Abstract
The code equivalence problem is to decide whether two linear codes over \(\mathbb{F}_{q}\) are identical up to a linear isometry of the Hamming space. In this paper, we review the hardness of code equivalence over \(\mathbb{F}_q\) due to some recent negative results and argue on the possible implications in code-based cryptography. In particular, we present an improved version of the three-pass identification scheme of Girault and discuss on a connection between code equivalence and the hidden subgroup problem.
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Sendrier, N., Simos, D.E. (2013). The Hardness of Code Equivalence over \(\mathbb{F}_q\) and Its Application to Code-Based Cryptography. In: Gaborit, P. (eds) Post-Quantum Cryptography. PQCrypto 2013. Lecture Notes in Computer Science, vol 7932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38616-9_14
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DOI: https://doi.org/10.1007/978-3-642-38616-9_14
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