An IND-CCA-Secure Code-Based Encryption Scheme Using Rank Metric

  • Hamad Al Shehhi
  • Emanuele Bellini
  • Filipe Borba
  • Florian Caullery
  • Marc Manzano
  • Victor MateuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11627)


The use of rank instead of Hamming metric has been proposed to address the main drawback of code-based cryptography: large key sizes. There exist several Key Encapsulation Mechanisms (KEM) and Public Key Encryption (PKE) schemes using rank metric including some submissions to the NIST call for standardization of Post-Quantum Cryptography. In this work, we present an Open image in new window PKE scheme based on the McEliece adaptation to rank metric proposed by Loidreau at PQC 2017. This Open image in new window PKE scheme based on rank metric does not use a hybrid construction KEM + symmetric encryption. Instead, we take advantage of the bigger message space obtained by the different parameters chosen in rank metric, being able to exchange multiple keys in one ciphertext. Our proposal is designed considering some specific properties of the random error generated during the encryption. We prove our proposal Open image in new window -secure in the QROM by using a security notion called disjoint simulatability introduced by Saito et al. in Eurocrypt 2018. Moreover, we provide security bounds by using the semi-oracles introduced by Ambainis et al.


Post Quantum Cryptography Code-based cryptography Rank metric Open image in new window PKE QROM 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Hamad Al Shehhi
    • 1
  • Emanuele Bellini
    • 1
  • Filipe Borba
    • 2
  • Florian Caullery
    • 1
  • Marc Manzano
    • 1
  • Victor Mateu
    • 1
    Email author
  1. 1.Darkmatter LLCAbu DhabiUnited Arab Emirates
  2. 2.Universidade Federal de Santa CatarinaFlorianópolisBrazil

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