Optical cryptosystems combined with compressed sensing can achieve compression and encryption simultaneously. But they usually use the same measurement matrix to sample all blocks of an image, which makes it easy to estimate the measurement matrix in the chosen plaintext attack. In this paper, we propose a robust scheme adopting multiple measurement matrices to overcome this shortcoming. The matrices can be efficiently derived by applying random row exchanging to a basic one, which is also encoded into the fractional Fourier transform (FrFT) domain to improve the visual effect of wrongly decrypted images. Chaos-based pixel scrambling is added into our double FrFT cryptosystem to guarantee its nonlinearity. Simulation results have shown the security and effectiveness of our scheme.

In traditional optical multiple-image encryption schemes, different images typically have almost the same encryption or decryption process. Provided that an attacker manages to correctly decrypt some image, the conventional attacks upon other images are much easier to be made. In this paper, a binary-tree encryption strategy for multiple images is proposed to resist the attacks in this case. The encryption schemes produced by this strategy can not only increase the security of multiple-image encryption, but also realize an authority management with high security among the users sharing a cipher image. For a simulation test, we devise a basic binary-tree encryption scheme, whose encryption nodes are based on an asymmetric double random phase encoding in the gyrator domain. The favorable simulation results about the tested scheme can testify to the feasibility of the strategy.

When directly applying optical transforms, such as fractional Fourier transform (FrFT), to a single image or real image (input image), the resulting image will become complex-valued, which leads to the doubling of data volume. This data expansion problem can be found in many existing single-image optical encryption schemes. We propose a folding technique to offset the data expansion by constructing a complex input image of half size. And we devise an optical single-image encryption scheme based on double FrFTs, in which this technique together with compressed sensing can bring about the possible maximum compression of encrypted images. Moreover, the chaos-based random circular shift for scrambling is introduced to enhance security. The chaotic random signum matrix is also tried as the measurement matrix, and it displays a good performance. Simulation results demonstrate the validity and security of the proposed scheme. Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 09/11/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx Optical Engineering 064111-4 June 2016 • Vol. 55(6) Yi and Tan: Halving the dimension of a single image to be encrypted optically to avoid data expansion Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 09/11/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx Optical Engineering 064111-8 June 2016 • Vol. 55(6) Yi and Tan: Halving the dimension of a single image to be encrypted optically to avoid data expansion Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 09/11/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx

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