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COMPUTER STEGANOGRAPHY. IMPLEMENTATION OF INFORMATION IN IMAGES ACCORDING TO STOCHASTIC MODULATION METHOD
       Ch.L. Larionova

The main methods of protection of multimedia information are algorithms based on steganography. Steganography is the science that ensures the exchange of information in such a way that it hides the existence of secret communication. It does not replace cryptography (encryption), but complements it with another level of security. When data are processed by steganographic methods the information is hidden in other objects (files, disks, etc.) so that an unauthorized person cannot guess the presence of a hidden secret message. In addition to the hidden messages, steganography is one of the most promising areas of authentication and labeling of the author's products. This information is usually implemented in the visual and audio works, and protected products.

In modern computer steganography there are two main types of files: a message - the file that is designed to be hidden, and a container - a file that can be used to hide the message. Containers can also be of two types. The container-original (or "empty" container) is a container, which contains no hidden information. Container-result (or "filled" container) is a container that contains some hidden information. A key is an element of security, which determines the procedure (algorithm) of recording a message into a container.

Using as a container image files, you can build not only textual information but also images and other files.

The only condition is that the hidden image cannot exceed the size of the image repository. To achieve this, each program uses its own technology, but they all are brought to the replacement of certain pixels in the image.

A digital image is a matrix of pixels. Most often, the secret message or CEH was originally encrypted using a cryptographic method based on the secret key.

Avoid photos with large bright and black areas. In these pictures big fields in the source file have color components 255 and 0, so stegobites will also stand out viewing a file in the code 254 and 1. 73 Using steganographic systems keep in mind that the more information is embedded in the file container, the lower the reliability of the system is.

One of the methods of modern steganography is to receive the stochastic modulation. On an example of an image file it looks as follows.

The message that you want to transfer, is denoted by m, consisting of consecutive 1 and -1 (logical 0).

First the probability function is determined - P (x, s) (-1,1), equal to 0 only if s = 0. It must also satisfy the property of antisymmetric for all x: P (x + s, s) =- P (xs, s). This feature is useful in cases when the values of x + s or x-s lie outside the range of allowable values.

During imposing of the secret information pixels are held in pseudorandom sequences constructed with the help of random number generator with a distribution that matches the distribution of noise, which will be imposed in the picture. This sequence is called stegonoise. During generation a special stegokey is used.

For each point x a random number s is generated. If s is not a zero, then if


                                                                         P (x + s, s) = m,


the value of a pixel is replaced by x + s, if


                                                                          P (x + s, s) =- m,


the value is replaced by x-s. Formally, the process of concealment is


                                                                         x'i = xi + miP (xi + si, si) si


As the very image and stegonoise si do not depend on secret communications, the signal


                                                                         vi = miP (xi + si, si)


is a pseudorandom sequence of 1 and -1. Thus, vi has the same statistical properties as stegonoise.

To extract the encoded message stegonoise is generated according to the same stegokey which was used during encoding. Applying probability function P to the pixel image, we get a secret message, formed from the nonzero values


                                                                         mi = P (xi, si).


In the discussed above method only one stegonoise si is used, which is added or subtracted from the pixel values in accordance with the probability function.

You may get more hidden information with the same noise characteristics. Improved method for the stochastic modulation uses two stegonoises, adding to the values of pixels the image is always either one stegonoise or another, based again on the coincidence bit messages u1080 and probability functions. This method works for stegonoise with arbitrary probability distributions.

The method of stochastic modulation can also be applied to images obtained by means of devices, whose noise depends on the content of the image.

There are many software products that are used for the purpose of steganography and realizing, as a rule, means of introduction of secret data in graphic, audio and video files. Many of them are free or conditionally free. The most popular ones are EZStego, DiSi-Steganograph, Steganos, etc. Usage of a majority of them is reduced to pressing a few buttons in dialog boxes - just select the message file that you want to hide, then file - the receiver of data, in which data are hidden (its capacity should be sufficient to store the embedded data) and click OK.


Literature


1. https://www.pgpru.com/biblioteka/steganografija

2 Digital image steganography using stochastic modulation, Jessica Fridrich and Miroslav Goljan,2003

3. Быков Р.Е., Фрайер Р., Иванов К.В., Манцветов А.А. Цифровое преобразование изображений: Учебное пособие для вузов. – М., 2003. – 228с.

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