416 research outputs found
New Set of Codes for the Maximum-Likelihood Decoding Problem
The maximum-likelihood decoding problem is known to be NP-hard for general
linear and Reed-Solomon codes. In this paper, we introduce the notion of
A-covered codes, that is, codes that can be decoded through a polynomial time
algorithm A whose decoding bound is beyond the covering radius. For these
codes, we show that the maximum-likelihood decoding problem is reachable in
polynomial time in the code parameters. Focusing on bi- nary BCH codes, we were
able to find several examples of A-covered codes, including two codes for which
the maximum-likelihood decoding problem can be solved in quasi-quadratic time.Comment: in Yet Another Conference on Cryptography, Porquerolle : France
(2010
Re-encoding reformulation and application to Welch-Berlekamp algorithm
The main decoding algorithms for Reed-Solomon codes are based on a bivariate
interpolation step, which is expensive in time complexity. Lot of interpolation
methods were proposed in order to decrease the complexity of this procedure,
but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a
technique, called re-encoding, which allows to reduce the practical running
time. However, this trick is only devoted for the Koetter interpolation
algorithm. We propose a reformulation of the re-encoding for any interpolation
methods. The assumption for this reformulation permits only to apply it to the
Welch-Berlekamp algorithm
Wet paper codes and the dual distance in steganography
In 1998 Crandall introduced a method based on coding theory to secretly embed
a message in a digital support such as an image. Later Fridrich et al. improved
this method to minimize the distortion introduced by the embedding; a process
called wet paper. However, as previously emphasized in the literature, this
method can fail during the embedding step. Here we find sufficient and
necessary conditions to guarantee a successful embedding by studying the dual
distance of a linear code. Since these results are essentially of combinatorial
nature, they can be generalized to systematic codes, a large family containing
all linear codes. We also compute the exact number of solutions and point out
the relationship between wet paper codes and orthogonal arrays
Improving success probability and embedding efficiency in code based steganography
For stegoschemes arising from error correcting codes, embedding depends on a
decoding map for the corresponding code. As decoding maps are usually not
complete, embedding can fail. We propose a method to ensure or increase the
probability of embedding success for these stegoschemes. This method is based
on puncturing codes. We show how the use of punctured codes may also increase
the embedding efficiency of the obtained stegoschemes
Image Watermaking With Biometric Data For Copyright Protection
In this paper, we deal with the proof of ownership or legitimate usage of a
digital content, such as an image, in order to tackle the illegitimate copy.
The proposed scheme based on the combination of the watermark-ing and
cancelable biometrics does not require a trusted third party, all the exchanges
are between the provider and the customer. The use of cancelable biometrics
permits to provide a privacy compliant proof of identity. We illustrate the
robustness of this method against intentional and unintentional attacks of the
watermarked content
Key Reduction of McEliece's Cryptosystem Using List Decoding
International audienceDifferent variants of the code-based McEliece cryptosystem were pro- posed to reduce the size of the public key. All these variants use very structured codes, which open the door to new attacks exploiting the underlying structure. In this paper, we show that the dyadic variant can be designed to resist all known attacks. In light of a new study on list decoding algorithms for binary Goppa codes, we explain how to increase the security level for given public keysizes. Using the state-of-the-art list decoding algorithm instead of unique decoding, we exhibit a keysize gain of about 4% for the standard McEliece cryptosystem and up to 21% for the adjusted dyadic variant
List-Decoding of Binary Goppa Codes up to the Binary Johnson Bound
International audienceWe study the list-decoding problem of alternant codes (which includes obviously that of classical Goppa codes). The major consideration here is to take into account the (small) size of the alphabet. This amounts to comparing the generic Johnson bound to the q-ary Johnson bound. The most favourable case is q = 2, for which the decoding radius is greatly improved. Even though the announced result, which is the list-decoding radius of binary Goppa codes, is new, we acknowledge that it can be made up from separate previous sources, which may be a little bit unknown, and where the binary Goppa codes has apparently not been thought at. Only D. J. Bernstein has treated the case of binary Goppa codes in a preprint. References are given in the introduction. We propose an autonomous and simplified treatment and also a complexity analysis of the studied algorithm, which is quadratic in the blocklength n, when decoding away of the relative maximum decoding radius
On Quasi-Cyclic Codes as a Generalization of Cyclic Codes
In this article we see quasi-cyclic codes as block cyclic codes. We
generalize some properties of cyclic codes to quasi-cyclic ones such as
generator polynomials and ideals. Indeed we show a one-to-one correspondence
between l-quasi-cyclic codes of length m and ideals of M_l(Fq)[X]/(X^m-1). This
permits to construct new classes of codes, namely quasi-BCH and
quasi-evaluation codes. We study the parameters of such codes and propose a
decoding algorithm up to half the designed minimum distance. We even found one
new quasi-cyclic code with better parameters than known [189, 11, 125]_F4 and
48 derivated codes beating the known bounds as well.Comment: (18/08/2011
- …