Generic Decoding in the Cover Metric

Abstract: 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 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.