Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography
Information Theory
2018-05-14 v2 Cryptography and Security
math.IT
Abstract
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.
Cite
@article{arxiv.1801.07003,
title = {Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography},
author = {Peter Beelen and Martin Bossert and Sven Puchinger and Johan Rosenkilde},
journal= {arXiv preprint arXiv:1801.07003},
year = {2018}
}
Comments
5 pages, accepted at: IEEE International Symposium on Information Theory 2018