Secure image encryption scheme using high efficiency word-oriented feedback shift register over finite field

Abstract

Image encryption is an evolving technique in the arena of data communication. In the last decade, many encryption schemes have been suggested. Unfortunately, most of the current schemes are unable to maintain a balance between security and computational complexity. To overcome this challenge, this paper introduces a novel encryption scheme that effectively maintains the trade-off between security and computational complexity. Initially, the plain image is randomized and scrambled by the Logistic map and Arnold’s scrambling technique. The intermediate image found above, is then encrypted by the special word-oriented feedback shift register (wfsr) to get the final cipher image. Wfsr is inherently suitable for high-quality pseudorandom number generation with good statistical properties. It usually posses high throughput. Further, the elliptic curve Diffie-Hellman (ECDH) is used for sharing the keys required for encryption and decryption process. The performance of the proposed cryptosystem is evaluated based on several statistical properties of the cipher image, the resistance of the cipher image to various attacks, and time required for encryption and key sharing process. The statistical properties of the encrypted image are found out through histogram analysis, correlation and entropy finding, key sensitivity analysis, chi-square test, and NIST randomness test. The resistance of the encrypted image to various attacks is either found out experimentally or indirectly by using metrics like Unified Average Changing Intensity (UACI), Number of Pixel Changing Rate (NPCR). The proposed encryption method compares favorably with similar image encryption schemes.

Appendices

Appendix A: wfsr details

Note for Test Vectors:

In [42, B, Page No. -13], all the polynomial equations are listed. As mentioned earlier, 32-bit wfsr has been considered. Initially, 16 blocks of Hex value (i.e., 16 × 32 = 512 bit key/seed value) are loaded in the wfsr and as shown in below.

Appendix B: PSNR, MSE, and SSIM

$$ \text{PSNR} = 1 - \log_{10}[m \times n]\frac{1}{\text{MSE}} $$

(12)

where,

m × n: image size

$$ \text{MSE} = \frac{1}{m \times n} \sum\limits_{i=0}^{m-1}\sum\limits_{i=0}^{n-1}\left[ I_{i,j} - K_{i,j}\right]^{2} $$

(13)

where,

• I_i,j: plain image pixel

• K_i,j: cipher image pixel

$$ \text{SSIM}_{x,y} = \frac{(2\eta_{x}\eta_{y} + l_{1})(2\tau_{xy} + l_{2})}{({\eta_{x}^{2}} + {\eta_{y}^{2}} + l_{1})({\tau_{x}^{2}} + {\tau_{y}^{2}} + l_{2})} $$

(14)

where,

• η_x: Average of x

• η_y: Average of y

• τ_xy: Covariance of x, y

• τ_x: St. Dev of x

• τ_y: St. Dev of y

• ε₁: 0.01

• ε₂: 0.03

• l₁: (ε₁b)²

• l₂: (ε₂b)²

• b: 2^{Number of bits per pixel} - 1