On Encryption with Continued Fraction

Merve Güney Duman

doi:10.24012/dumf.1038230

On Encryption with Continued Fraction

Öz

Many mathematicians have investigated the properties of continued fractions. They made continued fraction expansions of the Pi number, the golden ratio and many more special numbers. With the help of continued fractions, solutions of some Diophantine equations are obtained. In this study, encryption was made using continued fractional expansions of the square root of non-perfect-square integers. Each of the 29 letters in the alphabet is represented by the root of nonperfect square integers starting from 2. Then, continued fraction expansions of the square root of each letter’s number equivalent were calculated. Afterwards, all numbers in the continued fraction expansion were considered as an integer by removing the comma. This information was tabulated for later usage. Each word is considered as individual letters, and a space is left between the encrypted versions of each letter. After the encryption process, the process of deciphering the encrypted text was dealt with. In the deciphering process, since there is a blank between the numbers, the numbers are written as a continued fraction and the integer expansion is calculated. Later, the letter corresponding to this number was found.

Anahtar Kelimeler

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Details

Primary Language

Turkish

Subjects

-

Journal Section

Research Article

Authors

Merve Güney Duman ^*
0000-0002-6340-4817
Türkiye

Publication Date

June 28, 2022

Submission Date

December 19, 2021

Acceptance Date

March 30, 2022

Published in Issue

Year 2022 Volume: 13 Number: 2

DOI

https://doi.org/10.24012/dumf.1038230

IZ

https://izlik.org/JA35HP94BM

Cite

RIS / Bibtex

IEEE

[1]M. Güney Duman, “On Encryption with Continued Fraction”, DUJE, vol. 13, no. 2, pp. 149–152, June 2022, doi: 10.24012/dumf.1038230.