Abstract
A recent paper by Coggia and Couvreur presents a polynomial time key-recovery attack on Loidreau’s encryption scheme, based on rank-metric codes, for some parameters. Their attack was formulated for the particular case when the secret matrix in Loidreau’s scheme is restricted to a 2-dimensional subspace. We present an extension of the Coggia–Couvreur attack to deal with secret matrices chosen over subspaces of dimension greater than 2.
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Notes
In the recent version of their paper [3], Coggia and Couvreur have indicated the form of the sum space to extend their argument for \( \lambda =2 \). We had independently arrived at a similar conclusion based on the original version of their paper ([2]) and have, moreover, presented the details of the proof for \( \lambda \ge 3 \).
The author is grateful to the anonymous reviewer for pointing this out.
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Acknowledgements
The author is deeply grateful to the anonymous referees whose comments have substantially improved both the content and presentation. In addition, the author would like to thank Arnab Chakraborty, Mridul Nandi and Anupam Chattopadhyay for several helpful discussions. Anupam’s assistance in running the simulations is gratefully acknowledged.
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Communicated by M. Lavrauw.
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Ghatak, A. Extending Coggia–Couvreur attack on Loidreau’s rank-metric cryptosystem. Des. Codes Cryptogr. 90, 215–238 (2022). https://doi.org/10.1007/s10623-021-00972-7
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DOI: https://doi.org/10.1007/s10623-021-00972-7