The paper is devoted to the development of a symmetric message encryption method based on the use of images. The presented method combines the book method, a disposable notebook, and the Diffie-Hellman protocol, which eliminates the disadvantages of book encryption, namely the transmission of special characters and the limitation of the key space. Modification of the Diffie-Hellman protocol for image transmission ensures the creation of the same unique image. Using such an image as a disposable notepad means that the stability will depend on the random number generator, which will be MT19937-64 with an initial startup time of seconds. To confirm the efficiency of the presented method, a software application has been developed that implements image mixing, subsequently forming a unique image for two users, and using it to perform the corresponding encoding using the book method.
The problem of information transmission and its protection
dates back to ancient times, so as transmission methods
have improved and become more popular, so have the
methods of protection [
Such data is usually discussed by people in private. Since it is the population that determines the political course of a state and its sovereignty, protecting private communications should be one of the top priorities of the state. The development of various encryption methods should be an important area of this work.
According to the RAS (Rise Above Research) study,
around 1.13 trillion photos were taken in 2020 alone [
A study (February 2024) by Rise Above Research predicts
that the number of photos taken and stored will increase in
2024 and continue to grow at a linear rate until 2028, with
the vast majority of these photos being taken on
smartphones. This will lead to a 10% increase in the number
of photos taken this year, reaching around 1.8 trillion
photos worldwide in 2024 [
Based on these facts, the paper proposes a cryptographic protection method that combines the book method as an encoding method and the Diffie-Hellman method for image transmission. 2. Analysis and problem statement The use of various methods of cryptographic information protection is an important and urgent task, so when considering programming technologies for secure systems, cryptography is one of the most important areas. Of course, researchers are constantly looking for new ways to protect information and systems from cybercriminals. Hence, various methods emerge as a combination of best practices in terms of cryptographic protection.
For example, a well-known simple but rather reliable
approach to security [
Another well-known digital encryption method that
provides a secure exchange of cryptographic keys between
0000-0003-0892-3494 (S. Buchyk); 0000-0002-1919-9174 (S. Toliupa);
0009-0003-4858-6258 (D. Tsapro); 0009-0008-4962-569X (A. Shabanova);
0000-0001-7102-2176 (O. Buchyk)
© 2024 Copyright for this paper by its authors. Use permitted under
Creative Commons License Attribution 4.0 International (CC BY 4.0).
two parties over a public channel without transmitting their
conversation is the Diffie-Hellman key exchange [
In [
Paper [
In [
The purpose of the study is to combine message transmission and encryption algorithms, to create an application for data transmission using the Diffie-Hellman protocol, using images and the book method.
The object of the study is the process of encrypting and transmitting photos over insecure communication channels.
The subject of the study is the Diffie-Hellman protocol, the book method of encryption, and the complexity of finding the key. 3. Summary of the main material
This method of cryptographic protection is based on the
book method of messaging: when users have the same book
and replace words with a reference to a specific page and
line in it. Of course, it is assumed that the attacker does not
have this book or that it is extremely difficult for him to
guess what kind of book it is. The method is easy to
implement and secure, but its use in real life is difficult.
Cryptanalysts agree that, if used properly, the book’s cipher
is virtually unbreakable, almost as good as a disposable
notebook [
Of course, such a book can be not only a book as an object, but, say, a video file, an audio message, a song, or, as in the case of this work, an image.
That is, you need to choose a common image and use the values of its pixels, which, as you know, can be encoded in different systems: such as HSV, HUE, CMYK, and, probably, the most famous RGB. It is RGB that we will use. So now a small image, such as Fig. 1, which has a size of 284×177, i.e. 50268 pixels, can encode 150804 letters, special characters, or numbers. So, our interlocutor, who has the same photo, just needs to send the pixel coordinates (conventionally x and y) and one of the 3 colors corresponding to our letter, in the presented work the following correspondence of values is performed: 0—Red, 1—Green, 2—Blue.
Sometimes it is necessary to encode a message containing numbers or special characters, so it is very difficult to read the decoded text without spaces. To solve this problem, we used the ASCII table, which allows us to encode any characters present in it.
At the same time, there is a threat of using frequency
analysis. Frequency analysis is the study of the frequency of
letters or groups of letters in an encrypted text. The method
is used to help break substitution ciphers (e.g.,
monoalphabetic substitution cipher, Caesar shift cipher).
Frequency analysis involves counting the occurrence of
each letter in the text and is based on the fact that in any
particular piece of text, certain letters and combinations of
letters occur with different frequencies [
The next problem is sharing photos, so the DiffieHellman transfer protocol was used to solve it. DiffieHellman key exchange is a digital encryption method that securely exchanges cryptographic keys between two parties over a public channel without transmitting their conversation over the Internet. Messages are transmitted using the Diffie-Hellman method according to the following formula, where g and n are primes representing the public keys, and k is the private key. Of course, we cannot substitute the values of the base pixels because their moduli are not large enough and the range includes zero, which will make the key selection very easy, so we need to create a table of primes that we will use to select the initial value with the interlocutor. This will increase the use of any prime numbers, i.e. in our case:
A prime number from the table with the corresponding index equal to the value of the base color in the open image.
A prime number from the table with an index as the sum of two values of other base colors in the open image.
A prime number from the table with the corresponding color index in the closed image. A schematic image is shown in Fig. 1.
The two parties use symmetric cryptography to encrypt and decrypt their messages, so the photos used will act as a public key (for example, Fig. 2) and a private key (Fig. 3 for the first user and Fig. 4 for the second user).
The open and closed images must not be identical. The closed image must have more pixels than the open one, otherwise you reduce the number of coding pixels.
The images should not be monotonous (i.e., consist of only one color, as this will simplify the selection of the private key).
Thus, the algorithm consists of two stages: encrypting the message and forming a shared key with the interlocutor. The encryption will be performed by selecting a random pixel from the generated closed image and converting the character value from the ASCII table into a ciphertext. The ciphertext will consist of five values: 1—the number of the photo, in case you decide to create an array of closed images, 2 and 3—the coordinates of the randomly selected pixel (this pixel will not be used later), 4—its hue, i.e. red, green or blue, and 5—the value required to make the pixel parameter independent of the transmitted character.
The formation of a shared key is implemented using the Diffie-Hellman method and a table with primes, in which each prime is the corresponding index equal to the hue value of a particular pixel.
Let us consider the implementation of the symmetric message encryption method based on the use of images.
To demonstrate how the algorithm works, we have developed an application shown in Fig. 5. The application can mix several images—the Mixer section, encrypt user text with the appropriate number of mixed images—the Coder section, and decode the message that was sent—the Decoder section.
The mixing functions consist of 8 threads that call the exponentiation and mod functions. Since the numbers we are entering are of high power—they will be very large and will not fall within the range of ordinary C++ data types, we split the number into an array, where each index is a bit of the number, so the possible number is increased to 100000 characters instead of 36 for the largest long data type. The corresponding functions for exponentiation and mod were created.
The next problem is the transmission of these numbers, because when taking mod 256, our numbers will end up being different, so an auxiliary image was implemented to store the values that need to be multiplied by 256 and added to the value of the corresponding pixel color in the sent image. This increases the number of maximum values to 65536.
Hence the difference between the first and second blending: the first one uses 2 photos (closed and open), and the second one operates with 4 images, namely:
unchanged.
The image was sent by the interlocutor.
Auxiliary image provided by the interlocutor.
Our closed image.
The result of the first blending: the open image and the first user’s closed image (Figs. 2 and 3, respectively) is shown in Fig. 6.
The result of blending this image with the second user’s closed image is shown in Fig. 7.
The result of blending the open and closed images of the second user, shown in Fig. 2 and Fig. 4, respectively, is shown in Fig. 8. The result of mixing Fig. 8 and Fig. 3. is the image shown in Fig. 9.
As you can see, Figs. 7 and 9 are identical, which proves that the Diffie-Hellman protocol was implemented correctly. Based on this fact, we can use the images for further encoding using the book method. the worst-case scenario where the attacker knows the public keys, the list of primes to be used, and the initial prime—that is, all the data that we will transmit over the unsecured channel. Based on this, we will calculate the speed of finding the encryption key—of course, this will depend on the direction of the attack.
The encoding is implemented as follows: the
function selects four random values and subtracts the
fifth, taken as mod 256, from the sum of the
corresponding pixel and the character value in the ASCII
table. The first random value is the index of the photo,
the next two are random values—x and y (pixel
coordinates), the fourth indicates the corresponding
base color and the fifth is an additional parameter. Since
security is directly proportional to the generation of
random numbers, we chose one of the generators with
high entropy, namely MT19937-64 [
As an example, consider encrypting the following text: “This_text is ex@mp!e?”. The program will split it into characters and encode each of them separately. An example of the finished encoding is shown in Fig. 10, and the decoded text on another device, which was implemented, is shown in Fig. 11.
If the decoded message is as originally set, it means that the message and photos have not been modified during transmission. We also make sure that the values are chosen randomly and do not repeat.
Let’s consider the vulnerability analysis of the symmetric image-based encryption method, presenting the disadvantages and advantages.
The success of an attacker directly depends on the amount of knowledge about the system. Let’s simulate
The first direction is an attack on specific pixels, i.e. those that were used in the transmission of the message. In such an attack, the security of each pixel will directly depend on the Diffie-Hellman protocol. Unfortunately, it can be cracked using the following algorithm for finding the value of a closed pixel (): 1. 2. 3.
Finding by the formula.
Finding by the formula.
Whatever the length of the key used, the number of operations will remain equal to 3, except for the fact that there is a search by degrees. However, this will not be a big problem if the calculations are performed using a program with a given algorithm. The speed of performing fairly simple operations is quite high, so the key will still be obtained in the end.
Of course, the time spent on the selection of the degree will be longer the larger the degree, and, according to this statement, the time for selecting the parameters will be longer, or there is a second solution— increasing the number of unknown operators by using double image mixing. That is, we will blend our image not once before sending it to our interlocutor, but twice (the number of blends can be more). Thus, for one pixel, the attacker will have neither the value of the private key nor the value of the first operation. If it is necessary to find a formula to reveal the desired value, the attacker will face the problem of finding the logarithm in the logarithm, provided that he does not know the intermediate results of the calculations that could make the task easier. Thus, it will be impossible to calculate the secret key. If you wish to increase the cryptographic strength of the encryption algorithm, the mixing procedure can be repeated more than twice, thereby increasing the number of unknowns in the final formula.
The second direction is to create a three-dimensional matrix that will store all possible outcomes of the operation. This table can also take a lot of time to create, which again depends on the size of the selected primes, but this situation is also possible to use.
To prevent the creation of this table, closed photos, along with open ones, should be changed regularly. The photo expiration time depends on the values of, and, i.e. on the values of the primes we use to mix the photos.
The blending time is a clear disadvantage of the system, as the program performs three operations for each pixel of the photo, so it takes a lot of time per pixel with small numbers. An example is shown in Table 1 and the graph in Fig. 12.
Since the program operates with very large numbers, of course, its speed will increase. To solve this problem, we used multithreading. Currently, the program uses only 8 threads, but if the number of threads is increased, the execution speed will increase accordingly.
The second disadvantage is the vulnerability of the
Diffie-Hellman method itself, as it is susceptible to
manin-the-middle attacks [
The third disadvantage is the use of pseudo-random numbers since it is impossible to achieve perfect entropy without using quantum computers, but we used one of the high entropy number generators, namely MT19937-64, and, according to the initial value, we chose a garter during the time, since the probability of selecting a specific second is very low.
The advantages of this method include: 1. 2. 3. 4. 5. 6.
creation of a common image—encoding large text is very fast.
It is security against linear and differential cryptanalysis since the book cipher is resistant to them.
The possibility of using spaces and special characters is implemented, which is also a disadvantage of the book method.
Difficulty in selecting a private key.
The use of shorthand in transmission is because, for an ordinary user, photos will not carry any information.
The ability to create a key anywhere, as you just need to create an image.
This paper presents a symmetric encryption method that uses the Diffie-Hellman protocol and the book method. The Diffie-Hellman protocol is used to transfer keys between users. The paper proves its effectiveness for this task and the possibility of its strengthening by repeated mixing. The book method is used to encode and decode the messages of the interlocutors using the generated joint image.
Also, in this paper, for the sake of demonstration, a software application was developed that implements the symmetric image-based message encryption method and demonstrates its effectiveness.
The disadvantages of the system, such as the speed of image mixing and the vulnerability of the DiffieHellman protocol, are listed, followed by the provision of solutions. Examples of possible attacks on this method are given and defense methods against them are proposed.
The advantages of this method are listed, which are associated with an increase in the level of security, encoding speed, and creation of a private and public key anywhere.
It should be noted that this method is not a panacea and has certain limitations in its application. It should also be noted that it can be used for malicious activities, such as crypto crackers, which is a clear disadvantage of any encryption method.
This research can also be used to implement
information hiding in images using the solutions
proposed by the authors in [