New Cryptosystem Using Two Improved Vigenere Laps Separated by a Genetic Operator

This document traces the development of a new cryptosystem using two circuits ensured by a deep Vigenere classical technique improvement, separated by a genetic operator. This new technique employs several dynamic substitutions matrices attached to chaotic replacement functions; whose construction will be detailed. Firstly, we will be start by modifying the seed pixels by an initial value calculated from the original image, and will be infected through the chaotic map used to overcome the uniform image problem, followed by the improvements Vigenere injection technology. The output vector will be subdivided into sub blocks for future application of deeply improved genetic mutations to better adapt to color and medicals image encryption. The second round will increase the compdlexity of the attack and improve the installed systems. Simulations performed on a large number of images of different sizes and formats ensure that our approach is not exposed to known attacks. Article Highlights This new algorithm offers two tricks ensured by a deep improvement of Vigenere. We mention the most important changes made.  First Vigenere’s rotation  Genetic mutation applied  Second Vigenere’s lap


I. Introduction
The rapid development of chaos theory in mathematics provides researchers with opportunities to further improve some classic encryption systems. In front of this great security focus, many techniques for color image encryption have flooded the digital world, mostly exploiting number theory and chaos Others are attempting to update their policies by improving some classical techniques, such as Hill , Cesar, Vignere

1) Vigenere's Classical technique
This technology is based on static matrix defined by the following algorithm. Despite the knowledge of the substitution matrix, this method has been able to withstand more than three centuries.
Let plain text, cypher text; Encryption key, Vigenere matrix and length of clear text. So Even though Vigenere's matrix was known, the encryption was able to withstand several centuries. But, Babagh's cryptanalysis is not efficient in not knowing the size of the encryption key. Several attempts to improve Vigenere's technique have invaded the digital world we quote . In this work, the new structure of the substitution matrix and its attached replacement function will be described in detail.

2) Our contribution
This work puts into practice the implementation of a deeply modified genetic operator in a color image encryption system. This operator will be surrounded by two improved Vigenere circuits

II. THE PROPOSED METHOD
Based on chaos , this new technology which acts at the pixel level by two Vigenere turns provided by a dynamic substitution's matrices and replacement functions These two rounds will be separated by a deeply improved genetic operator for future use in color image encryption. The following steps describe this algorithm Chaotic permutation application At the end of this work, the follow-up operations of each encryption round will be described in detail to show the development of the system. and detailed analysis of the performance of our methodology will be discussed and compared with other referencing systems.
Step 1: Chaotic Sequences Development All the encryption parameters required to successfully run our system come from the two most commonly used chaotic maps in the field of cryptography. This choice is due to the simplicity of its development and its high sensitivity to the initial parameters.

1) The Logistics Map
The logistic map is a recurrent sequence described by a simple polynomial of second degree defined by the following equation

2) HENON'S Map
Henon's chaotic two-dimensional map was first discovered in 1978. It is described by equation below We can convert the two-dimensional map expression to a onedimensional map that is easy to implement in the encryption system. This formula is described by next equation

3) Chaotic used Vector design
Our work requires the construction of three chaotic vectors , and , with a coefficient of , and the binary vector will be regarded as the control vector. This construct is seen by the following algorithm The binary vector is considered as a control vector the complexity of our algorithm.

Axe 2: plain Image preparation
After the three color channels extraction and their conversion into size vectors each, a concatenation is established to generate a vector of size . This operation is described by the following algorithm This step slightly reduces the high correlation between the pixels.

1) Initialization Value Design
First, the initialization value must be recalculated to change the value of the starting pixel. Ultimately, the value is provided by the next algorithm The presence of the vector is to overcome the problem of the uniform image.
Step3: Vigenere upgrade In the first stage, Vigenere's technology was greatly modified by integrating the new substitution matrix provided by the new powerful replacement function.

1) Vigenere's Advanced Methods
This classical technique requires the generation of a substitution matrix and a replacement function

a) Classic Vigenere function expression
These two matrices will be used together in the encryption process and will be completely under vector control We remember to pass Vigenere's classic replacement function through the following formula key duplicated to the size of the text to be encrypted.

b) New Vigenere function expression
The following equation illustrates the effective expression of the image of the pixel through the new Hill technology.

c) First-round spread function Expression
The first round will be equipped with a powerful diffusion function to connect encrypted pixels with subsequent transparent pixels to increase the impact of the avalanche effect and protect the system from any differential attacks. The expression of this new diffusion function is given by the formula below

2) The first-round analysis
This first round is defined by the following algorithm, The figure below shows the first round For a better follow-up of our algorithm, several reference images were tested by this first round, we quote At the end of the first round, the output vector (Y) will be treated as a clear image and subdivided into three sub-blocks of equal size for future submission to genetic mutation.

3) Genetic mutation
Gene mutation is the exchange of sub-blocks between three blocks of the same size. This exchange is provided by two chaos constants and The first indicates the starting position of the sub-block to be swapped, and the second indicates the size of the sub-block. In our method, these two constants are defined as The mutation process between three blocks of size each is illustrated by the following figure This mutation process follows the following formula

1) Second round analysis
For a better follow-up of our algorithm, several reference images were tested by this first round, we quote The generated vector will be submitted to a second round of Vigenere provided by two other substitution matrices.

1) Second Vigenere round
At the end of the first round, the new initialization value will be calculated according to the following algorithm In the second round, by simply replacing the position of the replacement matrix, the output vector will be treated as a new image to be encrypted by the same method as the first round.
a) Second round analysis The second round can also be ensured by using a different same matrix in the first round.
The same mold will be used in the second round, but in a different way a) Second-round spread function Expression The second round will be equipped with the diffusion ensured by the replacement matrix generated. The expression of this function is defined by the following notation

a) The Second-round analysis This second round is defined by the following algorithm
The figure below shows the first round

2) Third round analysis
For a better follow-up of our algorithm, several reference images were tested by this first round, we quote The output vector will be subjected to permutation (PH) to possibly suppress any correlation.
Step 5: Decryption of encrypted images In the literature, the classic Vigenere method uses the same matrix in both processes. Our contribution in this work is that the matrix used in encryption is different from the matrix used in decryption. Therefore, the calculation of the decryption matrix is necessary.

2) Decryption matrix structure
Each row of the encrypted S-box is a permutation in , so the decryption matrix will consist of reverse permutations. For this reason, two decrypted generations are given by the following algorithm

1) Decryption function
By following the same logic of Vigenere's traditional technique, we obtain

In the first round
In the second round

2) Decrypt the encrypted image
Our algorithm is a symmetric encryption system, so the same key will be used in the decryption process. In addition, installing the broadcast function requires us to start the decryption process from the last pixel to the first pixel, and recalculate the initialization value to get the exact value of the first pixel. In addition, decryption uses the countdown function of encryption.

a) Reverse permutation
The inverse permutation of is given by the following algorithm After vectorization of the image encrypted in vector an intervention of the permutation to recover the vector This operation is determined by the following algorithm

b) The reciprocal of the Second lap function
A recalculation of the initialization value will make it possible to retrieve the exact value of pixel

c) The reciprocal of the First lap function
A recalculation of the initialization value will make it possible to retrieve the exact value of pixel

d) The reverse mutation
In general, mutation is an involutive operation, therefore we have

III. deep simulations
We randomly selected 150 images from a chaotic vector that contained a database of thousands of color images in different sizes and formats. All these images were tested by our system. all experiments are performed under the Matlab software running under Windows 7, on a basic i7 personal computer, , and we found the following results.

1) Key-space analysis
The chaotic sequence used in our method ensures strong sensitivity to initial conditions and can protect it from any brutal attacks. The secret key to our system is If we use single-precision real numbers to operate, the total size of the key will greatly exceed , which is enough to avoid any brutal attacks.

2) Secret key's sensitivity Analysis
Our encryption key has a high sensitivity, which means that a small degradation of a single parameter used will automatically cause a large difference from the original image. The image below illustrates this confirmation

Figure6: Encryption key sensitivity
This ensures that in the absence of the real encryption key, the original image cannot be restored.

1) Statistics Attack Security a) Entropy Analysis
The entropy of an image of size is given by the equation below is the probability of occurrence of level in the original image.
The entropy values on the tested by our method are represented graphically by the following figure  These values are largely sufficient to affirm that our crypto system is protected from known differential attacks The study of the revealed the following diagram

fIgure13: UACI of 150 images of the varying sizes
All detected values are inside the confidence interval .
These values are largely sufficient to affirm that our crypto system is protected from known differential attacks. d) Avalanche effect Our algorithm uses a strong link between encrypted pixels and subsequent clear pixels in the strategy. This leads to a gradual change in the value, which becomes more and more important as the data spreads through the structure of the algorithm. The avalanche effect is the number of bits that have been changed if a single bit of the original image is changed. The mathematical expression of this avalanche effect is given by Our encryption keys are large, which can ensure that the new system is protected from brute force attacks. At the same time, the randomness of the operators described in the system makes it difficult to unlock any encrypted images, which increases the difficulty of statistical attacks. In addition, due to the high sensitivity to the initial parameters of our three chaotic cards, and the broadcast installed in each tower confirmed the robustness of our encryption system.

V. Conclusion
Due to their high sensitivity to initial conditions, our algorithm can prevent sudden attacks. This new technology is based on two deeply improved Vigenere rounds, using dynamic substitution matrices to attach to highly developed substitution functions. These two techniques are separated by genetic mutations suitable for color image encryption. The two calculated initialization values increase the complexity of the system. The monitoring of encryption in three rounds showed robustness and improved results from round to round. The global analysis of the system, ensures that our algrithm can cope with any known attack.

Conflict of Interest
All the authors of this article, there is no conflict of interest and add that no organization or private or public laboratory finances its research, moreover the research carried out no experiment on animals or human beings.

Informed consent
We all have the approval to write and write this article giving a new method of encryption of color images.

Ethical approval
We have respected the ethics of the journal