| Abstract [eng] |
Visual cryptography is a method of hiding information in digital images, when a secret image is split into two or more different images in such a way that it is impossible to see the secret information in any of them, taken separately. When all the parts of the image are put together, the secret information is decoded simply with the naked eye. In dynamic visual cryptography, a secret image is encoded by embedding it in a grid of moiré gratings in such a way that it is impossible to see the secret information in the encoded static image, but the information can be decoded with the naked eye, as in classical visual cryptography. This requires oscillating the coded image in a predetermined pattern with pre- fixed parameters. Most dynamic visual cryptography schemes are based on embedding secret information into periodic moiré gratings and are therefore not immune to statistical analysis algorithms. In 2023, a this kind of scheme was introduced to hide information in one-dimensional non-periodic stochastic moiré gratings. This scheme has greater resistance to statistical analysis algorithms compared to dynamic visual cryptography schemes based on information coding in periodic moiré gratings. Unfortunately, it is only possible to use horizontal or vertical harmonic oscillations in this scheme to encode and decode secret information. The use of harmonic or even elliptical oscillations in different directions in this type of scheme would not only increase the security of the inserted information, but also expand the application possibilities of dynamic visual cryptography. Therefore, the aim of this study is to propose a dynamic visual cryptography scheme based on non- periodic stochastic moiré gratings and harmonic and elliptical oscillations of different directions. Two-dimensional stochastic aperiodic moiré gratings will be used to integrate harmonic or elliptical oscillations of any direction. The study generates two stochastic images: for secret information and background embedding. At the equilibrium these images are very similar but distinctly different when averaged over time. Specific objective functions are constructed to generate such images; evolutionary optimization algorithms are used to optimize them. The effectiveness of information hiding in such stochastic images is illustrated by numerical experiments and graphical results. |
