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Title: :  Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature
PaperId: :  15464
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 7 Issue 5 2021
DUI:    16.0415/IJARIIE-15464
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
Ombana Fenofahasoavana RAZAFIMAHEFATASI, ED-STII, Antananarivo, Madagascar
Paul Auguste RANDRIAMITANTSOATASI, ED-STII, Antananarivo, Madagascar
RANDRIANANDRASANA Marie EmileTASI, ED-STII, Antananarivo, Madagascar

Abstract

Computer Science & Engineering
Quantum Computer, Post Quantum Cryptosystem, Module LWE, CRYSTALS-Kyber, CRYSTALS-Dilithium, Key Encapsulation Mechanism (KEM), Signature.
Quantum computers, but still with a low number of qubits, are starting to emerge as we write. It is more crucial than ever to work on new cryptosystems. Cryptosystems that will be based on mathematical problems that are robust enough to withstand the increased computational power that these new types of computers will provide. In the course of our research, we came across the mathematical object that is the Lattice. The latter is one of the promising candidates in terms of fundamental problem for post-quantum cryptosystems. But the mathematical tool on which we will open this article is the MLWE or Module Learning With Error. The LWE (or Learning With Error), in the first instance, is a generalization of the problem Learning from parity with error. It has been shown that this problem is equivalent, in terms of difficulty, to the SIVP or Shortest Independent Vector Problem of a lattice. Coming back to MLWE, we have another designation, Learning With Error other Module Lattices. Module lattices can be considered as lattices between those used in the LWE problem definitions and those used for the R-LWE problem (Ring LWE). The Module-LWE offers a compromise between the two extremes of the LWE and the R-LWE. Thereafter we will focus on the CRYSTALS cryptosystem, a cryptosystem based on the MLWE. Our choice to study this cryptosystem is based on the fact that it was submitted to the NIST (National Institute of Standards and Technology) project of post-quantum cryptosystem standardization. CRYSTALS was able to progress to step 3 of the project. But above all, it is the only one among the few that have progressed to this final stage, to have both a KEM type cryptosystem (Key Encapsulation Mechanism) and another signature type one.

Citations

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IJARIIE Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, and RANDRIANANDRASANA Marie Emile. "Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature" International Journal Of Advance Research And Innovative Ideas In Education Volume 7 Issue 5 2021 Page 1194-1206
MLA Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, and RANDRIANANDRASANA Marie Emile. "Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature." International Journal Of Advance Research And Innovative Ideas In Education 7.5(2021) : 1194-1206.
APA Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, & RANDRIANANDRASANA Marie Emile. (2021). Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature. International Journal Of Advance Research And Innovative Ideas In Education, 7(5), 1194-1206.
Chicago Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, and RANDRIANANDRASANA Marie Emile. "Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature." International Journal Of Advance Research And Innovative Ideas In Education 7, no. 5 (2021) : 1194-1206.
Oxford Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, and RANDRIANANDRASANA Marie Emile. 'Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature', International Journal Of Advance Research And Innovative Ideas In Education, vol. 7, no. 5, 2021, p. 1194-1206. Available from IJARIIE, https://ijariie.com/AdminUploadPdf/Application_of_the_MLWE_in_the_cryptosystem_CRYSTALS_–_KYBER_as_KEM_and_Dilithium_as_signature_ijariie15464.pdf (Accessed : 28 May 2024).
Harvard Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, and RANDRIANANDRASANA Marie Emile. (2021) 'Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature', International Journal Of Advance Research And Innovative Ideas In Education, 7(5), pp. 1194-1206IJARIIE [Online]. Available at: https://ijariie.com/AdminUploadPdf/Application_of_the_MLWE_in_the_cryptosystem_CRYSTALS_–_KYBER_as_KEM_and_Dilithium_as_signature_ijariie15464.pdf (Accessed : 28 May 2024)
IEEE Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, and RANDRIANANDRASANA Marie Emile, "Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature," International Journal Of Advance Research And Innovative Ideas In Education, vol. 7, no. 5, pp. 1194-1206, Sep-Oct 2021. [Online]. Available: https://ijariie.com/AdminUploadPdf/Application_of_the_MLWE_in_the_cryptosystem_CRYSTALS_–_KYBER_as_KEM_and_Dilithium_as_signature_ijariie15464.pdf [Accessed : 28 May 2024].
Turabian Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, and RANDRIANANDRASANA Marie Emile. "Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 7 number 5 (28 May 2024).
Vancouver Ombana Fenofahasoavana RAZAFIMAHEFA, Paul Auguste RANDRIAMITANTSOA, and RANDRIANANDRASANA Marie Emile. Application of the MLWE in the cryptosystem CRYSTALS – KYBER as KEM and Dilithium as signature. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2021 [Cited : 28 May 2024]; 7(5) : 1194-1206. Available from: https://ijariie.com/AdminUploadPdf/Application_of_the_MLWE_in_the_cryptosystem_CRYSTALS_–_KYBER_as_KEM_and_Dilithium_as_signature_ijariie15464.pdf
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