-This work is devoted to the development of the method of information concealment, in the raster image using steganography together with cryptography the solving the problem of recovering a message if the image which contains hidden data is damaged. It proposes a method of implementing the steganography for insert data on digital image not in its entirety, but previously using (t, n)-threshold scheme and inserting each of the parts received independently. The software was developed for approbation of the proposed method. A series of experiments confirming the possibility of applying the proposed method was carried out. Text information is inserted into the raster image. Further, the image was subjected to modification, simulates container damage when it was transmitted through the communication channel or as a result of intentional actions of an intruder. As a result of the experiments, it can be said about the possibility of applying the proposed method.
INTRODUCTION
The issue of maintaining and ensuring the confidentiality of
information is relevant. The software, allowing transferring
data securely, is encrypted. If an open channel is used, a man in
the middle (MITM) attack is possible, and the attacker, if not
able to decrypt the data, may violate their integrity. The
solution to this problem can be the use of steganography, i.e.
concealment of the fact of the transfer of classified
information. A lot of scientific works are devoted to this topic,
for example [
The article [
The [
In [
In the article [
In steganography, the following problems can be distinguished: 1. detection of a steganography inserts (stegoanalysis); 2. reliability of information concealment during its transmission.
The solution of the second problem is proposed in [
In the article [
This work is also devoted to the problem of increasing the reliability of information hiding when it is transmitted, i.e. the task of restoring information in case the image which contains hidden data is damaged (image-container).
Consider the possibility of combining the steganography method and the (t, n)-threshold scheme. The analysis of existing steganography algorithms and threshold schemes is carried out.
We will analyze the existing methods of steganography and find which one is most suitable.
Next, we will consider algorithms for embedding information in the part of the original image. The advantage of these algorithms is that for implementation, you do not need to perform complex linear transformations of the image. Information will be introduced by manipulating the brightness or the color components of the image.
In this algorithm, the information will be embedded in the blue channel because the changes in this color are less visible to the human eye. A pseudo-random position is selected in the image into which the information will be inserted and further into the blue channel. This information is introduced by modifying the brightness.
In work [
This algorithm works with blocks of 8x8 pixels from the original image. Initially, a pseudo-random mask of 8x8 pixels is created, consisting of zeros and ones. At the first stage, each block is divided into a pair of subblocks, depending on the value of the mask. Then, for each of them, the average brightness value is calculated. At the second stage, some arbitrary threshold is selected, after which the embedded information bit will be built in the following way: 1 is written if the difference between the average brightness values is greater than the selected threshold; 0 is written if the difference between the average brightness values is less than the selected threshold. If this condition is not met, the changes will occur in the pixel values of the second subblock.
The embedded information is a two-dimensional matrix, which consists of ones and zeros. Their number is almost equal to each other. On the basis of some characteristic function, computed locally in the course of analyzing neighboring pixels, those pixels in which information can be embedded are recognized. The number of these pixels is about 0.01 of the total number, so not all units will be embedded in these pixels. To increase the number of these pixels initially proposed to carry out a slight distortion of the image.
The essence of this method is that the least significant bit of
the image carries in itself the least information. When you
change them to the bits of the hidden message, the difference
from the original object is almost insignificant for human
perception. This method allows you to embed large amounts of
information, which is a significant plus, as well as it is easy to
implement [
In this article [
After analyzing known methods of data concealment in
raster images to achieve the goal and studying works [
Briefly, this algorithm can be described as follows. Let a finite field G be given. We fix n different non-zero non-secret elements of this field. Each of these elements is assigned to a certain member of the group. Next, an arbitrary set of t elements of the field G from which the polynomial f (x) is composed over the G field of degree t-1, 1<t≤n. After obtaining the polynomial, we calculate its value at non-secret points and report the results to the corresponding members of the group.
To restore the secret, you can use the interpolation formula, for example, the Lagrange formula.
2.
The secrets to be solved in the Blackley’s scheme are one of the coordinates of a point in an m-dimensional space. The shares of secret, distributed to the sides, are the equations of (m-1) -dimensional hyperplanes. To restore the point, it is necessary to know the m equations of hyperplanes. Less than m sides cannot recover the secret, since the intersection set of m-1 planes is straight, and the secret cannot be recovered. 3. Secret sharing using the Chinese remainder theorem (Mignotte's threshold secret sharing scheme, AsmuthBloom's threshold secret sharing scheme).
For a certain number (in Mignotte's scheme this is the secret itself, in the Asmuth-Bloom's scheme-some derived number), the remainders from dividing by the sequence of numbers that are distributed to the sides are calculated. Due to the restrictions on the sequence of numbers, only a certain number of sides can restore the secret.
For the further analysis, two schemes were chosen: 1 and 3.
The Blackley’s scheme was not included in the analysis because it is less effective than Shamir's scheme: in the Shamir’s scheme, each share is the same size as the secret, and in the Blackley’s scheme, each share is t times larger.
The results of comparison schemes are presented in the Table 1. The Shamir’s secret sharing scheme was chosen. Shamir’s secret sharing scheme Secret separation time: Secret recovery time: Amount of memory required: 5 ms 1 ms Secret separation time: Secret recovery time: Amount of memory required: Asmuth-Bloom's threshold secret sharing scheme 7 ms 2 ms 1560 byte 6720 byte
100608 byte
The idea of the proposed method is to combine the steganography method LSB with the (t, n) -threshold scheme, which allows for damage to the stack container to n-t parts, where tn and n - is the total number of shares of the secret, and t - is the minimum number of shares of the secret for its successful recovery, all the same ensure a reliable recovery of secret.
The proposed approach can be described in two stages: 1. embedding information in the image container (Fig. 2);
The embedded information is processed according to the selected (t, n) -threshold scheme, i.e. secret shares are formed.
The original image into which the insert will be inserted is divided into n parts in width, according to the secretion (t, n) threshold scheme used to form the shares of the secret. Further, each of the obtained parts is considered as an independent image. The image is represented as an array of bits in which for each of the colors of the pixel is encoded with 8 bits. Write the secret by making changes to the low-order bits. The first pixel of the image will record the length of the secret part, and the next part of the secret itself. Such changes will occur with all n blocks. After finishing the embedding procedure, the imagecontainer is formed from n parts that already contain the secret parts.
To retrieve information, you need to know the number of parts to which the original image and its length were divided.
Next, from each of the parts of the container image, the first pixel is read, and the presence of the length record of the secret portion from the hidden message is checked. If such information is present, then the secret share is read. Then checksums are checked. They will be counted again from each part of the image and will be compared to those that were recorded in the file. In case of their coincidence, the share of the secret will be written into the array, which will be transferred to the input of the secret recovery function.
APPROBATION
To approbate the proposed method, a C # program was
implemented. As a (t, n) -threshold scheme, the Shamir’s secret
sharing scheme [
Block scheme of the program can be seen in Figures 3, 4.
A set of experiments were carried out. For a greater probability of recovering a secret, it is best to choose as small as possible t, and n as much as possible. In the first experiment, the values were chosen 4 and 10, respectively. As the embedded information, the phrase "Тестирование программы!!!".
After cutting the image-container by ~ 30%, in order to simulate damage or attack, the original message was restored. If the container is damaged by more than 60%, it will be impossible to restore the secret. Improve the results by decreasing the threshold or increasing the number of parts.
Then experiments were conducted in which various changes were made to the image-container, imitating damage to the container during transmission or deliberately assigning it to an attacker: imposing "noise", cutting out a part of the picture, imposition of extraneous images.
In cases where the image was damaged by cutting out its part or imposing foreign images (Fig. 7), the experiments were successful, i.e. the image was restored, if the damage is less than 60% of the container.
In experiments, when the damage was done by applying "noise", the results were worse. The result is presented in Table 2, where "+" - it was possible to restore the information, "-" - it was not possible to recover the information.
Overcoming the threshold of 0.2% noise, the message was not restored when selecting any threshold scheme. This meant that the maximum Gaussian noise that could be applied and the message could be recovered was 0.19%. Significantly improve the results can be by selecting the shares to restore information for a particular algorithm. The task of finding the algorithm for choosing the shares was not set in this paper. It was necessary to test the hypothesis of the possibility of combining the steganography method LSB with the (t, n) -threshold scheme. The search for a choice algorithm for shares can be a direction for further work on this topic.
CONCLUSION
The work presented a method that solves one of the problems of steganography, namely, increasing the reliability of information hiding during its transmission, as well as increasing the resistance to attacks aimed at corrupting the image-container. The essence of the method consists in combining the steganography method LSB and (t, n) -threshold scheme. The software was developed and approbated. As a (t, n) -threshold scheme, the Shamir's secret sharing scheme was chosen. A set of experiments was carried out: a steganography insertion of the text was made to the original image. Then the image-container was modified, thereby simulating damage during transmission or deliberate actions by the attacker. During the experiments it was revealed that:
1. In case of damage by imposition of an extraneous image or by deleting part of the image-container, the threshold for successful recovery of the embedded information is 60%; 2. In case of damage to the image-container by imposing "noise", the threshold of successful recovery is 0, 19%.
The low threshold of successful recovery when the container is damaged by superimposing "noise" is explained by the unsuccessful choice of the sampling scheme of shares for recovery. In general, we can talk about the possibility of applying the proposed method to improve the reliability of information concealment during its transmission or damage to the container.