Finding low-weight polynomial multiples using discrete logarithm

Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an improvement to this approach using discrete logarithm rather than a direct representation of the involved polynomials. This gives an algorithm which improves the theoretical complexity, and is also very flexible in practice

A Lower Bound on the Higher Order Nonlinearity of Algebraic Immune Functions

We extend the lower bound, obtained by M. Lobanov, on the first order nonlinearity of functions with given algebraic immunity, into a bound on the higher order nonlinearities

Information Hiding by Coverings

We propose a formal model for embedding information in black-white images and prove the equivalence between existence of embedding schemes and covering codes. An asymptoticly tight bound on the performance of embedding schemes is given. We construct e#cient embedding schemes via known coverings. In particular, one of those schemes allows to embed up to #log 2 (n 1)# bits in coverwords of n bits, changing at most one bit, which is twice better than [6]. We rewrite some previous schemes with a look towards their covering structures. Finally, we address the problem of active warden in a similar way, giving a model, establishing the relationship with centered codes and concluding by a construction of schemes resisting to active warden

A new algorithm for finding minimum-weight words in a linear code: application to primitive narrow-sense BCH codes of length 511

: An algorithm for finding small-weight words in large linear codes is developed. It is in particular able to decode random [512,256,57]-linear codes in 9 hours on a DEC alpha computer. We determine with it the minimum distance of some binary BCH codes of length 511, which were not known. Key-words: error-correcting codes, decoding algorithm, minimum weight, random linear codes, BCH codes. (R'esum'e : tsvp) submitted to IEEE Transactions on Information Theory Also with ' Ecole Nationale Sup'erieure de Techniques Avanc'ees, laboratoire LEI, 32 boulevard Victor, F-75015 Paris. Laboratoire d'Informatique de l'Ecole Normale Sup'erieure, 45 rue d'Ulm, 75230 Paris Cedex 05 Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telephone : (33 1) 39 63 55 11 -- Telecopie : (33 1) 39 63 53 Un nouvel algorithme pour trouver des mots de poids minimum dans un code lin'eaire : application aux codes BCH primitifs au sens strict de l..