544 research outputs found
Variations of the McEliece Cryptosystem
Two variations of the McEliece cryptosystem are presented. The first one is
based on a relaxation of the column permutation in the classical McEliece
scrambling process. This is done in such a way that the Hamming weight of the
error, added in the encryption process, can be controlled so that efficient
decryption remains possible. The second variation is based on the use of
spatially coupled moderate-density parity-check codes as secret codes. These
codes are known for their excellent error-correction performance and allow for
a relatively low key size in the cryptosystem. For both variants the security
with respect to known attacks is discussed
A Distinguisher-Based Attack of a Homomorphic Encryption Scheme Relying on Reed-Solomon Codes
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 . We give here a distinguisher that detects if one or
several columns belong to 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
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 with . This allows an attack which recovers the full set
and which can then decrypt any ciphertext.Comment: 11 page
- …