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A New Gabidulin-Like Code and Its Application in Cryptography

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Codes, Cryptology and Information Security (C2SI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11445))

Abstract

We introduce a new rank-metric code, namely \(\varvec{\lambda }\)-Gabidulin code by multiplying each of the columns of the generator of Gabidulin codes with entries from \(\varvec{\lambda }=(\lambda _1,\ldots ,\lambda _n) \in \mathbb {F}_{q^m}^n\). We discuss the motivation of introducing \(\varvec{\lambda }\)-Gabidulin code and prove some of its properties. Then, we design a new McEliece type rank metric based encryption scheme on \(\varvec{\lambda }\)-Gabidulin code, with a scrambler matrix depending on \(\varvec{\lambda }\). We show that this new cryptosystem is secure against the existing attacks on Gabidulin codes based encryption, in particularly how it resists Overbeck’s structural attack, annulator polynomial attack and the Frobenius weak attack. Finally, we also propose some parameters for the new cryptosystem and show that our proposal has smaller key size than the Loi17 Encryption [29] using Gabidulin codes proposed in PQCrypto 2017.

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Authors and Affiliations

  1. Temasek Laboratories, National University of Singapore, 5A Engineering Drive 1, #09-02, Singapore, 117411, Singapore

    Terry Shue Chien Lau & Chik How Tan

Authors
  1. Terry Shue Chien Lau
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  2. Chik How Tan
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Correspondence to Terry Shue Chien Lau .

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Editors and Affiliations

  1. Université Paris 8, Saint-Denis, France

    Claude Carlet

  2. Institut MINES-TELECOM, Paris, France

    Sylvain Guilley

  3. Université de Caen, Caen, France

    Abderrahmane Nitaj

  4. Mohammed V University, Rabat, Morocco

    El Mamoun Souidi

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Lau, T.S.C., Tan, C.H. (2019). A New Gabidulin-Like Code and Its Application in Cryptography. In: Carlet, C., Guilley, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2019. Lecture Notes in Computer Science(), vol 11445. Springer, Cham. https://doi.org/10.1007/978-3-030-16458-4_16

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  • DOI: https://doi.org/10.1007/978-3-030-16458-4_16

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