A Novel Method for Image Encryption Based on Chaos and Transcendental Numbers

A Novel Method for Image Encryption Based on Chaos and Transcendental Numbers

In this paper, a method for image encryption is proposed based on a novel approach using chaos and transcendental numbers for generating the substitution box and the ciphering keys. The Chaotic Pi Ciphering (CPC) is a robust symmetric cryptosystem of the substitution-permutation-network type, that c...

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Bibliographic Details
Published in:IEEE access Vol. 7; pp. 163729 - 163739
Main Authors: Silva Garcia, Victor Manuel, Gonzalez Ramirez, Marlon David, Carapia, Rolando Flores, Vega-Alvarado, Eduardo, Rodriguez Escobar, Eduardo
Format: Journal Article
Language:English
Published: Piscataway IEEE 2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Chaos
Chi-square test
Computer systems
Cryptography
Data loss
discrete Fourier transform
Discrete Fourier transforms
Encryption
Fourier transforms
Goodness of fit
High resistance
image encryption
Nonlinear differential equations
Nonlinearity
Permutations
Randomness
Schedules
Statistical tests
Substitutes
transcendental numbers
Walsh function
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Summary:In this paper, a method for image encryption is proposed based on a novel approach using chaos and transcendental numbers for generating the substitution box and the ciphering keys. The Chaotic Pi Ciphering (CPC) is a robust symmetric cryptosystem of the substitution-permutation-network type, that ciphers images in ten rounds. The objective of CPC is to avoid some general weakness points in cryptosystems, such as the vulnerability to certain types of attacks or the encryption with data loss. The number of rounds can be increased up to 14, with an even further increment of the ciphering security. An 8×8 substitution box is constructed using chaos, and its value of the Differential Power Analysis is lower than the corresponding to the Advanced Encryption Standard (AES). It makes CPC more resistant to differential and linear attacks than AES. CPC has approximately 2 512 keys, presenting a high resistance to brute-force attacks. Chaos is produced by a nonlinear differential equation, and the Walsh function is applied to measure the nonlinearity of the box. The transcendental number pi and a positive integer are employed to generate the schedule keys, and the key length is equal to the image size. The randomness of the encrypted images is evaluated with four tests: entropy, correlation, Discrete Fourier Transform, and a goodness-of-fit test using the chi square distribution χ 2 . CPC was tested using well-known images from the related literature, and its performance was compared to the corresponding to AES. The results show a good entropy and a high randomness, indicating a high-quality ciphering.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2019.2952030