi-dyadic (QD) alternant/Goppa codes. We show that the use of such symmetric alternant/Goppa codes in cryptography introduces a fundamental weakness. It is indeed possible to reduce the key-recovery on the original symmetric public-code to the key-recovery on a (much) smaller code that has not anymore symmetries. This result is obtained thanks to a new operation on codes called folding that exploits the knowledge of the automorphism group. This operation consists in adding the coordinates of codewords which belong to the same orbit under the action of the automorphism group. The advantage is ...
Jean-Charles Faugère, Ayoub Otmani, Ludovic
Added 11 Apr 2016
Updated 11 Apr 2016
Type Journal
Year 2016
Where TIT
Authors Jean-Charles Faugère, Ayoub Otmani, Ludovic Perret, Frédéric de Portzamparc, Jean-Pierre Tillich
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