Related papers: Polynomial time key-recovery attack on high rate r…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…
The main practical limitation of the McEliece public-key encryption scheme is probably the size of its key. A famous trend to overcome this issue is to focus on subclasses of alternant/Goppa codes with a non trivial automorphism group. Such…
We present a new distinguisher for alternant and Goppa codes, whose complexity is subexponential in the error-correcting capability, hence better than that of generic decoding algorithms. Moreover it does not suffer from the strong regime…
We propose a new method for retrieving the algebraic structure of a generic alternant code given an arbitrary generator matrix, provided certain conditions are met. We then discuss how this challenges the security of the McEliece…
The Goppa Code Distinguishing (GD) problem asks to distinguish efficiently a generator matrix of a Goppa code from a randomly drawn one. We revisit a distinguisher for alternant and Goppa codes through a new approach, namely by studying the…
In this article, we continue the analysis started in \cite{CMT23} for the matrix code of quadratic relationships associated with a Goppa code. We provide new sparse and low-rank elements in the matrix code and categorize them according to…
In this paper we study the security of the key of compact McEliece schemes based on alternant/Goppa codes with a non-trivial permutation group, in particular quasi-cyclic alternant codes. We show that it is possible to reduce the…
L\"ondahl and Johansson proposed last year a variant of the McEliece cryptosystem which replaces Goppa codes by convolutional codes. This modification is supposed to make structural attacks more difficult since the public generator matrix…
We present a polynomial time structural attack against the McEliece system based on Wild Goppa codes from a quadratic finite field extension. This attack uses the fact that such codes can be distinguished from random codes to compute some…
In this paper, it is shown that the syndromes of generalized Reed-Solomon (GRS) codes and alternant codes can be characterized in terms of inverse fast Fourier transform, regardless of code definitions. Then a fast decoding algorithm is…
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…
In this note we first review the classical Petterson-Gorenstein-Zierler decoding algorithm for the class of alternant codes (which includes Reed-Solomon, Bose-Chaudhuri-Hocquenghem and classical Goppa codes), then we present an improvement…
McEliece cryptosystem represents a smart open key system based on the hardness of the decoding of an arbitrary linear code, which is believed to be able to resist the advent of quantum computers. But the original McEliece cryptosystem,…
We give polynomial time attacks on the McEliece public key cryptosystem based either on algebraic geometry (AG) codes or on small codimensional subcodes of AG codes. These attacks consist in the blind reconstruction either of an Error…
We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently list-decodable codes, as…
In this paper, we introduce a family of codes that can be used in a McEliece cryptosystem, called Goppa--like AG codes. These codes generalize classical Goppa codes and can be constructed from any curve of genus $\mathfrak{g} \geq 0$.…
In the \emph{trace reconstruction problem}, an unknown source string $x \in \{0,1\}^n$ is transmitted through a probabilistic \emph{deletion channel} which independently deletes each bit with some fixed probability $\delta$ and concatenates…
The BBCRS scheme is a variant of the McEliece public-key encryption scheme where the hiding phase is performed by taking the inverse of a matrix which is of the form $\mathbf{T} +\mathbf{R}$ where $\mathbf{T}$ is a sparse matrix with…
Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Grobner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Grobner bases based…
The interesting properties of classical Goppa code and its effective decoding algorithm (algorithm of patterson) make the most appropriate candidate for use in the MC Eliece cryptosystem. Information leakage which results from the…