Abstract: Aiming at the problem that the magic square scrambling algorithm has insufficient variable-scale scrambling ability, poor scrambling effect and low security, based on the four-square theorem and the magic square scrambling method, a four-block magic square scrambling algorithm (FMSS) is proposed. Firstly, according to the four-block rule of the Four Square Theorem, the plain image is divided into four square image blocks. Secondly, the magic square matrix required for scrambling is generated. Thirdly, each image block is scrambled. Stitching, transpose, shape change and other operations are used to makes all pixels fully diffused and restored to the size of the plaintext image. Finally, the ciphertext image is obtained through multiple scrambling methods. Experimental results show that the algorithm can effectively enhance the image scrambling effect and can scramble and restore the rectangular image. It effectively reduces the image pixel correlation and has better security. The algorithm satisfies the requirements of the image scrambling algorithm in terms of robustness, scrambling and recovery speed.

Key words: rectangular image, Four Square Theorem, image block, four-block magic square scrambl-ing