Coding theory on Lucas p numbers

Prasad, Bandhu

doi:10.1142/s1793830916500749

Cited by 12 publications

(8 citation statements)

References 6 publications

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“…Many studies have been done in different fields related to Lucas and Fibonacci numbers. For more information on Lucas, refer to references [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Encryption and Decryption of the Data by Using the Terms of the Lucas Series

Duman

2021

Düzce Üniversitesi Bilim Ve Teknoloji Dergisi

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The sequence, whose initial condition is 2 and 1, obtained by summing the two terms preceding it, is called the Lucas sequence. The terms of this series continue as 2, 1, 3, 4, 7, 11, 18, 29, ... respectively. The features of the Lucas sequence have been studied in many projects in the literature and many studies have been done on Lucas series in applied sciences. Cryptology is the science that deals with encrypting data, transferring it securely from one point to another, and converting the encrypted data to the previous one. It includes cryptography and cryptoanalysis. Different encryption-decryption methods have been developed to ensure the security of the data from the past to the present. Some of these are Caesar, Affine, Vigenere and RSA. There are two types of encryption systems in cryptology. The first one is symmetric (secret key) encryption and the another one is asymmetric (public key) encryption. In this study; using the features of the Lucas sequence, studies on cryptology, which deals with the correct encryption, transfer and decryption of data, have been carried out and an example of cryptology algorithm has been given. With Lucas cipher, the letters in the alphabet and the space character are each mapped to the terms of the Lucas sequence. Later, starting from the first term of the Lucas sequence, the encryption was strengthened by adding Lucas terms. As a result, the text to be encrypted has been turned into a symbolic representation of the numbers. Then, the necessary information for deciphering the text which is encrypted with numbers is given.

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“…Many studies have been done in different fields related to Lucas and Fibonacci numbers. For more information on Lucas, refer to references [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Encryption and Decryption of the Data by Using the Terms of the Lucas Series

Duman

2021

Düzce Üniversitesi Bilim Ve Teknoloji Dergisi

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“…In [14], it was constructed an application of mobile phone encryption based on Fibonacci structure of chaos using Fibonacci series. In [8], Prasad developed a new coding and decoding method using Lucas p numbers given in [6]. Recently, a new cryptography algorithm has been introduced by blocking matrices and Fibonacci numbers in [13].…”

Section: Introductionmentioning

confidence: 99%

A New Application to Coding Theory via Fibonacci and Lucas Numbers

Uçar¹,

Taş²,

Özgür³

2019

Mathematical Sciences and Applications E-Notes

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Coding/decoding algorithms are of great importance to help in improving information security since information security is a more significant problem in recent years. In this paper we introduce two new coding/decoding algorithms using Fibonacci Q-matrices and R-matrices. Our models are based on the blocked message matrices and the encryption of each message matrix with different keys. These new algorithms will not only increase the security of information but also has high correct ability.

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“…There are many studies including Fibonacci, Fibonacci quaternion, Lucas, Pell, Pell (p,i)-numbers and their applications such as coding theory in the literature [1][2][3][4][5][6][7]. Here we consider two classes of right circulant matrices whose entries are generalized Fibonacci and Lucas polynomials to obtain new coding/decoding algorithms.…”

Section: Introductionmentioning

confidence: 99%