基于变形FrFT和线性同余的光学图像加密算法  

Optical image encryption algorithm combining anamorphic FrFT with linear congruence

作　　者：张文全[1] 王轶娴[1] 周南润[1] 

机构地区：[1]南昌大学电子信息工程系,江西南昌330031

出　　处：《光电子．激光》2011年第9期1405-1410,共6页Journal of Optoelectronics·Laser

基　　金：国家自然科学基金资助项目(10647133);江西省自然科学基金资助项目(2009GQS0080;2010GZC0160);江西省教育厅科技资助项目(GJJ11339)

摘　　要：基于双随机相位编码光学图像加密系统,利用线性同余发生器(LCG)生成随机相位,结合变形分数傅里叶变换(AFrFT),提出了一种改进的光学图像加密方法。方法的特点是:LCG函数的4个参数都可作为密钥;相比常规FrFT,变形FrFT的分数阶数目多1倍;算法密钥的数量从2重增加到8重,并且还有2个辅助密钥,大大提高了加密系统的安全性;由于随机相位掩模的放置位置有多种选择,因此具有灵活多变的加密系统结构。数值模拟表明,只有8重密钥都正确时,才能正确解密出原图像。加密和解密图像的均方差(MSE)评估了加密算法的可靠性。Based on the double random phase encoding,a new method for image encryption using anamorphic fractional Fourier transform（AFrFT） and linear congruence theory is proposed.Random phase masks are generated by using the linear congruential generator（LCG）.This encryption algorithm is characterized by that four parameters of the linear function can be keys.The AFrFT has two more fractional orders compared with the conventional FrFT.Since the number of keys increases from 2 to 8 and the proposed algorithm has two more auxiliary keys,the encryption system is more secure.Moreover,the structure of the encryption system is more flexible due to more choices for placing the random phase masks.The results of simulation show that only when the eight keys are exactly correct,can the original image be reconstructed.Reliability of the technique has been evaluated by calculating the mean square error（MSE） between the decrypted image and the original image.

关 键 词：分数傅里叶变换(FrFT) 光学图像加密 线性同余 

分 类 号：TN241[电子电信—物理电子学]