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On tensor products of CSS Codes
A criterion is given which provides a lower bound on the minimum distance of $\ mathcal{C} \otimes \mathcal{D}$ for every CSS code $\mathcal D$ and this result is applied to study the behaviour of iterated tensor powers of codes.
Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
An alternative to Sidelnikov and Shestakov attack is given by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed–Solomon code.
Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and Their Subcodes
We give polynomial time attacks on the McEliece public key cryptosystem-based either on algebraic geometry (AG) codes or on small co-dimensional subcodes of AG codes. These attacks consist in the
A Polynomial-Time Attack on the BBCRS Scheme
A key-recovery attack when \(z =1\) and \(m\) is chosen between \(1+R+O(\frac{1}{\sqrt{n}})\) where \(R\) denotes the code rate and this attack has complexity \(O(n^6) and breaks all the parameters suggested in the literature.
A polynomial time attack against algebraic geometry code based public key cryptosystems
A polynomial time attack on the McEliece public key cryptosystem based on algebraic geometry codes allows to recover a decoding algorithm for the public key even for codes from high genus curves.
Evaluation codes from smooth quadric surfaces and twisted Segre varieties
The parameters of any evaluation code on a smooth quadric surface are given and a BCH structure on twists of the Segre embedding of a product of any d copies of the projective line is detected.
An upper bound on the number of rational points of arbitrary projective varieties over finite fields
We give an upper bound on the number of rational points of an arbitrary Zariski closed subset of a projective space over a finite field. This bound depends only on the dimensions and degrees of the
On the security of a Loidreau rank metric code based encryption scheme
A polynomial time attack of a rank metric code based encryption scheme due to Loidreau for some parameters is presented and it is shown that the attack time is proportional to the number of parameters.
Construction of rational surfaces yielding good codes
  • Alain Couvreur
  • Computer Science
    Finite Fields Their Appl.
  • 13 August 2010