Journal of Global Research in Computer Sciences
MenuISSN: 2229-371X
ISSN: 2229-371X
?natoliy ?ovalchuk*1, Yuriy Borzov2, Dmytro Peleshko3, ?gor ?alets4, Ivan Izonin5
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| Corresponding Author: ?natoliy ?ovalchuk, E-mail: akm805@ukr.net |
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The authors in the article propose two modifications of the method of image encryption based on the use of the ideas underlying the algorithm RSA, in particular the combination of the properties of the RSA algorithm and bitwise additively-difference operations. The advantage of these methods is to maintain resistance to decrypt, which is provided by the RSA algorithm and eliminating the use of visual methods of image processing for decryption. The methods shows best results in the case that makes it easy to highlight contours of images .
Keywords |
| algorithms for encryption-decryption of image, modifications of the RSA algorithm, El-Gamal cryptosystem, additive-difference operations. |
INTRODUCTION |
| Image is one of the most commonly used types of information in today's information society. The urgent task is to protect the image from unauthorized access and use. The problem of unauthorized use of images is solved by provisions of copyright law to the methods of cryptography and steganography, printing grids, etc. The main basis for the organization of image protection is supported by the assumption: the image is a stochastic signal [4, 6, 8, 9, 12-16, 18, 20, 21]. This causes the transfer of classical methods of signal encryption to the case of images. However, a specific image signal, in addition to the standard informative (informative data), is still visual informative. And the latter brings to the protection of new challenges These very developed modern informative methods of image processing allow for the organization of unauthorized access [2]. In fact, a hacker attack on the encrypted image is possible in two cases: a traditional breaking of encryption [2] or through methods of visual image processing (filtration techniques, edge detection, etc.). Using those encryption methods there is another task - the total noisiness of encrypted image. This is in order to prevent the use of visual methods of image processing. Data protection problems are described in the works of K. Shannon, M. Diffie and M. Hellman. Having studied their works, it can be stated that today the most widespread data coding method is the RSA method [1], which main advantage is high cryptographic firmness. However, the method implementation for image coding is not optimum, as far as from the coded image it is possible to obtain informative data with the use of certain algorithms of image filtration. As a result, a new research direction in the sphere of image protection in communication systems emerged. The method is based on the development of symmetric methods [3, 7, 10, 17, 19, 21] of cryptographic analysis and representation in the works of Kwok-Wo Wong, Hai Yu, Zhi-Liang Zhu. The main disadvantage of methods of this direction is informative losses, which are critical for the problems of intellectual data analysis. |
PURPOSE |
| The urgent task is to develop a modification of method RSA regarding images to: |
| - Save resistance to decipherment |
| - Ensure total noisiness, in order to prevent the use of visual methods of image processing. One of the best solutions of this problem is to combine the properties of RSA algorithm with the bit-and additivedifference operations in software implementation. |
CHARACTERISTICS OF IMAGE |
| A pattern P of width l and height h is given. It can be regarded as a matrix of pixels |
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| where dtpij – is the pixel with coordinates i and j, n and m – a number of dots by width l and height. In general, n and m are dependent on l and h, and therefore more correct to write: |
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| The Matrix (1) is put in to compliance matrix pixel intensities |
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| For gradation of brightness a byte is usually given, with 0 - black and 255 - white (maximum intensity). |
| An important characteristic of image is the availability of contours. The task of edge detection requires certain operations of adjacent elements that are sensitive to changes in the area and reduce constant levels of brightness, i.e. contours: these are the areas of image becoming lighter, while others remain dark [2]. Mathematically, perfect contour is a gap of spatial features of brightness levels in the image plane. Therefore, the selection of contour means a search of the most drastic changes, i.e. the maximum of modulus of gradient vector [2]. This is one of reasons why the contours of image remain when encryption RSA, because encryption is based on exponentiation modulo some integer. In this case, exponentiation brightness value gives an even greater gap on the contour and adjacent pixels. |
USING OF BIT OPERATIONS DESCRIPTIONS OF THE ALGORITHM RSA MODIFICATION |
ENCRYPTION AND DECRYPTION OF ONE ROW OF IMAGE. |
| Suppose P and Q are arbitrary numbers, and N = P Q. Encryption is performed item by item using further transformation matrix elements of C image: |
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| 4. ÃÂ is constructed by subtracting from the obtained number of pixel intensity values (A– 3). |
| 5. Encrypted intensity value i pixel i = 1, 2, … , m, m– a number of elements in a row selected by á ÃÂe(modN) Decoding is performed in the reverse order to the encryption after the number of ád (ÃÂe)d(modN), performing the opposite operations to the contents of paragraphs 4), 3), 2), 1). The results are shown in Figures 1 – 3 |
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ENCRYPTION OF TWO ROWS OF THE MATRIX |
| Encryption is performed using elements of two rows according to the algorithm described above to encrypt the elements of one row intensities, except item 5, where each row of the selected two lines is encrypted independently with its own algorithm item 5 modified for it. Item 5 is: 5.1.Forthe first row of encrypted value of intensity i pixel i = 1, 2, …, m, m – a number of elements in arrow, selected number is á ÃÂe(modN). 5.2. For the second row of encrypted value of intensity i pixel i = 1, 2, …, m, m a number of elements in arrow, selected number is á ÃÂd(mod N). Decryption is in the reverse order with the items 5.1and 5.2. The results are shown in Figures 4- 6. |
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| From a comparison of Fig. 2 and Fig. 5 is clear that the encryption of one row of the matrix (3) is not much different from the encryption of two rows of matrix. The contours of both encrypted images are missing. Primary and decrypted images are slightly different in brightness levels. |
USING OF BIT OPERATIONS DESCRIPTIONS OF THE ALGORITHM RSA MODIFICATION |
ENCRYPTION AND DECRYPTION OF ONE ROW OF IMAGE |
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| ENCRYPTION AND DECRYPTION OF ONE ROW OF MATRIX WITH ADDITIONAL NOISE LEVEL. |
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| A comparison of Fig. 7.2 and Fig.8.2 shows that the encryption with additional noise is different from the encryption with out it. The contours of both encrypted images are missing. Primary and decrypted images are slightly different in brightness level. Functions of additional noise f(i , j) can be arbitrary and full functions, and, in addition to the noise generated by the RSA algorithm, increase the cryptographic security of the se modifications. |
| APPLYING OF EL-GAMAL CRYPTOSYSTEM. DESCRIPTION OF THE ALGORITHM RSA MODIFICATIONS |
| ENCRYPTION AND DECRYPTION OF ONE ROW OF IMAGE. |
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| ENCRYPTION AND DECRYPTION OF TWO ROWS OF MATRIX WITH ADDITIONAL NOISE IMAGES. |
| Suppose P, Q – are arbitrary integers and N = P Q, (N) = (P- 1)(Q- 1). |
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| Note that the encryption of noise structure with additional properties is visually different, depending on the choice of structure and the order of selected noise pixels of input image. It can be used in a topological modifications encryption-decryption algorithm. |
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CONCLUSIONS |
| 1. Proposed modifications are intended to encrypt the grayscale images and are based on the use of basic algorithm RSA. |
| 2. Suggested modifications can be used for any type of image, but the greatest results are obtained in case of images which can clearly detect contours. |
| 3. Both types of modifications for sure can be applied for color images. |
| However, regardless of the type of image, proportionally to the dimension of input image, the size of the encrypted image can grow. |
| 4. Resistance to unauthorized decryption of proposed modification provides algorithm RSA. |
| `5. In case of El-Gamal algorithm the stability of modified cryptographic algorithm is determined by resistance of two used algorithms - El-Gamal and RSA, and while ensuring the quality of image, it does not require much processing power. |
References |
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