k-Order Fibonacci Polynomials on AES-Like Cryptology (original) (raw)

A New Encryption Algorithm Based on Fibonacci Polynomials and Matrices

Traitement Du Signal, 2022

Confusion and diffusion features are two fundamental needs of encoded text or images. These features have been used in various encryption algorithms such as Advanced Encryption Standard (AES) and Data Encryption Standard (DES). The AES adopts the Sbox table formed with irreducible polynomials, while the DES employs the Feistel and Sbox structures. This study proposes a new encryption algorithm based on Fibonacci polynomials and matrices, which meets the fundamental needs of image encryption and provides an alternative to other encryption algorithms. The success of the proposed method was tested on three different images, as evidenced by the histogram analysis results of the sample images, together with the number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI). In addition, the root mean squared error (RMSE) suggests that the decoded images are consistent with the original images. It can therefore be summarized that the proposed encryption algorithm is suitable for image encryption.

Cryptography utilizing the Affine-Hill cipher and Extended Generalized Fibonacci matrices

Electronic Journal of Mathematical Analysis and Applications

We are aware that a major cryptosystem element plays a crucial part in maintaining the security and robustness of cryptography. Various researchers are focusing on creating new forms of cryptography and improving those that already exist using the principles of number theory and linear algebra. In this article, we have proposed an Extended generalized Fibonacci matrix (recursive matrix of higher order) having a relation with Extended generalized Fibonacci sequences and established some properties in addition to that usual matrix algebra. Further, we proposed a modified public key cryptography using these matrices as keys in Affine-Hill Cipher and key agreement for encryption-decryption with the combination of terms of Extended generalized Fibonacci sequences under prime modulo. This system has a large key space and reduces the time complexity as well as space complexity of the key transmission by only requiring the exchange of pair of numbers(parameters) as opposed to the entire key matrix.

Cryptography Protection of Digital Signals using Fibonacci - Pell Transformation via Golden Matrix

International Journal of Engineering and Advanced Technology

At this time the security of communication can be the important role of electronic communication. In this paper we can discuss the new transform for the protection of digital signals using with golden matrix. Fibonacci - Pell (FP) Transform can be find sufficient results to secure the signals and the aims of this paper to describe the security of signals using new type of recurrence formula. The recurrence relation can be find sufficient results to secure the signals. Multiple encryptions are used in this algorithm. Fibonacci - Pell (FP) Transform used for encryption and affine cipher can be used for super encryption. It ensures that to secure the data from attackers in this cryptographic method is fast and simple.

The linear algebra of the k-Fibonacci matrix

Linear Algebra and its Applications, 2003

For a positive integer k 2, the k-Fibonacci sequence {g(k) n } is defined as: g(k) 1 = • • • = g(k) k−2 = 0, g(k) k−1 = g(k) k = 1 and for n > k 2, g(k) n = g(k) n−1 + g(k) n−2 + • • • + g(k) n−k. The n × n k-Fibonacci matrix F(k) n = [f (k) ij ] n is defined as: for fixed k 2, f (k) ij = g i−j +1 i − j + 1 0, 0 i − j + 1 < 0, where g n = g(k) n+k−2. Also, the n by n k-symmetric Fibonacci matrix Q(k) n = [q(k) ij ] n is defined as q(k) ij = q(k) ji = k l=1 q(k) i,j −l i + 1 j, k l=1 q(k) i,i−l + g 1 i = j, where q(k) ij = 0 for j 0. If k = 2, then F(2) n is the Fibonacci matrix and Q(2) n is the symmetric Fibonacci matrix. The properties of the Fibonacci matrix and the symmetric Fibonacci matrix are well-known. In this paper, we discuss the linear algebra of the k-Fibonacci matrix and the symmetric k-Fibonacci matrix.

A note on complete polynomials over finite fields and their applications in cryptography

Finite Fields and Their Applications, 2014

A recursive construction of complete mappings over finite fields is provided in this work. These permutation polynomials, characterized by the property that both f (x) ∈ F q [x] and its associated mapping f (x) + x are permutations, have an important application in cryptography in the construction of bent-negabent functions which actually leads to some new classes of these functions. Furthermore, we also provide a recursive construction of mappings over finite fields of odd characteristic, having an interesting property that both f (x) and f (x + c) + f (x) are permutations for every c ∈ F q. Both the multivariate and univariate representations are treated and some results concerning fixed points and the cycle structure of these permutations are given. Finally, we utilize our main result for the construction of so-called negabent functions and bent functions over finite fields.

Cryptography based on the Matrices

Boletim da Sociedade Paranaense de Matemática, 2017

In this work we introduce a new method of cryptography based on the matrices over a finite field Fq, were q is a power of a prime number p. The first time we construct the matrix M = A 1 A 2 0 A 3 were A 1 , A 2 and A 3 are matrices of order n with coefficients in Fq and 0 is the zero matrix of order n. We prove that M l = A l 1

A novel approach for information security with automatic variable key using Fibonacci Q-matrix

International Journal of Computer and Communication Technology, 2014

Abstract - Information security is essential nowadays. Large number of cipher generation and decryption algorithms exists and are being evolved due to increasing demand of users and e-commerce services. In this paper we propose a new approach for secure information transmission over communication channel with key variability concept in symmetric key algorithms using Fibonacci Qmatrix. Proposed approach will not only enhance the security of information but also saves computation time and reduces power requirements that will find it’s suitability for future hand held devices and online transaction processing. Keywords-cipher; key; encryption; decryption; fibonacci; Q- matrix;, symmetric key algorithm, automatic variable key. PRAJAPAT, SHALIGRAM; JAIN, AMBER; and THAKUR, R. S. (2014) "A Novel Approach For Information Security With Automatic Variable Key Using Fibonacci Q-Matrix," International Journal of Computer and Communication Technology: Vol. 5: Iss. 4, Article 15. DOI: 10.47893/IJCCT.2014.1262 Available at: https://www.interscience.in/ijcct/vol5/iss4/15

Construction of polynomial over finite field

Lately researches are going on to combine both cryptography and biometric systems for more reliability and security of a system. It can be accomplished using fuzzy vault technique. Fuzzy vault stores the secret key. Unlocking phase of fuzzy vault is based on construction of polynomial over a finite field system GF(2"). As the size of a key increases, the time taken for construction of polynomial increases exponentially. We have designed and implemented an efficient algorithm for construction of polynomial over a finite field GF(2").

A Heuristic Cryptosystem Based on Bernstein Polynomial on Galois Fields GF(P) and GF(2m)

Public key cryptosystem or the asymmetric crypto system is more secure than secret key method because a pair of related key is being used by both sender and receiver. The problem occurring in most of the cryptosystem is plain text being considered as an integer number that leads to poor security. In this paper we propose an efficient polynomial based public key cryptography technique over Galois field GF(p) and extended to GF(2m), which considers plaint text as a (x,y) coordinate elements derived from the polynomial.