图像信息安全处理的矩阵序列的周期性性质

Cyclical nature of matrix sequence in image information security processing

针对图像处理中实现无损信息隐藏,提出了有限域Fq上矩阵序列线性变换移位寄存器的概念。揭示n维Arnold模型变换的置乱变换周期的内在规律,把置乱变换的周期归结为求模为素数的变换矩阵的周期性问题,确定了模为素数幂的矩阵的周期,求出模为合数的周期。变换矩阵周期性计算方法在图像信息处理方面,可以实现较大容量的信息嵌入和保持较小的图像失真,并在提取机密信息时实现无损恢复原宿主图像。

Concerning the non-destructive information hiding in the image processing, the concept of the shift register of matrix sequence linear transformation in finite field Fq was proposed. The inherent law of scrambling transformation cycle for n-dimensional Arnold model transformation was revealed. Attributing the cycle scrambling transformation to cyclical problem of transformation matrix for modulo a prime number, the cycle of modulo the power of a prime number was determined, and the cycle of modulo a composite number was calculated. Cyclical calculation method of transformation matrix in the image information processing can achieve greater capacity of information embedded and less image distortion, and extract confidential information to realize non-destructive restoration of the original host image.