Monaghan David S, Gopinathan Unnikrishnan, Situ Guohai, Naughton Thomas J, Sheridan John T
UCD Communications and Optoelectronic Research Centre, SFI-Strategic Research Cluster in Solar Energy Conversion, and School of Electrical, Electronic and Mechanical Engineering, College of Engineering, Mathematics and Physical Sciences, University College Dublin, Belfield, Dublin 4, Ireland.
J Opt Soc Am A Opt Image Sci Vis. 2009 Sep;26(9):2033-42. doi: 10.1364/josaa.26.002033.
The amplitude-encoding case of the double random phase encoding technique is examined by defining a cost function as a metric to compare an attempted decryption against the corresponding original input image. For the case when a cipher-text pair has been obtained and the correct decryption key is unknown, an iterative attack technique can be employed to ascertain the key. During such an attack the noise in the output field for an attempted decryption can be used as a measure of a possible decryption key's correctness. For relatively small systems, i.e., systems involving fewer than 5x5 pixels, the output decryption of every possible key can be examined to evaluate the distribution of the keys in key space in relation to their relative performance when carrying out decryption. However, in order to do this for large systems, checking every single key is currently impractical. One metric used to quantify the correctness of a decryption key is the normalized root mean squared (NRMS) error. The NRMS is a measure of the cumulative intensity difference between the input and decrypted images. We identify a core term in the NRMS, which we refer to as the difference parameter, d. Expressions for the expected value (or mean) and variance of d are derived in terms of the mean and variance of the output field noise, which is shown to be circular Gaussian. These expressions assume a large sample set (number of pixels and keys). We show that as we increase the number of samples used, the decryption error obeys the statistically predicted characteristic values. Finally, we corroborate previously reported simulations in the literature by using the statistically derived expressions.
通过定义一个代价函数作为一种度量标准，来比较尝试解密的结果与相应的原始输入图像，从而研究了双随机相位编码技术的幅度编码情况。对于已获得密文对但正确解密密钥未知的情况，可以采用迭代攻击技术来确定密钥。在这种攻击过程中，尝试解密时输出场中的噪声可以用作衡量可能的解密密钥正确性的指标。对于相对较小的系统，即涉及少于5x5像素的系统，可以检查每个可能密钥的输出解密结果，以评估密钥空间中密钥的分布与其解密时的相对性能之间的关系。然而，对于大型系统来说，检查每一个密钥目前是不切实际的。一种用于量化解密密钥正确性的度量标准是归一化均方根（NRMS）误差。NRMS是输入图像与解密图像之间累积强度差异的一种度量。我们确定了NRMS中的一个核心项，我们将其称为差异参数d。根据输出场噪声的均值和方差推导出了d的期望值（或均值）和方差的表达式，结果表明该噪声呈圆高斯分布。这些表达式假设样本集较大（像素和密钥的数量）。我们表明，随着所使用样本数量的增加，解密误差服从统计预测的特征值。最后，我们通过使用统计推导的表达式，证实了文献中先前报道的模拟结果。
