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LowMS: a new rank metric code-based KEM without ideal structure

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Abstract

We propose and analyze \(\textsf{LowMS}\), a new rank-based key encapsulation mechanism (KEM). The acronym stands for Loidreau with Multiple Syndromes, since our work combines the cryptosystem of Loidreau (presented at PQCrypto 2017) together with the multiple syndromes approach, that allows to reduce parameters by sending several syndromes with the same error support in one ciphertext. Our scheme is designed without using ideal structures. Considering cryptosystems without such an ideal structure, like the FrodoKEM cryptosystem, is important since structure allows to compress objects, but gives reductions to specific problems whose security may potentially be weaker than for unstructured problems. For 128 bits of security, we propose parameters with a public key size of 4.8 KB and a ciphertext size of 1.1 KB. To the best of our knowledge, our scheme is the smallest among all existing unstructured post-quantum lattice or code-based algorithms, when taking into account the sum of the public key size and the ciphertext size. In that sense, our scheme is for instance about 4 times shorter than FrodoKEM. Our system relies on the hardness of the Rank Support Learning problem, a well-known variant of the Rank Syndrome Decoding problem, and on the problem of indistinguishability of distorted Gabidulin codes, i.e., Gabidulin codes multiplied by a homogeneous matrix of given rank. The latter problem was introduced by Loidreau in his paper.

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Notes

  1. In the comparison paper [45], r is noted \(t_{\text {pub}}\).

  2. We traditionally choose m prime to avoid any potential attacks.

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Authors and Affiliations

  1. NAQUIDIS Center, Talence, France

    Nicolas Aragon

  2. XLIM, Université de Limoges, Limoges, France

    Victor Dyseryn & Philippe Gaborit

  3. DGA-MI, CNRS, IRMAR, Université de Rennes, Rennes, France

    Pierre Loidreau

  4. Institute for Communications Engineering, Technical University of Munich, Munich, Germany

    Julian Renner & Antonia Wachter-Zeh

Authors
  1. Nicolas Aragon
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  2. Victor Dyseryn
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  3. Philippe Gaborit
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  4. Pierre Loidreau
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  6. Antonia Wachter-Zeh
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Correspondence to Victor Dyseryn.

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Communicated by T. Helleseth.

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Aragon, N., Dyseryn, V., Gaborit, P. et al. LowMS: a new rank metric code-based KEM without ideal structure. Des. Codes Cryptogr. 92, 1075–1093 (2024). https://doi.org/10.1007/s10623-023-01330-5

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