A New Gabidulin-Like Code and Its Application in Cryptography

  • Terry Shue Chien LauEmail author
  • Chik How Tan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11445)


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.


Post-quantum cryptography McEliece Gabidulin code Public-key encryption 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Temasek LaboratoriesNational University of SingaporeSingaporeSingapore

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