Original Research Article

Article volume = 2024 and issue = 2

Pages: 136–151

Article publication Date: August 07, 2024

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# A New Useful Efficient Text Encryption by a Finite Field

#### Özen ÖZER(a), Hana Ali-Pacha(b), Adda Ali-Pacha(c), Naima HADJ-SAID(c)

(a) Quartz Laboratory, ECAM-EPMI, 13 Bd de l’Hauli 95092 Cergy Pontoise Cedex, France.

(b) Krklareli University, Fac. Science and Arts, Dept of Mathematics, Kayal Campus, Kirklareli, TURKEY.

(c) LACOSI laboratory, University of Sciences and Technologies of Oran, Mohamed Boudiaf, Algeria.

##### Abstract:

Cryptology has experienced significant advancement in the development of computer systems. They are artisanal and confidential era to very high-tech systems requiring remarkable computing power. In this paper, we propose a new useful efficient text encryption system. Firstly, we build a new alphabet of 89 characters including the Arabic and Latin alphabets with the numbers of the decimal base as well as some punctuation with specific symbols. Our cryptosystem is based on the principle established by Shannon that a good cryptosystem must satisfy the principles of confusion and diffusion like any modern encryption system. In order to make it harder to break we come up with a concatenation of some substitutions that relies on the use of the Hill cipher surrounded by two different affine ciphers. The diffusion is a permutation of 89-symbols blocks and it is a dynamic permutation carried out using the logistic map under an appropriate program. Knowing that 89 is a prime number, so all calculations are in the algebraic quotient set Z/89Z. The key space is of around 2197 bits which is very large to make a brute force attack impossible. That is why paper is useful and significant both in science and real life.

##### Keywords:

Text Encryption, Hill Cipher, Affine Cipher, Permutation Cipher, Logistic Map, Algebraic Finite Fields, Prime number.

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##### Cite this article as:

- Özen ÖZER, Hana Ali-Pacha, Adda Ali-Pacha, Naima HADJ-SAID, A New Useful Efficient Text Encryption by a Finite Field, Communications in Combinatorics, Cryptography & Computer Science, 2024(2), PP.136–151, 2024
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