Generic Decoding in the Cover Metric [article]

Sebastian Bitzer, Julian Renner, Antonia Wachter-Zeh, Violetta Weger
2022 arXiv   pre-print
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give a polynomial-time reduction from the classical Hamming-metric decoding problem, which proves the NP-hardness of the decoding problem in the cover metric. We then provide a generic decoder, following the information set decoding idea from Prange's algorithm in
more » ... the Hamming metric. A study of its cost then shows that the complexity is exponential in the number of rows and columns, which is in contrast to the behaviour in the Hamming metric, where the complexity grows exponentially in the number of code symbols.
arXiv:2205.12738v1 fatcat:siid6xcu7rd6tdjkbudz3fzjuy