scholarly journals Image encryption based on permutation polynomials over finite fields

2020 ◽  
Vol 50 (3) ◽  
Author(s):  
Jianhua Wu ◽  
Hai Liu ◽  
Xishun Zhu
Keyword(s):  
Image Encryption ◽  
Finite Fields ◽  
High Efficiency ◽  
Symmetric Matrix ◽  
Permutation Polynomial ◽  
Encryption Algorithm ◽  
Permutation Polynomials ◽  
Polynomials Over Finite Fields ◽  
Intrinsic Nonlinearity ◽  
Image Encryption Algorithm

In this paper, we propose an image encryption algorithm based on a permutation polynomial over finite fields proposed by the authors. The proposed image encryption process consists of four stages: i) a mapping from pixel gray-levels into finite field, ii) a pre-scrambling of pixels’ positions based on the parameterized permutation polynomial, iii) a symmetric matrix transform over finite fields which completes the operation of diffusion and, iv) a post-scrambling based on the permutation polynomial with different parameters. The parameters used for the polynomial parameterization and for constructing the symmetric matrix are used as cipher keys. Theoretical analysis and simulation demonstrate that the proposed image encryption scheme is feasible with a high efficiency and a strong ability of resisting various common attacks. In addition, there are not any round-off errors in computation over finite fields, thus guaranteeing a strictly lossless image encryption. Due to the intrinsic nonlinearity of permutation polynomials in finite fields, the proposed image encryption system is nonlinear and can resist known-plaintext and chosen-plaintext attacks.

scholarly journals An Image Encryption Algorithm Based on Multichaotic System and DNA Coding

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Jiming Zheng ◽  
Zheng Luo ◽  
Zhirui Tang
Keyword(s):  
Image Encryption ◽  
Chaotic Systems ◽  
High Efficiency ◽  
Encryption Algorithm ◽  
Two Dimensional ◽  
Dna Encoding ◽  
Dna Coding ◽  
Chaotic Sequences ◽  
Xor Operation ◽  
Image Encryption Algorithm

In this paper, an improved two-dimensional logistic-sine coupling map (N2D-LSCM) and an improved Henon map (NHenon) are proposed. Furthermore, by combining N2D-LSCM and NHenon map, an image encryption algorithm is proposed based on these two chaotic systems and DNA coding. The chaotic sequences generated by N2D-LSCM are used as the parameters of NHenon. In the scrambling stage, DNA encoding is carried out for pixels after scrambling by two chaotic sequences generated by N2D-LSCM; in the stage of diffusion, DNA random coding acts on random matrix obtained by two chaotic sequences generated by NHenon, and DNA XOR operation is carried out with the image obtained in the scrambling stage to diffuse. Compared with other 2D map for image encryption algorithm, this algorithm exhibits good security and holds high efficiency.

scholarly journals CONSTRUCTING PERMUTATION POLYNOMIALS OVER FINITE FIELDS

2013 ◽  
Vol 89 (3) ◽  
pp. 420-430 ◽  
Author(s):  
XIAOER QIN ◽  
SHAOFANG HONG
Keyword(s):  
Finite Fields ◽  
Open Problem ◽  
Symmetric Polynomial ◽  
Permutation Polynomial ◽  
Permutation Polynomials ◽  
Elementary Symmetric Polynomial ◽  
Polynomials Over Finite Fields

AbstractIn this paper, we construct several new permutation polynomials over finite fields. First, using the linearised polynomials, we construct the permutation polynomial of the form ${ \mathop{\sum }\nolimits}_{i= 1}^{k} ({L}_{i} (x)+ {\gamma }_{i} ){h}_{i} (B(x))$ over ${\mathbf{F} }_{{q}^{m} } $, where ${L}_{i} (x)$ and $B(x)$ are linearised polynomials. This extends a theorem of Coulter, Henderson and Matthews. Consequently, we generalise a result of Marcos by constructing permutation polynomials of the forms $xh({\lambda }_{j} (x))$ and $xh({\mu }_{j} (x))$, where ${\lambda }_{j} (x)$ is the $j$th elementary symmetric polynomial of $x, {x}^{q} , \ldots , {x}^{{q}^{m- 1} } $ and ${\mu }_{j} (x)= {\mathrm{Tr} }_{{\mathbf{F} }_{{q}^{m} } / {\mathbf{F} }_{q} } ({x}^{j} )$. This answers an open problem raised by Zieve in 2010. Finally, by using the linear translator, we construct the permutation polynomial of the form ${L}_{1} (x)+ {L}_{2} (\gamma )h(f(x))$ over ${\mathbf{F} }_{{q}^{m} } $, which extends a result of Kyureghyan.

scholarly journals A Symmetric Image Encryption Algorithm Based on a Coupled Logistic–Bernoulli Map and Cellular Automata Diffusion Strategy

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 504 ◽  
Author(s):  
Wei Zhang ◽  
Zhiliang Zhu ◽  
Hai Yu
Keyword(s):  
Cellular Automata ◽  
Image Encryption ◽  
High Efficiency ◽  
Chaotic Map ◽  
Logistic Map ◽  
Three Dimensional ◽  
Encryption Algorithm ◽  
Original Structure ◽  
One Dimensional ◽  
Image Encryption Algorithm

In this paper, the properties of the classical confusion–substitution structure and some recently proposed pseudorandom number generators using one-dimensional chaotic maps are investigated. To solve the low security problem of the original structure, a new bit-level cellular automata strategy is used to improve the sensitivity to the cryptosystem. We find that the new evolution effects among different generations of cells in cellular automata can significantly improve the diffusion effect. After this, a new one-dimensional chaotic map is proposed, which is constructed by coupling the logistic map and the Bernoulli map (LBM). The new map exhibits a much better random behavior and is more efficient than comparable ones. Due to the favorable properties of the new map and cellular automata algorithm, we propose a new image-encryption algorithm in which three-dimensional bit-level permutation with LBM is employed in the confusion phase. Simulations are carried out, and the results demonstrate the superior security and high efficiency of the proposed scheme.

scholarly journals On a Symmetric Image Encryption Algorithm Based on the Peculiarity of Plaintext DNA Coding

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1393
Author(s):  
Yulan Kang ◽  
Linqing Huang ◽  
Yan He ◽  
Xiaoming Xiong ◽  
Shuting Cai ◽  
...  
Keyword(s):  
Image Encryption ◽  
High Efficiency ◽  
Security Analysis ◽  
Chaotic Sequence ◽  
Encryption Algorithm ◽  
Differential Attack ◽  
Dna Coding ◽  
Chaotic Sequences ◽  
Xor Operation ◽  
Image Encryption Algorithm

Many plaintext-related or non-plaintext-related image encryption algorithms based on chaotic systems have been found inefficient and insecure under chosen plaintext attacks. In this paper, a novel plaintext-related mechanism based on the peculiarity of plaintext DNA coding (PPDC) is presented and used to developed a symmetric image encryption algorithm. In our scheme, a hyper-chaotic Lorenz system is used to produce four chaotic sequences. Firstly, by using one chaotic sequence to control the DNA rules, the original image is encoded to obtain the image DNA coding and PPDC, and another chaotic sequence is encoded into a DNA sequence, which is used in the DNA XOR operation. Then, the processing of the remaining two chaotic sequences by using the PPDC is performed to obtain two key streams, which are used in the permutation stage. After performing the traditional permutation operation and DNA XOR operation, the cipher image is obtained. Because of the use of the PPDC, the key streams used in the permutation stage are related to the secret keys and plaintext image, which gives the encryption system higher plaintext sensitivity and security. The simulation experimental results and security analysis demonstrate that the proposed encryption system possesses high efficiency and security and can resist various typical attacks like exhaustive attack, statistical attack, and differential attack effectively.

scholarly journals On permutation polynomials over finite fields

1987 ◽  
Vol 10 (3) ◽  
pp. 535-543 ◽  
Author(s):  
R. A. Mollin ◽  
C. Small
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Permutation Polynomial ◽  
Permutation Polynomials ◽  
Polynomials Over Finite Fields ◽  
One To One ◽  
Necessary And Sufficient

A polynomialfover a finite fieldFis called a permutation polynomial if the mappingF→Fdefined byfis one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integerm, the cardinality of finite fields admitting permutation polynomials of degreemis bounded.

On permutation polynomials over finite fields of characteristic 2

2016 ◽  
Vol 15 (07) ◽  
pp. 1650133 ◽  
Author(s):  
Rohit Gupta ◽  
R. K. Sharma
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Permutation Polynomial ◽  
Permutation Polynomials ◽  
Polynomials Over Finite Fields ◽  
Characteristic 2 ◽  
Polynomial Formula

Let [Formula: see text] denotes the finite field of order [Formula: see text] where [Formula: see text] A permutation polynomial [Formula: see text] over [Formula: see text] with [Formula: see text] and [Formula: see text] such that for each [Formula: see text] is a permutation polynomial satisfying [Formula: see text] is called a o-polynomial. In this paper, we determine all o-polynomials up to degree [Formula: see text].

Image Encryption Algorithm Based on Substitution Principle and Shuffling Scheme

2020 ◽  
Vol 38 (3B) ◽  
pp. 98-103
Author(s):  
Atyaf S. Hamad ◽  
Alaa K. Farhan
Keyword(s):  
Image Encryption ◽  
Chaotic Map ◽  
Logistic Map ◽  
Encryption Algorithm ◽  
Second Phase ◽  
Cipher Text ◽  
The Face ◽  
Substitution Principle ◽  
2D Logistic Map ◽  
Image Encryption Algorithm

This research presents a method of image encryption that has been designed based on the algorithm of complete shuffling, transformation of substitution box, and predicated image crypto-system. This proposed algorithm presents extra confusion in the first phase because of including an S-box based on using substitution by AES algorithm in encryption and its inverse in Decryption. In the second phase, shifting and rotation were used based on secrete key in each channel depending on the result from the chaotic map, 2D logistic map and the output was processed and used for the encryption algorithm. It is known from earlier studies that simple encryption of images based on the scheme of shuffling is insecure in the face of chosen cipher text attacks. Later, an extended algorithm has been projected. This algorithm performs well against chosen cipher text attacks. In addition, the proposed approach was analyzed for NPCR, UACI (Unified Average Changing Intensity), and Entropy analysis for determining its strength.

Image Encryption Algorithm with Plaintext Related Chaining

2019 ◽  
Vol 38 (3) ◽  
pp. 647-678 ◽  
Author(s):  
Ľuboš Ovseník ◽  
Ján Turán ◽  
Tomáš Huszaník ◽  
Jakub Oravec ◽  
Ondrej Kováč ◽  
...  
Keyword(s):  
Image Encryption ◽  
Encryption Algorithm ◽  
Image Encryption Algorithm
Sign in / Sign up

Export Citation Format

Share Document