Symmetric encryption using logistic map

2012 ◽  
Author(s):  
P. Jhansi Rani ◽  
S. Durga Bhavani
Keyword(s):  
Logistic Map ◽  
Symmetric Encryption

scholarly journals Construction of S-Box Based on Chaotic Map and Algebraic Structures

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 351 ◽  
Author(s):  
Iqtadar Hussain ◽  
Amir Anees ◽  
Temadher Al-Maadeed ◽  
Muhammad Mustafa
Keyword(s):  
Chaotic Map ◽  
Logistic Map ◽  
Symmetric Encryption ◽  
Secret Key ◽  
Substitution Box ◽  
Differential Approximation ◽  
Security Applications ◽  
Strict Avalanche Criterion ◽  
Main Component ◽  
Independence Criterion

The Advanced Encryption Standard (AES) is widely used in different kinds of security applications. The substitution box (S-box) is the main component of many modern symmetric encryption ciphers that provides confusion between the secret key and ciphertext. The S-box component that is used in AES is fixed. If we construct this component dynamically, the encryption strength of AES would be greater than before. In this manuscript, we used chaotic logistic map, Mobius transformation and symmetric group S 256 to construct S-box for AES. The idea behind the proposed work is to make supplementary safe S-box. The presented S-box is analyzed for the following analyses: linear approximation probability (LP), nonlinearity (NL), differential approximation probability (DP), strict avalanche criterion (SAC), and bit independence criterion (BIC). The analyses show that the proposed technique is useful in generating high resistance S-box to known attacks.

scholarly journals JPEG Images Encryption Scheme Using Elliptic Curves and A New S-Box Generated by Chaos

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 413
Author(s):  
Erick Hernández-Díaz ◽  
Héctor Pérez-Meana ◽  
Víctor Silva-García ◽  
Rolando Flores-Carapia
Keyword(s):  
Power Analysis ◽  
Logistic Map ◽  
Symmetric Encryption ◽  
Substitution Box ◽  
Suitable Alternative ◽  
Jpeg Images ◽  
Cipher Text ◽  
Solution Point ◽  
Single Block

This paper proposes a new symmetric encryption system based on an elliptical curve and chaos, where the encryption is done in a single block and runs for 14 rounds. Here, the 15 encryption keys have the same size as the image and are generated using a solution point of a strong elliptic curve. Using a string of random numbers obtained with a logistic map, a permutation and its inverse are generated, which improve the encryption level and add diffusion to the cryptosystem. Another important contribution to this research is the generation of a substitution box with a non-linearity of 100, which strengthens the cryptosystem against differential and linear attacks that add confusion to the scheme. Moreover, the cryptographic properties of the proposed S-Box are compared with those of the S-Box of the Advanced Encryption Standard (AES) to ascertain that it is a suitable alternative that it is resistant to differential power analysis (DPA) attacks. To verify the robustness of proposed cryptosystem against cryptanalysis and the quality of the cipher text obtained, this system is subjected to different tests, such as entropy, correlation coefficient, χ2, Changing Pixel Rate (NPCR), and Unified Averaged Changing Intensity (UACI). The results are shown and compared with recently proposed systems.

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.

Chaotic logistic map, parabola, and gravity

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Logistic Map ◽  
Chaotic Logistic Map

I am trying to connect gravity with chaos via the parabola in the logistic map.

Linear and Nonlinear Dynamic Behaviour

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Systems ◽  
Dynamic Behaviour ◽  
Nonlinear Dynamical Systems ◽  
Logistic Map ◽  
Nonlinear Dynamical ◽  
Deterministic Dynamic ◽  
Random Behavior ◽  
Single Solution ◽  
Equivalent Systems

In this chapter, we describe how highly erratic dynamic behavior can arise from a nonlinear logistic map, and how this apparently random behavior is governed by a surprising order. With this lesson in mind, we should not be overly surprised that highly erratic and random appearing observed data might also be generated by parsimonious deterministic dynamic systems. At a minimum, we contend that researchers should apply NLTS to test for this possibility. We also introduced tools to analyze dynamic behavior that form the foundation for NLTS. In particular, we have stressed the quite unexpected capability to achieve some form of predictability even with only one trajectory at hand. In subsequent chapters, we treat known nonlinear dynamical systems as unknown, and investigate how NLTS methods rely on a single solution (or multiple solutions) generated by them to reconstruct equivalent systems. This is a conventional approach in the literature for seeing how NLTS methods work since we know what needs to be reconstructed.

scholarly journals Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 474 ◽  
Author(s):  
Lazaros Moysis ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jesus M. Munoz-Pacheco ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Image Encryption ◽  
Fuzzy Numbers ◽  
Statistical Tests ◽  
Logistic Map ◽  
Simple Rule ◽  
Pseudorandom Number ◽  
Bifurcation Diagrams ◽  
Triangular Numbers ◽  
Pseudorandom Number Generation

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

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