Information Protection Service using Topological Image Coverage

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Procedia Computer Science 160 (2019) 503–508

The International Workshop on Digitalization and Servitization within Factory-Free Economy (D&SwFFE 2019) The International Workshop on Digitalization Servitization within Factory-Free Economy November 4-7, 2019,and Coimbra, Portugal (D&SwFFE 2019) November 4-7, 2019, Coimbra, Portugal

Information Protection Service using Topological Image Coverage Information Protection Service using ImageKustra Coverage a a Anatoliy Kovalchuk , Ivan Izonina*, MihalTopological Gregush ml.b, Natalya Anatoliy Kovalchuk , Ivan Izonin *, Mihal Gregush ml. , Natalya Kustra

a Technologies, Lviv Polytechnic a b a Department of Publishing Information National University, S. Bandera, 12, Lviv, 79013, Ukraine b Faculty of management, Comenius University in Bratislava, Odbojárov 10, Bratislava, Slovak Republic a Department of Publishing Information Technologies, Lviv Polytechnic National University, S. Bandera, 12, Lviv, 79013, Ukraine b Faculty of management, Comenius University in Bratislava, Odbojárov 10, Bratislava, Slovak Republic a

Abstract

Information protection services based on the use of elements of the RSA algorithm are quite reliable because the cryptostability Abstract of this method is high (RSA keys from 2048 bits and more). However, in terms of image encryption, in some cases, this Information protection services based use of image. elements of imposes the RSA aalgorithm quite reliable because algorithm leaves outlines of objects in on an the encrypted This number ofareadditional limitations onthe the cryptostability application of thisthis algorithm. partially saving in encryption RSA can be by of splitting initial image into parts so this that of methodAvoiding is high (RSA keys fromcontours 2048 bits and more).using However, in terms imagethe encryption, in some cases, the image leaves coatingoutlines is topologically finite, thatimage. is, compact. The paper proposes a methodlimitations of encryption-decryption using algorithm of objectslocally in an encrypted This imposes a number of additional on the application of this algorithm. partiallyand saving in encryption using RSA be by splitting initial image parts so elements of theAvoiding RSA algorithm the contours topological image coverage. Suchcan a combination willtheprovide both ainto avoiding of that the aforementioned disadvantage and an additional cryptostability. The simulation of the of method was done on grayscale the image coating is topologically locally finite,increase that is, in compact. The paper proposes a method encryption-decryption using and color of images usingalgorithm two developed absence of contours objects of input images in encrypted images of elements the RSA and thealgorithms. topologicalThe image coverage. Such aofcombination will provide both a avoiding of the aforementioned disadvantageestablished. and an additional increasesolution in cryptostability. The of image, the method wasgreatest done on grayscale both types is experimentally The proposed can be used forsimulation any type of but the benefits are achieved using images fluctuation intensity function. and colorwhen images using two with developed algorithms. The absence of contours of objects of input images in encrypted images of both types is experimentally established. The proposed solution can be used for any type of image, but the greatest benefits are achieved when using images with fluctuation intensity function. © 2019 The Authors. Published by Elsevier B.V. © 2019 The Authors. by Elsevier This is an open accessPublished article under the CC B.V. BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) © 2019 The under Authors. Published by Elsevier B.V. Program Chairs. Peer-review responsibility ofthe theConference Conference Peer-review under responsibility of Program Chairs. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Keywords: encryption, decryption, image, stability, the topological Peer-review under responsibility of thecontour, Conference Program Chairs.coverage ; Keywords: encryption, decryption, image, contour, stability, the topological coverage ;

* Corresponding author. Tel.: +38098 888 96 87. E-mail address: [email protected] * Corresponding author. Tel.: +38098 888 96 87. 1877-0509 © 2019 The Authors. Published by Elsevier B.V. E-mail address: [email protected] This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review the Conference Program 1877-0509 ©under 2019responsibility The Authors. of Published by Elsevier B.V. Chairs. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the Conference Program Chairs. 1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the Conference Program Chairs. 10.1016/j.procs.2019.11.057

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Anatoliy Kovalchuk et al. / Procedia Computer Science 160 (2019) 503–508 Anatoliy Kovalchuk et. al. / Procedia Computer Science 00 (2018) 000–000

1. Introduction The problem of protecting various kinds of information by transforming it in such a way as to eliminate the possibility of unauthorized access is an important problem of the present [1, 2]. Information security systems based on a wide range of algorithms are used in a variety of domains [3-8]. The security of modern ICTs is based on the stability of cryptographic transformations that they use for cryptographic processing of information. Cryptographic stability is based on the complexity of solving certain mathematical operations, which is characterized by high complexity of the solution on modern computers [9]. However, besides stability, an important problem is the development of methods and algorithms that can encrypt images with the fluctuation intensity function [10]. Such images are characterized by large areas of contours in images that remain after encoding on the encrypted sample [11]. This can lead to unauthorized access and encrypted information, using a large arsenal of existing image processing technics [12-13]. In [14-15] developed methods of encryption based on ateb-functions. However, these methods are more suitable for encrypting text images. In [16] a scheme of stenographic image protection using neural-like structures of the Successive Geometric Transformations Model is proposed. The peculiarities of this method on the basis of machine learning are its speed and simple hardware implementation [17-18]. However, this method requires qualitative samples for the implementation of the training procedure. The RSA [19] algorithm and its modifications are described in [20-21]. Services based on this public key algorithm are widely used for secure data transmission. Due to the low speed of this algorithm, it is most often used to transfer encrypted general keys to encrypt information with a symmetric key, which in turn can perform massive encryption-decryption operations at a higher speed [22]. Despite the high efficiency of their use for both grayscale and for color images, these methods do not always provide an effective result in the processing of images with pronounced contours. After processing by such methods, the contours of objects of attention are visible on the encrypted sample. This does not satisfy one of the encryption conditions. 2. Problem statement Encryption-decryption services based on the use of RSA algorithm are fairly reliable because the cryptostability of this method is high (RSA keys for 2048 bits and more). It is based on the complexity of decomposition into largescale factors, namely, on the exceptional complexity of determining a secret key based on open-ended operations [22]. To do this, it is necessary to solve the problem of the existence of divisors of an integer. In addition, this algorithm is asymmetric. It provides the ability to share information over unprotected communication channels to multiple users. Among the disadvantages of this method should be highlighted the low speed of its work. In addition, when it comes to image encryption, in some cases this algorithm leaves outlines of objects in an encrypted image. This imposes a number of additional limitations on the application of this algorithm. Avoiding partially saving contours during encryption using RSA can be by splitting the initial image into parts so that the image coating is topologically locally finite, that is, compact. Because of that, this paper proposes a method of encryption-decryption using elements of the RSA algorithm and the topological image coverage. Such a combination will provide both an avoidance of the aforementioned disadvantage and an additional increase in cryptostability. The security of the developed method will be based on the security of the RSA algorithm which is based on the difficulty of solving the problem of decomposing numbers into simple numbers. 3. Information protection scheme based on the topological image coverage We will form the topological cover of the image. We will suppose that the image has the form of a rectangular area [0, a] x [0, b], where, a - the number of pixels of the horizontal image, b - the number of pixels of the vertical image in the Cartesian coordinate system. According to the well-known Poincare-Volterra theorem, the assumption about the view of the image is not significant. To form the partition of the segment [0, a] we will split it into  parts - subsets of unspecified length [20-21].



Anatoliy Kovalchuk et al. / Procedia Computer Science 160 (2019) 503–508 Anatoliy Kovalchuk et. al. / Procedia Computer Science 00 (2018) 000–000

 I

0, a

[0, a1 )  [a1 , a2 )  [a2 , a3 ) ...  [a 1 , a]

I U s1 I s , s1 , s2 : I s1  I s2   0, a 

505 3

(1) (2)

Here I s [as 1 , as ), s 1,   1, a0 0, a a, I [a 1 , a] in (2). Similarly, the segment [0, b] will be split into  parts - subsets of unspecified length:

 I

0, b

[0, b1 )  [b1 , b2 )  [b2 , b3 ) ...  [b 1 , b]

I Ut1 It , t1 , t2 : It1  It2   0, b 

(3) (4)

Here It [bt 1 , bt ), t 1,   1, b0 0, b b, I  [b 1 , b] in (4). Conducting parallel lines to the coordinate axes the straight lines at the points of partitioning the segments [0, a] and [0, b], we will obtain the coverage of the image area by a system of rectangular regions of the pixels such that (Fig. 1):   s ,t

 pxl

i, j

: s1  i  s2 , t1  j  t2 , 

Fig. 1. Topological image coverage

Each covered element is encrypted and decrypted using scheme from [20-21]. 3.1. Encryption and decryption of eight rows in the image matrix. If P and Q, R and T ,V and U , F and G are the pairs of arbitrary primes, then numbers are as follows:

(5)

Anatoliy Kovalchuk et al. / Procedia Computer Science 160 (2019) 503–508 Anatoliy Kovalchuk et. al. / Procedia Computer Science 00 (2018) 000–000

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N PQ,   N    P  1 Q  1 , e1d1  1 mod   N  

(6)

M RT ,   M   R  1T  1 , e2 d 2  1 mod   M  

(7)

L VU ,   L   V  1U  1 , e3 d3  1 mod   L  

(8)

K FG,   K    F  1 G  1 , e4 d 4  1 mod   K  

(9)

Encryption occurs using elements of eight lines in the following way: from each successive pair of lines of the image matrix C, two corresponding color intensity values are selected and the following two values are calculated:

u  x e  mod n  ,

(10)

 v x e  mod n   y d  mod n  ,

where the numbers e e1 , e2 , e3 , e4 ; d d1 , d2 , d3 , d4 ; n N , M , L, K ; are obtained from the relations (6) - (9) respectively.

a

b

c

Fig. 2. Encryption and decryption of eight rows in the image matrix: (a) initial image; (b) encrypted image; (c) decrypted image

The values u, v , are obtained from equation (10) and are written in two consecutive lines of the encrypted image, each value in one line. Decryption is done in reverse order by the equation:

 v  u   mod n  , x  u d  mod n  y

e

(11)



Anatoliy Kovalchuk et al. / Procedia Computer Science 160 (2019) 503–508 Anatoliy Kovalchuk et. al. / Procedia Computer Science 00 (2018) 000–000

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The results of such simulations are shown in Fig. 2. 3.2. Encryption and decryption of four rows in the image matrix In each four rows in the image matrix C, two consecutive color intensity values are selected for each row x and y. As in previously case, values u, v are calculates using (12):

u  x e  mod n  ,

(12)

 v x e  mod n   y d  mod n  ,

where the numbers e e1 , e2 , e3 , e4 ; d d1 , d2 , d3 , d4 ; n N , M , L, K ; , are obtained from the relations (6) - (9) respectively. The values u, v are two consecutive values of the encrypted image, both values in one row. Decryption is done in reverse order by the equations:

 v  u   mod n  , x  u d  mod n  y

e

(13)

The results are shown in Fig. 3.

a

b

c

Fig. 3. Encryption and decryption of four rows in the image matrix: (a) initial image; (b) encrypted image; (c) decrypted image

The comparison of Fig. 2b and Fig. 3b shows that the encryption of the matrix of the image by different algorithms are different. The common feature is that there are no contours in all encrypted images. In addition, the input image (Fig. 2a and Fig. 3a) and decrypted (Fig. 2c and Fig. 3c) are no different. The specified algorithms can be used to encrypt and transfer graphic images. The proposed modifications can be used for any type of image, but the greatest benefits are achieved when using images with fluctuation intensity function [23].

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Anatoliy Kovalchuk et al. / Procedia Computer Science 160 (2019) 503–508 Anatoliy Kovalchuk et. al. / Procedia Computer Science 00 (2018) 000–000

As shown above, algorithmic realizations of the developed method can be used both for color images and for grayscale ones. However, regardless of the image type, in proportion to the size of the input image, the encryption time and the size of the encrypted image may increasing. Further research will be conducted in the direction of estimating the working time of the described method for encrypting various images. In addition, it will be necessary to conduct a series of studies to assess the cryptostability of the developed method Conclusion An encryption-decryption method was developed using elements of the RSA algorithm and the topological image coverage. Such a combination provides additional enhancement of cryptographic stability and avoiding the boundaries of objects in an encrypted image. The algorithmic realizations of the developed method are given. Model experiments on grayscale and color images were carried out. 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