Attack on Optical Double Random Phase Encryption Based on the Principle of Ptychographical Imaging

The principle of ptychography is applied in known plain text attack on the double random phase encoding （DRPE） system. We find that with several pairs of plain texts and cipher texts, the model of attack on DRPE can be converted to the model of ptyehographical imaging. Owing to the inherent merits of the ptyehographical imaging, the DRPE system can be breached totally in a fast and nearly perfect way, which is unavailable for currently existing attack methods. Further, since the decryption keys can be seen as an object to be imaged from the perspective of imaging, the ptychographical technique may be a kind of new direction to further analysis of the security of other encryption systems based on double random keys.

A Hybrid Security Framework for Medical Image Communication

Authentication of the digital image has much attention for the digital revolution.Digital image authentication can be verified with image watermarking and image encryption schemes.These schemes are widely used to protect images against forgery attacks,and they are useful for protecting copyright and rightful ownership.Depending on the desirable applications,several image encryption and watermarking schemes have been proposed to moderate this attention.This framework presents a new scheme that combines a Walsh Hadamard Transform(WHT)-based image watermarking scheme with an image encryption scheme based on Double Random Phase Encoding(DRPE).First,on the sender side,the secret medical image is encrypted using DRPE.Then the encrypted image is watermarking based on WHT.The combination between watermarking and encryption increases the security and robustness of transmitting an image.The performance evaluation of the proposed scheme is obtained by testing Structural Similarity Index(SSIM),Peak Signal-to-Noise Ratio(PSNR),Normalized cross-correlation(NC),and Feature Similarity Index(FSIM).

On the Strong Limit Theorems for Double Arrays of Blockwise M-dependent Random Variables

For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1,n ≥ 1}, ∑i^m=1 ∑^nj=1 strong laws of large numbers are established for double sums ∑m i=1 ∑j^n=1 ij, m≥ 1, n 〉 1. The main results are obtained for （i） random variables {Xmn, m≥ 1, n ≥ 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and （ii） random variables {Xmn, m ≥ 1, n ≥ 1} being stochastically dominated. The result in Case （i） generalizes the main result of M6ricz et al. [J. Theoret. Probab., 21, 660-671 （2008）] from dyadic to arbitrary blocks, whereas the result in Case （ii） extends a result of Gut [Ann. Probab., 6, 469-482 （1978）] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.

On the Laws of Large Numbers for Double Arrays of Independent Random Elements in Banach Spaces

For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ≥ 1,n ≥ 1 are equivalent.Both the identically distributed and the nonidentically distributed cases are treated.In the main theorems,no assumptions are made concerning the geometry of the underlying Banach space.These theorems are applied to obtain Kolmogorov,Brunk–Chung,and Marcinkiewicz–Zygmund type strong laws of large numbers for double sums in Rademacher type p（1 ≤ p ≤ 2） Banach spaces.