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A Distinguisher-Based Attack of a Homomorphic Encryption Scheme Relying on Reed-Solomon Codes | | Valérie Gauthier
; Ayoub Otmani
; Jean-Pierre Tillich
; | | Date: |
30 Mar 2012 | | Abstract: | Bogdanov and Lee suggested a homomorphic public-key encryption scheme based
on error correcting codes. The underlying public code is a modified
Reed-Solomon code obtained from inserting a zero submatrix in the Vandermonde
generating matrix defining it. The columns that define this submatrix are kept
secret and form a set $L$. We give here a distinguisher that detects if one or
several columns belong to $L$ or not. This distinguisher is obtained by
considering the code generated by component-wise products of codewords of the
public code (the so called "square code"). This operation is applied to
punctured versions of this square code obtained by picking a subset
$I$ of the whole set of columns. It turns out that the dimension of the
punctured square code is directly related to the cardinality of the
intersection of $I$ with $L$. This allows an attack which recovers the full set
$L$ and which can then decrypt any ciphertext. | | Source: | arXiv, 1203.6686 | | Services: | Forum | Review | PDF | Favorites | |
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