A Public Key Cryptosystem Using Matrix Over the Finite Ring

Juraev, Gayrat; Mavlonov, Alisher

doi:10.2478/tmmp-2025-0018

Abstract

This paper is the first of two complementary papers. In this paper, we present a novel algorithm in the field of cryptography, an area that has garnered significant attention from researchers. Our algorithm is based on matrix calculus over finite rings, enabling efficient encryption and decryption processes without requiring additional computational resources. A key feature of this approach is its formulation of a mathematical problem involving the solution of a system of nonlinear equations, which significantly enhances the system’s security and complexity. Furthermore, we provide a detailed mathematical proof of the algorithm’s correctness.

References

KAUR, R.—GABRIJELČIČ, D.—KLOBUČAR, T.: Artificial intelligence for cybersecurity: Literature review and future research directions, Information Fusion 97 (2023), Article (KAUR2023101804).
Search in Google Scholar Back to article
JURAEV, G. U.—MAVLONOV, A. B.: Delving into potential asymmetric cryptographic algorithms for the post-quantum era, In: 2024 IEEE 25th International Conference of Young Professionals in Electron Devices and Materials (EDM). IEEE, 2024, pp. 2510–2513.
Search in Google Scholar Back to article
KASHEFI, E.—KERENIDIS, I.: Statistical zero knowledge and quantum one-way functions,Theoret.Comput.Sci. 378 (2007), no. 1, 101–116.
Search in Google Scholar Back to article
ADAMS, C.—FARRELL, S.: Rfc2510: internet X. 509 Public Key Infrastructure Certificate Management Protocols, March 1999.
Search in Google Scholar Back to article
HILL, L.: Cryptography in an algebraic alphabet, Amer. Math. Monthly 36 (1929), no. 6, 306–312.
Search in Google Scholar Back to article
HILL L.: Concerning certain linear transformation apparatus of cryptography, Amer. Math. Monthly 38 (1931), no. 3, 135–154.
Search in Google Scholar Back to article
LEELA D.—SHAW, S-M.—NANDAKISHORE S. —ARUNAKUMARI, M.—SAI, M. G.—MAHABOOB, B.: Matrix applications in cryptography, In: AIP Conference Proceedings, International Conference on Recent Advances in Materials and Manufacturing, ICRAMM 2023.
Search in Google Scholar Back to article
NASERI, A. R.—ABBASI, A.—ATANI, R. E.: A new public key cryptography using M_q matrix,J.Math. Modeling 11 (2023), no. 4, 681–693
Search in Google Scholar Back to article
HONG, M.—CHEE, W. L.: Hill cipher modifications and dynamic cryptosystem design, In: Proc. - 2023 7th International Conference on Cryptography, Security and Privacy, CSP 2023, pp. 176–180.
Search in Google Scholar Back to article
SUNDARAYYA, P.—VARA PRASAD, M. G.: A public key cryptosystem using Affine Hill Cipher under modulation of prime number, J. Inf. Optim. Sci. textbf40 (2019), no. 4, 919–930.
Search in Google Scholar Back to article
MESHRAM, C,—LI, X.: New efficient key authentication protocol for public key cryptosystem using DL over multiplicative group, J. Inf. Optim. Sci. 39 (2018), no. 2, 391–400.
Search in Google Scholar Back to article
EZHILMARAN, D.—MUTHUKUMARAN, V.: Key exchange protocol using decomposition problem in near ring,GaziUniv. J. Sci. 29 (2016), no. 1, 123–127.
Search in Google Scholar Back to article
KRISHNA, A. V. N.—NARAYANA, A. H.—VANI, K. M.: A novel approach with matrix based public key cryptosystems, J. Discret. Math. Sci. Cryptogr. 20 (2017), no. 2, pp. 407–412.
Search in Google Scholar Back to article
KARATAS, Z. Y.—LUY, E.—GONEN, B.: Public key cryptosystem based on matrices, Int. J. Comput. Appl. 182 (2019), no. 42, 47–50.
Search in Google Scholar Back to article
YUMMAN, M.—SHAH, T.—HUSSAIN, I.: Asymmetric cryptosystem on matrix algebra over a chain ring, Symmetry 13 (2021), no. 45, 1–11.
Search in Google Scholar Back to article
M. MAXRIZAL: Public key cryptosystem based on singular matrix, Trends Sciences 19 (2022), no. 3, p. 2147.
Search in Google Scholar Back to article
AHMED, MD. H.—TANTI, J.—PUSHP, S.: A public key cryptosystem using cyclotomic matrices, Coding Theory — Recent Adv. New Perspect. Appl. (2021), 86–132.
Search in Google Scholar Back to article
SREE PARVATHI, P. M.—SRINIVASAN, C .: Matrix Lie group as an algebraic structure for NTRU like cryptosystem, J. Discret. Math. Sci. Cryptogr. 23 (2020), no. 7, 1455–1464.
Search in Google Scholar Back to article
LIU, J.—ZHANG, H.—JIA, J.: Cryptanalysis of schemes based on polynomial symmetrical decomposition, Chinese J. Electron. 26 (2017), no. 6, 1139–1146.
Search in Google Scholar Back to article
AUERBACH, B.—GÜNTHER, C. U.—PIETRZAK, K.: Trapdoor memory-hard functions, In: Advances in Cryptology — EUROCRYPT 2024. 43rd Annual international conference on the theory and applications of cryptographic techniques, Zurich, Switzerland, May 26–30, 2024; Proceedings. Part III, pp. 315–344.
Search in Google Scholar Back to article
TAO, C.—DIENE, A.—TANG, S.—DING, J.: Simple matrix scheme for encryption, In: Gaborit, P., ed. Post-Quantum Cryptography (PQCrypto 2013), Lecture Notes in Computer Science, Vol 7932. Springer-Verlag, Berlin, 2013. pp. 231–242.
Search in Google Scholar Back to article
TAO, C.—XIANG, H.—PETZOLDT, A.—DING, J.: Simple matrix a multivariate public key cryptosystem (MPKC) for encryption, Finite Fields Appl. 35 (2015), 352–368.
Search in Google Scholar Back to article
C. GU: Cryptanalysis of simple matrix scheme for encryption, IACR Cryptol. ePrint Arch. 2016 (2016), p. 1075.
Search in Google Scholar Back to article
MOLDOVYAN, A. A.—MOLDOVYAN, D. N.—MOLDOVYAN, N. A.: A new approach to the development of multivariate cryptography algorithms, Cryptography 2 (2023), p. 54. (In Russian)
Search in Google Scholar Back to article
MAVLONOV, A.: Investigation of the possibility of using matrix multiplication in asymmetric cryptographic systems, Academic research in educational sciences, 2 (2021), no. 10, 89–93.
Search in Google Scholar Back to article

A Public Key Cryptosystem Using Matrix Over the Finite Ring

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