Abstract
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.
Highlights
Image security is an important issue since frequently images contain sensitive information that should not be made public
Several symmetric cryptosystems considered as encryption standards, such as the Data Encryption Standard (DES) [28], Triple DES [29], and Advanced Encryption Standard (AES) [30] use substitution boxes
In AES, the substitution boxes (S-boxes) are produced in an algebraic way while the ones in Chaotic Pi Ciphering (CPC) are created in a dynamic way, excluding CPC from algebraic attacks
Summary
Image security is an important issue since frequently images contain sensitive information that should not be made public. A novel image encryption method is presented, the Chaotic Pi Ciphering (CPC), where the cipher-decipher process is carried out without any loss of information. There are important developments on image encryption that use no such boxes [4]–[8]. The third aspect is the application of the randomness measurements included in NIST 800-22 In spite of their importance, they are not applied in diverse developments [11]–[14]. The design of several image ciphering systems includes compression with data loss during the encryption process, to reduce the required memory [18], [19]. This paper is organized as follows: in Section 2, the mathematical cryptography tools used in this research are presented; in Section 3, the algorithm for S-box generation is developed, while in Section 4 the encryption procedure is detailed.
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