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- Title
On Encryption with Continued Fraction.
- Authors
GÜNEY DUMAN, Merve
- Abstract
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, they obtained solutions of some Diophantine equations were. In this study, we make encryption using continued fractional expansions of the square root of non-perfect-square integers. We represent each of the 29 letters in the alphabet as the root of nonperfect square integers starting from 2. Then, we calculate the continued fraction expansions of the square root of each letter's number equivalent. Afterwards, we consider all numbers in the continued fraction expansion as an integer by removing the comma. We consider each word as individual letters, and left spaces between the encrypted versions of each letter. After the encryption process, we deal with the process of deciphering the encrypted text. In the deciphering process, since there is a blank between the numbers, we write the numbers as a continued fraction and calculate the integer expansion. Later, we find the letter corresponding to this number.
- Subjects
CONTINUED fractions; DATA encryption; DIOPHANTINE equations; CRYPTOGRAPHY; INTEGERS
- Publication
Dicle University Journal of Engineering / Dicle Üniversitesi Mühendislik Dergisi, 2022, Vol 13, Issue 2, p149
- ISSN
1309-8640
- Publication type
Article
- DOI
10.24012/dumf.1038230