Paper 2012/168 Original: eprint.iacr.org/2012/168 ↗
A Distinguisher-Based Attack of a Homomorphic Encryption Scheme Relying on Reed-Solomon Codes
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.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2012-03-30: last updated
- 2012-03-30: published
- Short URL
- https://ia.cr/2012/168
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2012/168,
author = {Valérie Gauthier and Ayoub Otmani and Jean-Pierre Tillich},
title = {A Distinguisher-Based Attack of a Homomorphic Encryption Scheme Relying on Reed-Solomon Codes},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/168},
year = {2012},
url = {https://eprint.iacr.org/2012/168}
}