A unified description of cryptosystems: From classical to quantum protocols

Riso, Giuseppe De; Noce, Marialaura

doi:10.47974/JDMSC-1718

Open Access Research Article

A unified description of cryptosystems: From classical to quantum protocols

Giuseppe De RisoDipartimento di Fisica “E. R. Caianiello”Via Giovanni Paolo II 132Università degli Studi di SalernoFisciano (SA), 84084, ItalyView full profile → , ^*Marialaura NoceCorresponding authormnoce@unisa.itDipartimento di MatematicaVia Giovanni Paolo II 132Università degli Studi di SalernoFisciano (SA), 84084, ItalyView full profile →

* Corresponding author · click or hover a name for details

pp. 2285–2299Vol. 26Issue 8December 2023DOI: 10.47974/JDMSC-1718 Crossmark XML

Received:: 05 May 2022
Accepted:: 13 Sep 2022
Published Online:: 28 Nov 2023
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1718
Pages:: 2285–2299

Abstract

The launch of quantum computing has created new challenges in the field of cryptography. Nowadays this field of research is extremely active in physics, mathematics and computer science. In this paper we present an overview of the most common classical and quantum protocols. The former are usually defined through a 5-uple given by a plaintext space, a ciphertext space, an encryption and decryption space, an encryption function and a decryption function. Here, we show how to unify quantum and classical protocols by using the same formalism of the 5-uple mentioned above.

Keywords

Quantum cryptography Cryptography

Subject Classifications

(2020) 81P94

References

[1] C. H. Bennett, Quantum cryptography using any two nonorthogonal states, Phys. Rev. Lett. 68 (1992May), 3121-3124.
[2] C. H. Bennett and Gilles Brassard, Quantum cryptography: Public key distribution and coin tossing, Theoretical Computer Science 560 (2014Dec), 7-11.
[3] J. F. Clauser, M. A. Horne, Abner Shimony, and Richard A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23 (1969Oct), 880-884.
[4] Artur K. Ekert, Quantum cryptography based on bell’s theorem, Phys. Rev. Lett. 67 (1991Aug), 661-663.
[5] R. Flores, D. Kahrobaei, and T. Koberda, Algorithmic problems in right-angled Artin groups: Complexity and applications, Journal of Algebra 519 (2019), 111-129.
[6] D. J. Griffths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018.
[7] J. Gryak and D. Kahrobaei, The status of polycyclic group-based cryptography: A survey and open problems, Groups Complexity Cryptology 8 (2016), 171-186.
[8] D. Kahrobaei, R. Flores, and M. Noce, Group-based cryptography in the Quantum Era, Notices of the American Mathematical Society 70 no. 5 (2023), pp. 752–763.
[9] D. Kahrobaei and M. Noce, Algorithmic problems in engel groups and cryptographic applications, International Journal of Group Theory 9 (2020), no. 4, 231-250.
[10] I. S. Kaushik, G. Deepak, and A. Santhanavijayan, QuantqueryEXP : A novel strategic approach for query expansion based on quantum computing principles, Journal of Discrete Mathematical Sciences and Cryptography 23 (2020), no. 2, 573-584.
[11] J. L. Park, The concept of transition in quantum mechanics, Foundations of Physics 1 (1970), 23-33.
[12] P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput. 26 (1997), no. 5, 1484-1509.
[13] D. K. Verma, M. Rani, R. K. Tyagi, and B. B. Sagar, Baptista chaotic cryptosystem based on alternate superior dynamic lookup table, Journal of Discrete Mathematical Sciences and Cryptography 22 (2019), no. 8, 1383-1392.
[14] D. Kahrobaei, M. Noce, E. Rordaro, Applications of Automaton Groups in Cryptography, preprint arXiv:2306.10522 [math.GR] (2023).
[15] D. Kahrobaei, R. Flores, M. Noce, M. Habeeb, C. Battarbee, Applications of Group Theory in Cryptography: Post-quantum group-based cryptography, The Mathematical Surveys and Monographs series of the American Mathematical Society, in press.

Views: 235Downloads: 95Citations: 0