{"id":20901,"date":"2018-06-25T10:52:47","date_gmt":"2018-06-25T10:52:47","guid":{"rendered":"http:\/\/biomedpharmajournal.org\/?p=20901"},"modified":"2020-04-23T07:43:50","modified_gmt":"2020-04-23T07:43:50","slug":"3d-lorenz-map-governs-dna-rule-in-encrypting-dicom-images","status":"publish","type":"post","link":"https:\/\/biomedpharmajournal.org\/staging\/vol11no2\/3d-lorenz-map-governs-dna-rule-in-encrypting-dicom-images\/","title":{"rendered":"3D Lorenz map Governs DNA Rule in Encrypting DICOM Images"},"content":{"rendered":"

Introduction<\/strong><\/p>\n

With the fast advancement in technology and its usage in the field of high speed networks, the security prospective the encryption is essential to keep the health information safe. When transmitted through public channel, this sensitive medical records needs to be secured to prevent damage from attackers. Image encryption plays a key role in protecting those images and hence provides information security in the field of medical imaging. Kanso et al<\/em>.,1<\/sup> proposed an algorithm scheme based on traditional encryption scheme with increase in algorithm rounds to encrypt the digital image but these schemes are not appropriate for encrypting the DICOM images owed to their characteristics like, the size of the data is huge, correlation between the pixels is much stronger and redundancy of the data is high. To provide more uncorrelated pixels on encrypted image chaotic map is used for efficient encryption. The main aim of migrating towards the chaos system is, due to its high ergodicity , chaotic system is completely deterministic, its initial seeds are extremely sensitive hence small changes in initial seeds will forever alter the future of chaos system and so on, therefore it has been suggested \u00a0for encrypting the medical images as considered in.<\/strong>2-5<\/sup> \u00a0Because of this characteristics, analysing and predicting the chaos is difficult. Ravichandran et al<\/em>.,6 <\/sup>discussed that recently DNA computing plays a major role in the domain of cryptography for encrypting the digital images and more random keys are generated using\u00a0 multiple chaotic maps . \u00a0Li et al<\/em>.,7<\/sup> developed an algorithm that uses DNA based computation, it\u2019s\u00a0 advantage are massive parallelism, power consumption is extremely low, \u00a0capacity for storing the data is large and offers unbreakable cryptosystem. <\/strong>Niyat8\u00a0<\/sup>and kalpana9<\/sup> proposed a scheme with basic idea of encryption based on DNA rule set. In the first stage is to encode the pixels of plain image into DNA sequence. Second stage is to encode using DNA rules like addition, subtraction or XOR operations to form the pixels of encrypted image.<\/p>\n

Wang et al<\/em>.,10 <\/sup>and Enayatifar et al.<\/em>,11<\/sup> discussed about DNA encoding rule with algebraic operations \u00a0like addition operation for encrypting images. Liu et al.<\/em>,12\u00a0<\/sup>proposed an algorithm to yield better entropy for the colour images. Fan et al.<\/em>,13\u00a0<\/sup>uses bit- level permutation and diffusion to boost the protection of the images while ensuring integrity. To ensure the robustness of algorithm, the ideal value of NPCR and UACI is discussed in14,15 <\/sup>Jangid et al.<\/em>,16<\/sup> algorithm gives the cryptographic approach using DNA rule set \u00a0between plain and cipher output. To highly increase the security of encryption and to minimise BER of data an algorithm is proposed by Dang et al.,<\/em>17<\/sup><\/p>\n

The proposed algorithm has the advantage of achieving good Quality metrics compared with available literature and also the algorithm results shows that the projected algorithm is proficient of resisting a variety of known attacks therefore, appropriate for enhancing security. The content of this paper is discussed as follows; in Section II the related work is discussed. \u00a0Section III gives the design information of the proposed image encryption algorithm. In Section IV, simulation results are illustrated and in Section V, security features of the algorithm is analyzed. Finally, Section VI is ended with the conclusion part.<\/p>\n

Related Work<\/strong><\/p>\n

Lorenz Chaotic System<\/strong><\/p>\n

3D \u2013 Lorenz map equations is as follows,<\/p>\n

\"Equations<\/p>\n

In equations (1),(2) and (3): \u03b1 , \u03b2 and \u00b5 are the control parameters \u00a0whereas \u00a0x1, y1 and z1 are the initial parameters. \u03b1, \u03b2 and \u00b5 equals to 10, 28 and 8 \/3 respectively and initial values are equal to 1, then 3D Lorenz map is in the chaotic state as in Fig 1a, hence it produces three different chaotic sequences.<\/p>\n\n\n\n
\"Figure<\/td>\nFigure 1a: 3D-Lorenz chaotic map.<\/strong><\/p>\n

 <\/p>\n

Click here to View figure<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Dna Encoding<\/strong><\/p>\n

DNA encoding is the process of encoding the binary pixel values into sequences. It has four nucleic acid bases such as Adenine (\u201cA\u201d), Cytosine (\u201cC\u201d), Guanine (\u201cG\u201d) and Thymine (\u201cT\u201d). Here, \u201cA\u201d is complement to \u00a0\u201cT\u201d and \u201cG\u201d is complement to \u201cC\u201d because in 21 <\/sup>binary combination, \u00a0\u201c0\u201d and \u201c1\u201d are complement to each other and in 22 <\/sup>binary combinations \u201c00\u201d and \u201c11\u201d are complement to each other, \u201c01\u201d and \u201c10\u201d are also complement to each other. In general rule, \u201cA\u201d corresponds to \u201c00\u201d, \u201cC\u201d corresponds to \u201c01\u201d, \u201cG\u201d corresponds to \u201c10\u201d and \u201cT\u201d corresponds to \u201c11\u201d then the coding schemes can be of 24 kinds, still only 8 satisfies the complementary\u00a0 rule as shown in table.1.10<\/sup> For easy understanding an example is considered, if pixel value is \u201c255\u201d its binary representation is\u201d 11100001\u201d then using general rule this binary value is encoded as \u201cTGAC\u201d each alphabets representing 2-bit respectivel.<\/p>\n

Table 1: 8- Sets of Encoding Rules for DNA<\/strong><\/p>\n\n\n\n\n\n
<\/td>\nRule 1<\/strong><\/td>\nRule 2<\/strong><\/td>\nRule 3<\/strong><\/td>\nRule 4<\/strong><\/td>\nRule 5<\/strong><\/td>\nRule 6<\/strong><\/td>\nRule 7<\/strong><\/td>\nRule 8<\/strong><\/td>\n<\/tr>\n
00<\/strong><\/td>\nA<\/td>\nA<\/td>\nT<\/td>\nT<\/td>\nC<\/td>\nC<\/td>\nG<\/td>\nG<\/td>\n<\/tr>\n
01<\/strong><\/p>\n

10<\/strong><\/p>\n

11<\/strong><\/td>\n

C<\/p>\n

G<\/p>\n

T<\/td>\n

G<\/p>\n

C<\/p>\n

T<\/td>\n

G<\/p>\n

C<\/p>\n

A<\/td>\n

C<\/p>\n

G<\/p>\n

A<\/td>\n

A<\/p>\n

T<\/p>\n

G<\/td>\n

T<\/p>\n

A<\/p>\n

G<\/td>\n

A<\/p>\n

T<\/p>\n

C<\/td>\n

T<\/p>\n

A<\/p>\n

C<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Addition Operation for DNA\u00a0Sequence<\/strong><\/p>\n

With the rapid development of computations in DNA, the algebraic operations like Addition operation is done. Once the pixels are DNA encoded then addition is done between the DNA encoded data and DNA encoded key sequence as shown in table.2.<\/p>\n

Table 2: Addition Rule for DNA<\/strong>
\n<\/strong><\/p>\n\n\n\n\n\n\n\n
+<\/strong><\/td>\nA<\/strong><\/td>\nT<\/strong><\/td>\nG<\/strong><\/td>\nC<\/strong><\/td>\n<\/tr>\n
A<\/strong><\/td>\nA<\/td>\nT<\/td>\nG<\/td>\nC<\/td>\n<\/tr>\n
T<\/strong><\/td>\nT<\/td>\nC<\/td>\nA<\/td>\nG<\/td>\n<\/tr>\n
G<\/strong><\/td>\nG<\/td>\nA<\/td>\nC<\/td>\nT<\/td>\n<\/tr>\n
C<\/strong><\/td>\nC<\/td>\nG<\/td>\nT<\/td>\nA<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Proposed Image Encryption Algorithm<\/strong><\/p>\n

Section III gives the details of designing the proposed image encryption. The procedure of algorithm includes 4 stages namely confusing, permuting, encoding and diffusing the image in order to enhance the security as in Fig 1b.<\/p>\n\n\n\n
\u00a0\"Figure<\/td>\nFigure 1b:\u00a0<\/strong>Block description of the proposed Encryption scheme.<\/strong><\/p>\n

 <\/p>\n

Click here to View figure<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

The encryption steps are described as follows,<\/p>\n

Step 1: First, 8-bit RGB DICOM image is used as the plain image IM and it is of size IM(M, N, 3) and S=M*N where M = no. of rows in input image and N = no. of columns in input image i.e. plain image.<\/p>\n

Step 2: Split the colour DICOM image IM of size (M, N, 3) into three colour planes as IM_red, IM_green and IM_blue. Separated three colour planes each of size (M,N,1).<\/p>\n

IM_ red = {R1, R2<\/sub>, ………, RM*N <\/sub>}<\/p>\n

IM_ green = {G1, G2<\/sub>, ………, GM*N <\/sub>}<\/p>\n

IM_ blue = {B1, B2<\/sub>, ………, BM*N <\/sub>}<\/p>\n

Step 3: Now, three sequences namely X sequence, Y sequence and Z sequence are generated using 3D Lorenz map. s=rows*columns of plain image and generating sequences as follows,<\/p>\n

X= {Xi, Xi+1, Xi+2,…………,\u00a0 Xi+(s-1) }<\/p>\n

Y= {Yi, Yi+1, Yi+2,…………, Yi+(s-1) }<\/p>\n

Z= {Zi, Zi+1, Zi+2,…………., Zi+(s-1) } , where i =1<\/p>\n

Now, quantize the X sequence as Key 1 = floor( mod (X*10^14, 256)) and similarly quantize Y and Z to generate other keys i.e. Key2 and Key 3.<\/p>\n

Step 4: Sorting the elements of X, Y and Z sequences in ascending order and taking the Index values as Index 1, Index 2 and Index 3 as in Fig 2a and b.<\/p>\n\n\n\n
\u00a0\"Figure<\/td>\nFigure 2a: Chaotic sequence with index.\u00a0<\/strong>(b). Sorted chaotic sequence with index.<\/strong><\/p>\n

 <\/p>\n

Click here to View figure<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Step 5: Confusing three colour planes IM_red, IM_green and IM_blue with corresponding Index1, Index2 and Index3.<\/p>\n

Step 6: By using the confused image, Permutation is done for three R, G and B planes as follows.1<\/sup><\/p>\n

Let IM = { IM(ii, jj) }\u00a0 denote the grayscale plain image, where ii=1 to M and jj=i to N.<\/p>\n

aq(ii, jj) = de2bi (IM(ii, jj)<\/p>\n

where function de2bi converts decimal values to binary values.<\/p>\n

b =\u00a0 aq(ii , : )<\/p>\n

where\u00a0 aq(ii , : ) = {aq(ii , 1), aq(ii , 2),…..,aq(ii , M)} be the ith <\/sup>row of aq,\u00a0 then<\/p>\n

c=sum (b)<\/p>\n

Taking\u00a0 mod,<\/p>\n

Pmod<\/sub> = mod (c, 2).<\/p>\n

Now, if Pmod<\/sub> = 0,<\/p>\n

a(ii , : ) is circular shifted towards right with Key steps<\/p>\n

If Pmod<\/sub> = 1,<\/p>\n

a(ii, : ) is circular shifted towards left with same Key steps.<\/p>\n

Each group with 8-bits of vector is converted back into binary values, thus permuted image<\/p>\n

PRimg <\/sub>= { PRimg<\/sub>(ii, jj) } is obtained as,<\/p>\n

PRimg <\/sub>(ii , : ) = bi2de ( a(ii , : )<\/p>\n

where ii=1 to M and jj=1 to N.<\/p>\n

NOTE: Key1 is used for red plane, Key 2 is used for green plane and Key3 is used for blue plane respectively.<\/p>\n

Step 7: BIT- XORing is performed for each R, G and B planes by using permuted image and corresponding key.<\/p>\n

q (1) = PRimg <\/sub>(1) \u2295 key (1)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(4)<\/p>\n

where\u00a0 \u2295 symbol represents Bit-wise XOR operation.<\/p>\n

\"Equation<\/p>\n

and<\/p>\n

XR<\/sub> (k) = q (k) \u2295 key (k)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(6)<\/p>\n

where k= {1, 2, 3, 4,………..,S } and S=rows*columns of image.<\/p>\n

Step 8: BITXORed image of R, G and B planes and 3 keys are individually encoded using DNA encoding and added using addition rule.<\/p>\n

Step 9: Then it is decoded using DNA decoding rule.<\/p>\n

Step 10: Finally, Diffusion is performed for each RGB planes to get cipher image as in Fig 3.<\/p>\n

Each RGB planes is first bitxored with Key 1 [row-wise],<\/p>\n

Pdif <\/sub>= { Pdif<\/sub> (ii, jj) } , where ii=1 to M and jj=1 to N\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (7)<\/p>\n

and<\/p>\n

Pdif <\/sub>\u00a0(ii , : ) =DNAout<\/sub> (ii , : ) \u2295 key1 (ii , : )\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0(8)<\/p>\n

Now, bitxoring the results of first stage with another key i.e Key2 [column-wise] is written as,<\/p>\n

Pdif <\/sub>\u00a0(: , jj) =Pdif<\/sub> (: , jj) \u2295 key2 (: , jj)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(9)<\/p>\n\n\n\n
\u00a0\"Figure<\/td>\nFigure 3: Flowchart representation of the proposed algorithm.<\/strong><\/p>\n

 <\/p>\n

Click here to View figure<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Simulation Results And <\/strong>Security Analysis<\/strong><\/p>\n

For experimental analysis, 3 colour DICOM images were considered. Encryption metrics like NPCR, UACI, and correlation were estimated to prove the strength of the proposed encryption scheme. Fig 4(a-e) and 5(a-e) shows the various stages output of the proposed algorithm. The proposed encryption algorithm is said to be superior, if it is indestructible in any cases and it should resist towards common attacks as discussed in this section and also this section demonstrates a security analysis on proposed encryption scheme.<\/p>\n\n\n\n
\"Figure<\/td>\nFigure 4:\u00a0<\/strong>Encryption Results<\/strong>(a). Plain image(256×256) (b). Confused image (c). Permuted image (d). Bitxored image (e). Diffused image(Encrypted image).<\/strong><\/p>\n

 <\/p>\n

Click here to View figure<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n
\u00a0\"Figure<\/td>\nFigure 5: Decryption Results (a). Encrypted image (b). Decrypt-Diffused image (c). Decrypt-Bitxored image (d). Decrypt-Permuted image (e). Decrypt-Confused image.<\/strong><\/p>\n

 <\/p>\n

Click here to View figure<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Statistical Attack Analysis<\/strong><\/p>\n

It can be estimated by analyzing the pixels in the encrypted histogram, global entropy and correlation coefficients of encrypted image.<\/p>\n

Entropy Analysis<\/strong><\/p>\n

The Shannon entropy is adopted, in this case the randomness of random variable XX is measured as follows,<\/p>\n

\"Equation<\/p>\n

where each \u00a0 is the possible value of\u00a0 \u00a0. For M=8-bit data and q levels [q=2M], the range of entropy will lies in range [0,M]. If the entropy is little in the input data then the resultant key will have higher entropy. In general, entropy of the encrypted\u00a0 image should have value close to M,\u00a0 else if entropy value is lesser then there is a possibility of attack which can reduce the security of image transmission. Table. 3 shows that all the values of each RGB planes for 3 test images are more closer to M and hence algorithm which is proposed is much efficient.<\/p>\n

Table 3: Entropy Analysis of 3 Test Images
\n<\/strong><\/p>\n\n\n\n\n
Images<\/strong><\/td>\n\u00a0<\/strong><\/td>\nPlain\u00a0Image<\/strong><\/strong><\/td>\nCipher Images<\/strong><\/strong><\/td>\n<\/tr>\n
Image 1<\/strong><\/td>\nR<\/td>\n

%0<\/p>\n","protected":false},"excerpt":{"rendered":"

Introduction With the fast advancement in technology and its usage […]<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[57],"tags":[],"class_list":["post-20901","post","type-post","status-publish","format-standard","hentry","category-vol11no2"],"_links":{"self":[{"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/posts\/20901","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/comments?post=20901"}],"version-history":[{"count":5,"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/posts\/20901\/revisions"}],"predecessor-version":[{"id":32259,"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/posts\/20901\/revisions\/32259"}],"wp:attachment":[{"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/media?parent=20901"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/categories?post=20901"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/biomedpharmajournal.org\/staging\/wp-json\/wp\/v2\/tags?post=20901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}