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A fault injection framework for the decryption algorithm of the Niederreiter public-key cryptosystem using binary irreducible Goppa codes and classical decoding techniques is described. In particular, we obtain low-degree polynomial equations in parts of the secret key. For the resulting system of polynomial equations, we present an efficient solving strategy and show how to extend certain solutions to alternative secret keys. We also provide estimates for the expected number of required fault injections, apply the framework to state-of-the-art security levels, and propose countermeasures against this type of fault attack.
Goppa codes are particularly appealing for cryptographic applications. Every improvement of our knowledge of Goppa codes is of particular interest. In this paper, we present a sufficient and necessary condition for an irreducible monic polynomial $g(
We give a general method to construct MDS one-dimensional convolutional codes. Our method generalizes previous constructions of H. Gluesing-Luerssen and B. Langfeld. Moreover we give a classification of one-dimensional Convolutional Goppa Codes and p
Projective Reed-Muller codes were introduced by Lachaud, in 1988 and their dimension and minimum distance were determined by Serre and S{o}rensen in 1991. In coding theory one is also interested in the higher Hamming weights, to study the code perfor
Generalized Goppa codes are defined by a code locator set $mathcal{L}$ of polynomials and a Goppa polynomial $G(x)$. When the degree of all code locator polynomials in $mathcal{L}$ is one, generalized Goppa codes are classical Goppa codes. In this wo
Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally recoverable codes. In this work we introduce a new family of codes wit