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pro vyhledávání: '"A. Tillich"'
We show that here standard decoding algorithms for generic linear codes over a finite field can speeded up by a factor which is essentially the size of the finite field by reducing it to a low weight codeword problem and working in the relevant proje
Externí odkaz:
http://arxiv.org/abs/2312.02607
The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders (ISD). However, recently a new algo
Externí odkaz:
http://arxiv.org/abs/2312.00747
Autor:
Chailloux, André, Tillich, Jean-Pierre
One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution problem to the Learning with Errors problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry that this redu
Externí odkaz:
http://arxiv.org/abs/2310.20651
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 product in t
Externí odkaz:
http://arxiv.org/abs/2306.10294
A long standing open question is whether the distinguisher of high rate alternant codes or Goppa codes \cite{FGOPT11} can be turned into an algorithm recovering the algebraic structure of such codes from the mere knowledge of an arbitrary generator m
Externí odkaz:
http://arxiv.org/abs/2304.14757
The Rank Decoding problem (RD) is at the core of rank-based cryptography. This problem can also be seen as a structured version of MinRank, which is ubiquitous in multivariate cryptography. Recently, \cite{BBBGNRT20,BBCGPSTV20} proposed attacks based
Externí odkaz:
http://arxiv.org/abs/2208.05471
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information
Externí odkaz:
http://arxiv.org/abs/2208.02201
The Dihedral Coset Problem (DCP) in $Z_N$ has been extensively studied in quantum computing and post-quantum cryptography, as for instance, the Learning with Errors problem reduces to it. While the Ettinger-Hoyer algorithm is known to solve the DCP i
Externí odkaz:
http://arxiv.org/abs/2206.14408
In this article we revisit smoothing bounds in parallel between lattices $and$ codes. Initially introduced by Micciancio and Regev, these bounds were instantiated with Gaussian distributions and were crucial for arguing the security of many lattice-b
Externí odkaz:
http://arxiv.org/abs/2205.10552
Autor:
Mora, Rocco, Tillich, Jean-Pierre
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 dimension
Externí odkaz:
http://arxiv.org/abs/2111.13038