Some weak keys in McEliece public-key cryptosystem
Pierre Loidreau
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France Pierre.Loidreau@inria.fr
Nicolas Sendrier
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France Nicolas.Sendrier@inria.fr
IEEE International Symposium on Information Theory, ISIT'98,
page 382, 1998
Abstract
We show that the Goppa codes \Gamma(L,g) where g is a binary
polynomial constitute a recognizable family of weak keys for the
McEliece public-key cryptosystem, inducing a structural attack against
the system that reduces very much the complexity of the known attacks.
In this paper we identify a set of weak keys of McEliece system -
Goppa codes generated by binary polynomials - thanks to a
polynomial time algorithm - the Support Splitting Algorithm which
recovers part of the automorphism group of a code. Such codes indeed
have a non trivial automorphism group which in general is the group of
automorphism of the field used as support of the code.