Statistical investigation of the double random phase encoding technique
Statistical investigation of the double random phase encoding technique
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DOI：
10.1364/josaa.26.002033
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发表时间：
2009-09-01
影响因子：
1.9
通讯作者：
Sheridan, John T.
中科院分区：
文献类型：
--
作者：
Monaghan, David S.;Gopinathan, Unnikrishnan;Sheridan, John T.
通过将成本函数定义为将尝试的解密与对应的原始输入图像进行比较的度量来检查双随机相位编码技术的幅度编码情况。对于已经获得密文对并且正确的解密密钥未知的情况，可以使用迭代攻击技术来确定密钥。在这种攻击期间，尝试解密的输出字段中的噪声可以用作可能解密密钥的正确性的度量。对于相对较小的系统，即涉及少于5×5像素的系统，可以检查每个可能的密钥的输出解密，以评估密钥空间中的密钥在执行解密时相对于它们的相对性能的分布。然而，为了对大型系统执行此操作，检查每个密钥目前是不切实际的。用于量化解密密钥的正确性的一个度量是归一化均方根值(NRMS)误差。NRMS是对输入图像和解密图像之间的累积强度差的测量。我们在NRMS中确定一个核心项，我们将其称为差参数d。d的期望值(或均值)和方差的表达式是根据输出场噪声的均值和方差导出的，其被证明是圆形高斯的。这些表达式假定采样集很大(像素数和关键点)。我们证明，随着使用的样本数的增加，解密误差服从统计预测的特征值。最后，我们使用统计导出的表达式证实了文献中先前报道的模拟。(C)2009年美国光学学会
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 5 x 5 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. (C) 2009 Optical Society of America