A novel discrete image encryption algorithm based on finite algebraic structures
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A novel discrete image encryption algorithm based on finite algebraic structures Dawood Shah 1 & Tariq Shah 1 Received: 4 March 2019 / Revised: 15 January 2020 / Accepted: 4 June 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
The arithmetic properties of a finite field have a remarkable impact on the security features of symmetric and asymmetric cryptosystems. Conventionally, in modern symmetric-key cryptosystems, a 256 elements Galois field depending on a single 8 degree primitive irreducible polynomial over ℤ2 is used for designing an S-box, the main nonlinear component in AES. The experience of S-box based image encryption schemes is not appreciable than chaotic systems based methods. In this study, we improve the S-box based image encryption algorithms by the usage of all 16 distinct degree 8 primitive irreducible polynomials over ℤ2 and by introducing a new role of the ring ℤn of integers modulo n in the permutation steps. The strength of this novel 2-algebraic structures based image encryption scheme is evaluated by some statistical analyses and a significant performance level is achieved. A comparison of encryption quality with some of the recent chaos-based image encryption algorithms is given and evidently the newly launched scheme spectacles high performance. Thus this new development in image encryption methods may provide an alternative to chaos dependent image encryption. Keywords Ring of integers modulo n . Galois field . Irreducible polynomials . Group action . Sbox . Image encryption
1 Introduction The rapid expansion of digital technologies have makes the traffic of communication fast and informal. Individuals can easily communicate and share information with each other’s in seconds of time over the wireless network. Though, due to the openness of wireless networks such as the internet, the confidentiality of secret information is a serious problem. Cryptography is the study of sharing confidential information over the unsecured channel, which deals with
* Dawood Shah [email protected]
1
Department of Mathematics, Quaid-i-Azam University Islamabad, Islamabad, Pakistan
Multimedia Tools and Applications
encryption, decryption, and key distribution, etc. Cryptography distributes further into two classes, symmetric, and asymmetric key cryptography. This distribution is made on the basis of the secret key. In symmetric-key cryptosystem, the interconnected parties use alike keys, while in an asymmetric key cryptosystem both parties use different keys namely public key and private key for secure communication. In symmetric-key cryptography substitution box (S-box) is the only main component responsible to produce confusion among the key and the plaintext. Thus a good quality S-box is essential to improve the nonlinearity of block ciphers [15, 1, 23]. Recently a large number of algorithms have been suggested for the construction of S-boxes [21, 22, 29]. In order to judge the quality of an S-box, some useful performance indexes have been established [28,
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