69 research outputs found
Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes
We give a polynomial time attack on the McEliece public key cryptosystem
based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes
on the distinguishability of such codes from random codes using the Schur
product. Wieschebrink treated the genus zero case a few years ago but his
approach cannot be extent straightforwardly to other genera. We address this
problem by introducing and using a new notion, which we call the t-closure of a
code
Improving the efficiency of the LDPC code-based McEliece cryptosystem through irregular codes
We consider the framework of the McEliece cryptosystem based on LDPC codes,
which is a promising post-quantum alternative to classical public key
cryptosystems. The use of LDPC codes in this context allows to achieve good
security levels with very compact keys, which is an important advantage over
the classical McEliece cryptosystem based on Goppa codes. However, only regular
LDPC codes have been considered up to now, while some further improvement can
be achieved by using irregular LDPC codes, which are known to achieve better
error correction performance than regular LDPC codes. This is shown in this
paper, for the first time at our knowledge. The possible use of irregular
transformation matrices is also investigated, which further increases the
efficiency of the system, especially in regard to the public key size.Comment: 6 pages, 3 figures, presented at ISCC 201
Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography
We present a generalisation of Twisted Reed-Solomon codes containing a new
large class of MDS codes. We prove that the code class contains a large
subfamily that is closed under duality. Furthermore, we study the Schur squares
of the new codes and show that their dimension is often large. Using these
structural properties, we single out a subfamily of the new codes which could
be considered for code-based cryptography: These codes resist some existing
structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the
code parameters from an obfuscated generator matrix.Comment: 5 pages, accepted at: IEEE International Symposium on Information
Theory 201
Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures
In this paper, we address the problem of achieving efficient code-based
digital signatures with small public keys. The solution we propose exploits
sparse syndromes and randomly designed low-density generator matrix codes.
Based on our evaluations, the proposed scheme is able to outperform existing
solutions, permitting to achieve considerable security levels with very small
public keys.Comment: 16 pages. The final publication is available at springerlink.co
- …