Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Distinguisher-Based Attack on a Variant of McEliece's Cryptosystem
  Based on Reed-Solomon Codes   Baldi et \textit{al.} proposed a variant of McEliece's cryptosystem. The main
idea is to replace its permutation matrix by adding to it a rank 1 matrix. The
motivation for this change is twofold: it would allow the use of codes that
were shown to be insecure in the original McEliece's cryptosystem, and it would
reduce the key size while keeping the same security against generic decoding
attacks. The authors suggest to use generalized Reed-Solomon codes instead of
Goppa codes. The public code built with this method is not anymore a
generalized Reed-Solomon code. On the other hand, it contains a very large
secret generalized Reed-Solomon code. In this paper we present an attack that
is built upon a distinguisher which is able to identify elements of this secret
code. The distinguisher is constructed by considering the code generated by
component-wise products of codewords of the public code (the so-called "square
code"). By using square-code dimension considerations, the initial generalized
Reed-Solomon code can be recovered which permits to decode any ciphertext. A
similar technique has already been successful for mounting an attack against a
homomorphic encryption scheme suggested by Bogdanoc et \textit{al.}. This work
can be viewed as another illustration of how a distinguisher of Reed-Solomon
codes can be used to devise an attack on cryptosystems based on them.

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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: dg-ga