Discrete differentiations and integrations and their possible applications to algebra and cryptography
Prikladnaâ diskretnaâ matematika, no. 3 (2023), pp. 5-14.

Voir la notice de l'article provenant de la source Math-Net.Ru

Generalized operations of discrete differentiation and integration are defined. Some of their properties are given. A brief review of the results obtained earlier with the use of these concepts in algebra and cryptography is given. A new message encryption scheme based on these operations is proposed. We also show how they can be used for authentication and key distribution.
Keywords: discrete differentiations and integrations, encryption scheme, key distribution.
Mots-clés : autentification
@article{PDM_2023_3_a0,
     author = {S. K. Voloshin and V. A. Roman'kov},
     title = {Discrete differentiations and integrations and their possible applications to algebra and cryptography},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {5--14},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2023_3_a0/}
}
TY  - JOUR
AU  - S. K. Voloshin
AU  - V. A. Roman'kov
TI  - Discrete differentiations and integrations and their possible applications to algebra and cryptography
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2023
SP  - 5
EP  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2023_3_a0/
LA  - ru
ID  - PDM_2023_3_a0
ER  - 
%0 Journal Article
%A S. K. Voloshin
%A V. A. Roman'kov
%T Discrete differentiations and integrations and their possible applications to algebra and cryptography
%J Prikladnaâ diskretnaâ matematika
%D 2023
%P 5-14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2023_3_a0/
%G ru
%F PDM_2023_3_a0
S. K. Voloshin; V. A. Roman'kov. Discrete differentiations and integrations and their possible applications to algebra and cryptography. Prikladnaâ diskretnaâ matematika, no. 3 (2023), pp. 5-14. http://geodesic.mathdoc.fr/item/PDM_2023_3_a0/

[1] Voloshin S. K. and Roman'kov V. A., “Generalized discrete operations of differentiation and integration”, Vestnik OmSU, 26:4 (2021), 4–8 (in Russian)

[2] Roman'kov V. A., “Generalized scheme of hidden compact storage of data of various users in a common open database”, Izvestiya ISU. Matematika, 20 (2022), 1–14 (in Russian)

[3] Roman'kov V. A., “About the hidden compact way to store data”, Prikladnaya Diskretnaya Matematika. Prilozhenie, 2020, no. 13, 56–59 (in Russian)

[4] Roman'kov V., “Embedding theorems for solvable groups”, Proc. AMS, 149 (2021), 4133–4143 | DOI | MR | Zbl

[5] Neumann P. M., “On the structure of standard wreath products of groups”, Math. Z., 84 (1964), 343–373 | DOI | MR | Zbl

[6] Roman'kov V. A., “Cryptanalysis of some schemes applying automorphisms”, Prikladnaya Diskretnaya Matematika, 2013, no. 3(21), 35–51 (in Russian)

[7] Myasnikov A. and Roman'kov V., “A linear decomposition attack”, Groups Complexity Cryptology, 7:1 (2015), 81–94 | DOI | MR | Zbl

[8] Roman'kov V. A., “A nonlinear decomposition attack”, Groups Complexity Cryptologogy, 8:2 (2017), 197–207 | MR

[9] Roman'kov V., Essays in algebra and cryptology: Algebraic cryptanalysis, Omsk State University, Omsk, 2018, 208 pp.

[10] Roman'kov V. A., Algebraic Cryptology, OmSU Publ., Omsk, 2020, 261 pp. (in Russian)

[11] Ben-Zvi A., Kalka A., and Tsaban B., “Cryptanalysis via algebraic spans”, Proc. 38th Ann. Intern. Cryptology Conf. (Santa Barbara, CA, USA, 2018), v. 1, 255–274 | MR | Zbl

[12] Menezes A. J., Oorschot P. C., and Vanstone S., Handbook of Applied Cryptography, CRC Press, Boca Raton, 1996, 816 pp. | MR

[13] Roman'kov V. A., Introduction to Cryptography. Lecture Course, Forum, M., 2012, 239 pp. (in Russian)

[14] Tsaban B., “Polynomial time solutions of computational problems in noncommutative algebraic cryptography”, J. Cryptology, 28:3 (2015), 601–622 | DOI | MR | Zbl