Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial-Time Key Recovery Attack on the Lau-Tan Cryptosystem Based on
  Gabidulin Codes   This paper presents a key recovery attack on the cryptosystem proposed by Lau
and Tan in a talk at ACISP 2018. The Lau-Tan cryptosystem uses Gabidulin codes
as the underlying decodable code. To hide the algebraic structure of Gabidulin
codes, the authors chose a matrix of column rank $n$ to mix with a generator
matrix of the secret Gabidulin code. The other part of the public key, however,
reveals crucial information about the private key. Our analysis shows that the
problem of recovering the private key can be reduced to solving a multivariate
linear system over the base field, rather than solving a multivariate quadratic
system as claimed by the authors. Solving the linear system for any nonzero
solution permits us to recover the private key. Apparently, this attack costs
polynomial time, and therefore completely breaks the cryptosystem.

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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an