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Text Encryption Using Pell Sequence and Elliptic Curves with Provable Security

Sumaira Azhar1, Naveed Ahmed Azam2,*, Umar Hayat1
1 Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan
2 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan
* Corresponding Author: Naveed Ahmed Azam. Email:

Computers, Materials & Continua 2022, 71(3), 4971-4988.

Received 17 September 2021; Accepted 11 November 2021; Issue published 14 January 2022


The demand for data security schemes has increased with the significant advancement in the field of computation and communication networks. We propose a novel three-step text encryption scheme that has provable security against computation attacks such as key attack and statistical attack. The proposed scheme is based on the Pell sequence and elliptic curves, where at the first step the plain text is diffused to get a meaningless plain text by applying a cyclic shift on the symbol set. In the second step, we hide the elements of the diffused plain text from the attackers. For this purpose, we use the Pell sequence, a weight function, and a binary sequence to encode each element of the diffused plain text into real numbers. The encoded diffused plain text is then confused by generating permutations over elliptic curves in the third step. We show that the proposed scheme has provable security against key sensitivity attack and statistical attacks. Furthermore, the proposed scheme is secure against key spacing attack, ciphertext only attack, and known-plaintext attack. Compared to some of the existing text encryption schemes, the proposed scheme is highly secure against modern cryptanalysis.


Text encryption; pell numbers; elliptic curves; key sensitivity; statistical cryptanalysis

Cite This Article

S. Azhar, N. Ahmed Azam and U. Hayat, "Text encryption using pell sequence and elliptic curves with provable security," Computers, Materials & Continua, vol. 71, no.3, pp. 4971–4988, 2022.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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