基于混沌动态随机分组与调制分数阶FFT旋转因子的图像加密

Image encryption based on chaotic dynamic random grouping and modulating fractional Fourier transform rotation factor

针对分数阶傅里叶变换(FRFT)图像加密中,由于FRFT旋转因子单一性和分组单一性而引起的安全性问题,提出一种新的加密方法——混沌动态随机分组与随机调制FRFT旋转因子。该方法采用3个混沌子系统:用子系统1(密钥)对明文进行无损预加密,得到(一次)密文;然后,用子系统2对FRFT进行动态分组;用子系统3对FRFT旋转因子进行随机调制。接着,用经动态分组、随机调制旋转因子后的FRFT对(一次)密文进行二次加密。相邻像素相关性、像素改变率等测试结果表明,该算法对统计攻击和差分攻击具有较强的抵御能力;实时性、还原性测试表明,一次加密中,采用无损方式与有损相比,其解密用时减少了52.5%,解密后明文相似度提高了4.5%,由此,免除了去噪处理,降低了系统开销。安全性测试表明,与单纯调制旋转因子方法相比,随机分组与调制旋转因子方法的信息熵提高了1.7%,抵御穷举法攻击的能力提高了10^(3635)倍。由此表明,该方法在实时性、还原性、安全性等方面,均优于混沌密钥单纯调制FRFT旋转因子算法。

Concerning the security problem caused by the singleness of rotation factor and grouping in FRactional Fourier Transform（ FRFT） image encryption algorithm,a novel encryption method,namely chaotic dynamic random grouping and random modulating FRFT rotation factor,was proposed. Three chaotic systems were adopted in this process. Firstly,the keys of subsystem 1 were utilized to realize the nondestructive encryption on plaintext and obtain the first cipher text. Then subsystem 2 was utilized to realize the dynamic grouping of FRFT,and the rotation factor of FRFT was randomly modulated by using subsystem 3. After that,the FRFT was utilized to realize the second encryption on first cipher text. The test results on adjacent pixels correlation and pixels change rate show that the method can effectively resist statistical attack and differential attack. Compared with destructive method,in the first encryption,the real-time and reduction test show that the decrypted time of nondestructive method decreases by 52. 5% and the similarity of decrypted image improves by 4. 5%; thus,the denoising process is avoided and the system overhead is reduced. Security test shows that the information entropy increases by 1. 7% and the ability to resist exhaustive attack increases by 10^（3635） times,compared with simple modulate FRFT rotation factor algorithm. The results show that the proposed method is better than the chaotic key simple modulating FRFT rotation factor algorithm in real-time,reduction,security and so on.