We address the problem of decoding Gabidulin codes beyond their unique error-correction radius. The complexity of this problem is of importance to assess the security of some rank-metric code-based cryptosystems. We propose an approach that introduces row or column erasures to decrease the rank of the error in order to use any proper polynomial-time Gabidulin code error-erasure decoding algorithm. The expected work factor of this new randomized decoding approach is a polynomial term times (Formula Presented), where n is the code length, q the size of the base field, m the extension degree of the field, k the code dimension, w the number of errors, and (Formula Presented). It improves upon generic rank-metric decoders by an exponential factor.
CITATION STYLE
Renner, J., Jerkovits, T., Bartz, H., Puchinger, S., Loidreau, P., & Wachter-Zeh, A. (2020). Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12100 LNCS, pp. 3–19). Springer. https://doi.org/10.1007/978-3-030-44223-1_1
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