Sequences with high linear complexity play a fundamental part in cryptography. In this study, the authors construct general forms of Whiteman's generalised cyclotomic quaternary sequences with period 2 p m +1 q n +1 of order two over 𝔽 4 and give the linear complexity of the proposed sequences. The conclusions reveal that such sequences have good balance property and high linear complexity.

In this study, the properties of the support tables of rotation symmetric Boolean functions (RSBFs for simplicity) are studied, and two sufficient and necessary conditions for RSBFs being 1‐ and 2‐resilient are obtained, respectively. Based on the relations between resilient functions and orthogonal arrays, with the help of the properties about the support tables of RSBFs, it is shown that the constructions of 1‐resilient RSBFs on given number of variables are equivalent to solving an equation system, and the number of functions is equal to the number of solutions of the equation system. Moreover, similar results are also obtained for 2‐resilient RSBFs. Lastly, a simple example is given to demonstrate our method. The results indicate that the constructions of n ‐variable 1‐resilient RSBFs are equivalent to studying the cyclotomic cosets C s modulo 2 n − 1 with respect to 2.

To improve the stego-image quality and provide a larger embedding capacity, a novel steganographic method based on four-pixel differencing and modulus function is presented. We process a block of four neighboring pixels, and form three two-pixel groups to record the information of secret data. In each group, the difference value between two pixels is exploited to estimate how many secret bits will be embedded. Two pixels will be adjusted so that the sum of the remainders of them is equal to secret data. In order to extract the secret data exactly, four pixel values in a block are adjusted synchronously by using modulus function. An optimization problem is formulated to minimize the embedding distortion. A theoretical proof is given to ensure the solvability of the problem. The experimental results show the proposed method not only has a larger embedding capacity but also provides better stego-image quality.