IMPROVED HISTOGRAM SHIFTING IN ENCRYPTED IMAGES …Lossless and Adjustable Data Hiding inEncrypted Images with Public -Key Cryptography [3]. In the lossless organization, the ciphert

IMPROVED HISTOGRAM SHIFTING IN ENCRYPTED

IMAGES FOR REVERSIBLE DATA HIDING

Mr. S. Lakshminarayanan 1 Dr.K.Sankaranarayanan

2 Dr. Vijayakumari.V

3Adhisha Dilip

4 Archana.G

5

Janani .B.T 6

Assistant Professor, ECE, Sri Ramakrishna Engineering College, Coimbatore1

Dean,ECE,PA college of Engineering and Technology,Pollachi2

Professor,ECE,Coimbatore Institute of Engineering and Technology,Narasipuram,Coimbatore3

Student, ECE, Sri Ramakrishna Engineering College, Coimbatore 4 5 6

ABSTRACT—Data hiding is a system for surrounding evidence into insurances such as image, audio, and

video files, which can be castoff for media cipher, right

fortification, integrity authentication, and covert

communication, etc. The need of substituting

communications and images covertly over unsecure linkages stimulated the formation of cryptosystems to

support phones to deduce the substituted facts. In this

paper, an individual public key cryptosystem called

the Amended RSA is open measured with the service

MATLAB Driver to be charity over Images. And also used Amended Histogram-Shifting- Imitated

Changeable Data Hiding System the unusual

protection can be lossless returned after the implanted

material is take out. The projected organization for

Raised RSA cryptosystem holds three key records and dazed more than a few round probable on Developed

RSA. The projected system has hurry perfection on

Developed RSA decryption side. And For

surrounding, we recommend an enhanced data hiding

scheme expending medium edge detection (MED) and hexadecimal exploiting modification direction (EMD).

In inserting way, a prophesied image is created by

using MED. The undisclosed numbers is implanted

into the greatest themes in divisions by expending

hexadecimal EMD. A succession of investigates have been directed, and power of the projected scheme is

publicized by matching the investigational effects with

those of new histogram-shifting constructed

techniques. A noble chattels of the anticipated manner

detected in the testing is that data hiding rates are enlarged starved of mortifying the juncture image

class stated by the greatest Entrench speed and signal-

to-noise ratio quota.

Keywords—Improved RSA, Improved Histogram-Shifting, Hexadecimal exploiting modification

direction.

I. INTRODUCTION Adjustable data hiding is used for privacy safety

in exposed atmosphere. Adjustable data hid ing is a

category of data hiding technique whereby mass

image can be unconcerned faithfully. Life lossless

kinds this performance right for medical and

military presentations. Show of existing adjustable

datahiding system in scrambled image is not

agreeable due to the signal handling in translated

territory. Ming Li, Yang Li used histogram.

This method inflates histogram of image by

spread over homomorphis m multiplication in

encrypted province twisted on public key

cryptosystem. Histogram fluid is completed by

using homomorphic count in the encrypteddominion

for embedding other records into mult itude images.

The embedded additional data tin be mined and host

duplicate can be improved. This process products a

records inserted rate whereas PSNR rate drops.

Homomorphic encryption can make presented an

in effect way to method gesticulations in held

territory and public key cryptosystem created RDH

methods.Shijun Xiang and Xinrong Luo proposed

homomorphic probabilistic mechanis m for

adjustable data hiding in encrypted images. In this

system, sets consists of location pixels and host

pixels, the condition p ixels are retune already

encryption and encrypted host pixels are switched

with location pixels in the equal group to custom

Emulating Cipher text Groups (MCG’S).

By consuming homomorphic development

position is reserved as locus pixel and is kept short

of unmovable and supplementary material is

International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 16095-16102ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

16095

surrounded into LSB of the host cryptogram text

pixels. This way has an entrenching rate of

0.2bpp.Later the entrenching rate/ability is low.

Wang and Hang Cheng suggested lossless,

adjustable, pooled records whacking organization

for converted imageries.

This manner uses homomorphic and probabilistic

apparatus. Pre-processing is used to therapist the

image h istogram and each p ixel is encrypted with

chemical homomorphic cryptosystem. In this, two

comportments of data entrenching job can be made

in which a part of surrounded data can be dig out

before decryption and added part can be take out

after decryption by the handset, original image is

gained. But this manner writhes slight spin. Set in

rate is 0.25bpp.Junxiang wang, JiangqumNi,Xing

Zhang and Yun-Qing Sh i used histogram flowing to

achieve high worth of stego-image.

This process disables the frequency

andfalsificat ion complications. Histogram

fluctuating based various surrounding is offered and

is engaged for hefty lading. The percentage and

falsification concert worry ingly be governed by on

the acuity of h istogram. It has a surrounding bulk of

0.6bpp

Hence larger surrounding rate and better

eminence of stego images can be reached by via

dual image.In instruction to be responsible for

higher sanctuary from the muggers; dual image

RDH structure is pragmatic. Th is scheme has two

images i.e., the transformation stuck between two

stego similes can be used as a supporting evidence

to refurbish the creative image.

The alteration will be less than earlier d iscussed

passes. This process has an entrenching ability of

0.75bpp.Bin Ma and Yun Q.Shi vacant novel Code

Disunion Multip lexing (CDM) algorithm.

Embedding ability in this method can be puffy by

using mult ilevel data embedding. Data can be

surrounded short of touching each other. Walsh

Hadamard Matrix is castoff to create orthogonal

circulat ion structure. Ghetto map free repetitive is

used to concentrate the data immediate locus. Image

histogram on both the trimmings can be shrined for

resolving overflow or underflow problem. In this

scheme, it is grim to guesstimate the size of the

locality map. It has a chief embedding ability of

0.9bpp.

II. RELATED WORK

Histogram shifting in converted images with

public key cryptosystem for ad justable data hiding

[1]. Histogram shift ing is an operative reversible

data hiding (RDH) line in handing out digital

images. When the host image is encrypted for

concealment safety in some open milieus including

the cloud, RDH has to be administered in the

encrypted domain accordingly.

Rescindable Data Hiding in Homomorphic

Encrypted Province by Imitating Cipher text Group

[2]. Th is weekly used a novel adjustable data

whacking scheme for translated images by

expending homomorphic andprobabilistic

belongings of Paillier cryptosystem. In the system,

assemblies of in line p ixels are randomly selected,

and reversibly fixed into the relaxation of the image

to kind room for data entrenching. In each cluster,

there are a position pixel and a few host pixels.

Least significant bits (LSBs) of the locus pixels are

reset formerly encryption and the encrypted horde

pixels are switched with the encrypted locus pixel in

the different group to custom mirroring cipher text

groups (MCGs).

Lossless and Adjustable Data Hiding inEncrypted

Images with Public-Key Cryptography [3]. In the

lossless organization, the ciphertext pixels are

changed with new ideals to entrench the

supplementary data into some least weighty bit flat

surface of cipher text pixels by mult ilayer wet paper

coding.

Rate and Distortion Optimizat ion for Adjustable

Data Hiding Consuming Multiple Histogram

Shift ing [4]. Th is shifting ensconcing as an

emblematical changeable data hiding structure is

frequently measured due to its high worth of stego-

image. For HS-based surrounding, the number of

side statistics, i.e ., peak and zero b ins, generally

greatly upsets the rate and spin show of the stego-

image.

Developed dual-image mutable data hiding

system using the variety strategy of shift able pixels

synchronizes with minutest bias [5]. Equated to

orthodox reversible data hiding (RDH) systems, the

dual-image RDH procedure is an operative way to

do greater set in rate and better quality of the stego

images. We advise an developed dual-image RDH

process by expending the choice stratagem of

modification able pixels' manages with tin iest

alteration. Evenif the stego dual-pixel in the

epicenter fold ing-based system is shifted with tin iest

distortion.

Adjustable Data Hid ing Scheme Based on Code

Dissection Multiplexing [6]. A novel code division

multip lexing (CDM) algorithm-based reversible

data hiding (RDH) scheme is accessible. The h idden

data are indicated by different orthogonal

dissemination sequences and inserted into the cover

image. The image can be finally recovered after the

data have been haul out exactly. The Walsh

Hadamard background is laboring to generate

International Journal of Pure and Applied Mathematics Special Issue

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orthogonal diffusion systems, by which the numbers

can be covering embedded minus snooping each

other, and multilevel data surrounding can be

consumed to enlarge the surrounding ability.

An Improved RSA Cryptographic System. [7]

RSA cryptosystem and its haven traits. RSA is a

public key algorithm that everyday commonly in the

field of data retreat in the Internet-Banking and

Ecommerce solicitations. The suggested order for

RSA cryptosystem holds three prime figures and

overcome some attack possible on RSA. The

proposed scheme has speed improvement on RSA

decryption side by using the Chinese Reminder

Theorem (CRT) and the scheme is semantically

locked also.

Value-added Histogram-Shifting-Imitated

Adjustable Data Hiding Scheme [8]. Histogram

shifting artificial based adjustable data hiding

scheme in 2013. They assistance the peak points of

image intensity-based subdivisions, instead of

developing the peak point of a histogram. Their

order has the control of the embedding ability due to

the engraining method.

In this rag, we advise a developed data thumping

outline using medium edge exposure (MED) and

hexadecimal exp lo iting modification direction

(EMD). In embedding procedure, apredicted image

is generated by using MED. The top-secret data is

surrounded into the peak points in sectors by using

hexadecimal EMD.

III. PROPOSED METHODOLOGY

Data hid ing is a p ractice for embedding

informat ion into asylums such as image, audio,and

video files, which can be used for media notation,

copyright protection, integrity authentication, and

covert communicat ion, etc. The want of trad ing

messages and images furtively over unsecure links

sponsored the conception of cryptosystems to

qualify telephones to deduce the bartered facts. In

this paper, a certain public key cryptosystem called

the Amended RSA is offered rash with the help

MATLAB Plug-in to be used over Images. And also

used Amended Histogram-Shift ing-Imitated

Changeable Data Hid ing Organization the orig inal

cover can be lossless restored after the embedded

evidence is dig out.

The anticipated scheme for Developed

RSA cryptosystem comprehends three chief records

and dazed quite a few attack thinkable on Upgraded

RSA. The wished-for pattern has speed advance on

Developed RSA decryption side. And For

surrounding, we proposal an amended data

walloping outline expending median edge detection

(MED) and hexadecimal ill-using variat ion

direction (EMD). In surrounding method, a

expected image is engendered by using MED.

The stealthy data is inserted into the peak

themes in subdivisions by using hexadecimal EMD.

A series of investigates have been steered, and

authority of the anticipated scheme is given missing

by equating the trial grades with persons of other

histogram-shifting constructed devices. A moral

assets of the anticipated method practical in the

experiment is that data hiding rates are improved

starved of mortifying the stego duplicate

worthcommunicated by the crowning Embed

frequency and signal-to-noise ratio portion.

Fig. 1.Framework of proposed scheme.

A. Methodologies

Functioning of Improved RSA

In Better RSA process each user of the structure

makes the two number public (e, n) also called

public key and keeps a numeral secret (d) is also

entitled private champion. If a user A desires to

send a message to user B, user A requests to look up

user B’s open key and have dispatch M (written in

the form of integer value) then user A creates the

block of message of size < n and then sends the

cipher text C=Me mod (n) to user B.

Then the mouthpiece user B decrypt the text by

M=Cd mod (n).the safekeeping of algorithm be

governed by on the choice of public and private

keys.They must be ominously large.

Key Generation of RSA

1. Select unsystematic bulky chief integers p and q

of crudely the same size.

2. Determine the classification modulus n= p*q.

3. Determine Euler totient task [7] φ(n) = (p-1)*(q-

1)).

4. Take a arbitrary encryption booster e such that

gcd [e, φ(n)] =1 and 1<e<φ(n).

5. Determine the decryption champion d, e*d≡1

mod φ(n).

6. Public Key Ku = (e, n) and Remote Key Kr = (d,

p, q,dp,dq,ds).

Encryption of RSA

In the Value-added RSA encryption method, the

user B encrypt the messageM by consuming the


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public key of handler A. User B ought do the

following:

(a) Attain user A free key (n, e).

(b) Epitomize the letter M in integer form in the

interval [0, n-1]

(c) Total c = me mod n.

(d) Lead the scrambled text C, to user A.

Decryption of RSA

To pull through plaintext or missive M from C,

user A should do the following:

Routine the private key d to recover M = Cd mod

n.

The wished-for pattern is frustrating to provide an

development to the Hamami and Aldariseh [18]

scheme by advising a manner that have speed

expansion on the Upgraded RSA decryption side

and similarly afford the retreat by elud ing several

rashes possible on Amended RSA. Using the

unsystematic number k if same letter is converted

more than one time it will look altered every time.

The general idea on the way to this scheme is to

use the Key peers algorithm of Hamami and

Aldariseh scheme and offered a proposed pattern for

encryption and decryption system.

The survival of three key numbers, the sweat of

breakdown of fickle n crucial be escalations and the

key generation time must be shrinks. The algorithm

for the wished-for scheme is asfollows:

Key Generation for Proposed Scheme (Improved

RSA)

To create the key consuming three chief

numbers handler A would do the following:

(a) Engender three large prime amounts p, q, s.

(b) Gauge n=p*q*s and φ(n) = (p-1)*(q-1)*(s-1).

(c) Select e such that (e, φ(n)) are relatively co-

prime.

(d) Get the assessment of d by expending e*d=1

mod φ(n).

(e) Find dp=d mod (p-1),dq=d mod(q-1), ds=d

mod(s-1).

(f) Public Key Ku=<e, n>and Private key Kr=<d,

p, q, s, dp, dq, ds>.

Encryption for Proposed Scheme (Improved RSA)

To encrypt the shiatsu M User B should do

the following:

User B ought acquired the public key of user A <e,

n>

(a) Represent the message M as an integer form in

interval [0 to n-1].

(b) Select k as a random integer gcd(k, n)=1 and

1< k < n-1.

(c) Compute C1=k^e mod n.

(d) Compute C2=M^e*k mod n.

(e) Send the cipher text values (C1, C2) to userA.

Decryption for the Proposed Scheme (Improved

RSA)

On decryption route use conception of Developed

RSA with CRT. To mend the missive from cipher

text C2 user A would do the following:

a. Calcu late Cp=C1 mod p,Cq=C1 mod q, Cs=C1

mod s. and then calculate kp=Cp^dp mod p, kq=Cq

^dq mod q and ks=Cs ^ds mod s. b. By using the

formula calcu late k k=[kp.(qs)^(p-1) mod n +

kq.(ps)^(q-1) mod n + ks.(pq)^ (s-1) mod n].

c. By using the Euclidean algorithm, calculate the

value of the unique integer t, t*k= 1mod n and 1< t

< n.

d. Then compute Me, C2*t = (Me .k)t = (Me) k.t =

Me mod n.

e. For getting the value of message M should do the

following steps First calculate C’p=Me mod p,

C’q=Me mod q, C’s=Me mod s and then calculate

Mp=C’p^dp mod p, Mq=C’q^dq mod q, Ms=C’s^ds

mod s.

f. Finally recover the note M by consuming the

following formula: M= [Mp.(qs)^(p-1) mod

n + Mq.(ps)^(q-1) mod n + Ms.(pq)^(s-1) mod n].

This rag describes the Developed RSA

cryptosystem and its departures. The proposed

system has speed upgrading on the decryption side

of Enhanced RSA system by using the concept of

Chinese balance theorem and the method also

expands the haven of Upgraded RSA system by

avoiding some attacks that are thinkable on

Developed RSA algorithm.

Improved Histogram-Shifting Median

Edge Detection

By using Median Edge Detection,it

generates a predicted image.difference value is

calculated with the cover image.peak points of

each segment has a secret message SMK that is

embedded into the cover image.Each segments

SEm has a peak point,first peak point of every

segment is made empty to confirm the pixel

values.

Hexadecimal EMD

This offered a nonary EMD-based data

whacking outline and, the main idea is to change the

secret data into the structure of nonary

demonstration [16]. We use a hexadecimal EMD

method.


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Hexadecimal EMD algorithm:

Input: Cover image and hexadecimal secret message

Output: Stego image

Step 1: Attain t ransformat ion duos (d1, d2) by using

transformation d1and d2 where d1, d2 ∈ [1, 4]

Step 2: Generate a hexadecimal EMD table Tm

according to

f (d1, d2) =(d1 + d 2 × 4) mod 16

Step 3: Embed undisclosed records to ultimate

argument rate of image by hexadecimal EMD table.

When the variance image as shown in Fig. it is

rumored that an undisclosed data is 11 and a

topmost point rate is 0. The harmonizes of the

hexadecimal EMD table matching to the secret data

11 is (3, 2). Then, the two peak topics of the

difference image are changed into (3, 2)

Embedding procedure

Entrenching algorithm:

Input: Cover image and hexadecimalsurreptitious

message

Output: Stego image

Step 1: Construct a prophesied image P by using the

MED appliance with c i,j

Step 2: Determine a d issimilarity image D between

p i,j and c i,j by d i,j = p i,j – c ,j

Step 3: Gap the histogram into SEm, where 1 ≤ m ≤

129. The size of each sector SEm is four. Step 4:

Obtain a segment peak SPm for each segment SEm

and mark a bit at the location map Lm(i,j).

Step 5: Surround the secret dispatch SMk into SPm

pair with spawned hexadecimal EMD table Tm.

And equation. S i,j = p i,j – d 0 i,j.

Extracting and recovery procedure

Removing algorithm:

Input: Stego image

Output: Asylum image and hexadecimal

undisclosed message

Step 1: Estimate a calculat ion value p i,j , 1 ≤ i, j ≤

512 of a solo pixel by consuming the

MEDmechanism with s i,j

Step 2: Gage a transformat ion value of a single

pixel value d0 i,j = p i,j – s i,j

Step 3: Abstract the secret message SMk from

SPm pair with spawned hexadecimal EMD

table Tm and idea a location map li,j.. The rate

of d i,j is deputize for d0 i,j.

IV. EXPERIMENTAL RESULTS AND DISCUSSION

MATLAB stays a high-performance

etymological for technical adding. It

incorporates multiplication, visualization, and

programming in an easy-to-use location where

complications and resolutions are voiced in

aware calculated cipher.

To gage the offered optimization order, we

test several 512×512×8 bits gray scale images

with unalike texture selves from catalog and

100 512×512×8 b its gray scale images casually

selected from catalogue. By matching the

suggested pattern with selected state-of-the-art

reversible data hiding methods, the preeminence

of our outline is shown.

RESULTS COMPARISON RSA_HS vs. RSA_IHS

PARAMETERS PERFORMENCE RATE


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GRAPH RESULTS COMPARISONRSA_HS vs.

IRSA_IHS

PSNR Rate Comparison

Embed Rate Comparison

V. CONCLUSION

The suggested algorithm has hustle progress on

the decryption side of developed RSA algorithm by

using the conception of Chinese what's left theorem

and the manner also develops the safekeeping of

upgraded RSA system by sidestepping some attacks.

We have wished-for a reversible data thumping

order centered on MED and the hexadecimal EMD

to expand Wang et al.’s scheme. The MED has been

used to create the anticipated image.

The hexadecimal EMD has been used to surround

the stealthy data. The investigationalmarks

publicized that the surrounding capacity is restored

than Wang et al.’s outline. Our organization h idden

that the PSNR was 93.25dB and surrounding

capacity was 821,355 bits on midd ling. Associated

to the expected association and Wang et al.’s

schemes, the whack capability was superior, and

also the PNSR was amended.

In past, work on those rounds that are not

tolerating for in this paper and run more sheltered

and reviewed RSA cryptosystem. Here, moreover

the encryption time is not rash. So in future also toil

on the encryption sideways so the stint for

encryption analysts. And also, we will

intensification PSNR while the contiguous

proficiency is well-kept.

REFERENCES [1] J. T ian, Reversible data embedding using a difference

expansion, IEEE Trans. Circuits Syst. Video Technol. 13 (8) (2003) 890–896. [2] Z. Ni, Y.Q. Shi, N. Ansari, W. Su, Reversible data hiding, IEEE Trans. Circuits Syst. Video Technol. 16 (3) (2006) 354–

362. [3] J.Y. Hsiao, K.F. Chan, J.M. Chang, Block-based reversible data embedding, Signal Process. 89 (4) (2009) 556–569. [4] X. Qu, H.J. Kim, Pixel-based pixel value ordering predictor

for high-fidelity reversible data hiding, Signal Process. 111 (2015) 249– 260. [5] X. Li, W. Zhang, X. Gui, B. Yang, A novel reversible data hiding scheme based on two-dimensional difference-histogram

modification, IEEE Trans. Inf. Forensics Secur. 8 (7) (2013) 1091–110 0. [6] G. Coatrieux, W. Pan, N. Cuppens-Boulahia, F. Cuppens, C.

Roux, Reversible watermarking based on invariant image classification and dynamic histogram shifting, IEEE Trans. Inf. Forensics Secur. 8 (1) (2013) 111–120. [7] I.C. Chang, Y.C. Hu, W.L. Chen, C.C. Lo, High capacity

reversible data hiding scheme based on residual histogram shifting for block truncation coding, Signal Process. 98 (2015) 376–388. [8] H.T. Wu, J. Huang, Y.Q. Shi, A reversible data hiding

method with contrast enhancement for medical images, J. Vis. Commun. Image Represent. 31 (2015) 146–153. [9] M. Cancellaro, F. Battisti, M. Carli, G. Boato, F.G. De Natale, A. Neri, A commutative digital image watermarking and

encryption method in the tree structured Haar transform domain, Signal Process.: Image Commun. 26 (1) (2011) 1–12. [10] S.Shanmugapriya, B.S.Sathishkumar, “Recognition Of

Human Identities Using Enhanced Knuckle Pattern Feat ures”, International Journal Of Innovations In Scientific And Engineering Research (Ijiser), Vol.1, No.12, Pp.448-451, 2014. [11] S. Lian, Z. Liu, Z. Ren, H. Wang, Commutative encryption

and watermarking in video compression, IEEE Trans. Circuits Syst. Video Technol. 17 (6) (2007) 774–778.


16100

[12] K.L. Ma, W. Zhang, X. Zhao, N. Yu, F. Li, Reversible data hiding in encrypted images by reserving room before

encryption, IEEE Trans. Inf. Forensics Secur.(3) (2011) 553–562. [13] W. Zhang, K. Ma, N. Yu, Reversibility improved data hiding in encrypted images, Signal Process. 94 (2014) 118–127. [13] X. Zhang,

Reversible data hiding in encrypted image, IEEE Signal Process. Lett. 18 (4) (2011) 255–258. [14] W. Hong, T.S. Chen, H.Y. Wu, An improved reversible data hiding in encrypted images using side match, IEEE Signal

Process. Lett. 19 (4) (2012) 199–202. [15] M. Li, D. Xiao, Z. Peng, H. Nan, A modified reversible data hiding in encrypted images using random diffusion and accurate prediction, ETRI J. 36 (2) (2014) 325–328.

[16] M. Li, D. Xiao, A. Kulsoom, Y. Zhang, Improved reversible data hiding for encrypted images using full embedding strategy, Electron. Lett. 51 (9) (2015) 690–691.

[17] M. Li, D. Xiao, Y. Zhang, H. Nan, Reversible data hiding in encrypted images using cross division and additive homomorphism, Signal Process.: Image Commun. 39 (2015) 234–248.

[18] Y.C. Chen, C.W. Shiu, G. Horng, Encrypted signal-based reversible data hiding with public key cryptosystem, J. Vis. Commun. Image Represent. 25 (5) (2014) 1164–1170. [19] X. Zhang, J. Wang, Z. Wang, H. Cheng, Lossless and

Reversible Data Hiding in Encrypted Images with Public Key Cryptography, IEEE Trans. Circuits Syst. Video Technol.(2015),http://dx.doi.org/10.1109/TCSVT.2015.2433194.

[20] P. Paillier, Public-key cryptosystems based on composite degree residuosity classes, in: Proceeding of the Advances Cryptology, EUROCRYPT'99, LNCS, 1592, 1999, pp. 223– 238.

[21] R.L. Rivest, A. Shamir, L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Commun. ACM 21 (2) (1978) 120–126.

[22] Standard picture collection: grayscale images and color images. Accessed 1 January 2016. Available at⟨http://www.media.cs.tsinghua.edu.cn/ ahz/di

gitalimageprocess/benchmark.htm⟩. [23] P.Y. Lin, J.S. Lee, C.C. Chang, Protecting the content integrity of digital imagery withfidelity preservation, ACM

Trans. Multimed. Comput. Commun. Appl. 7 (3) (2011) 1–20.


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IMPROVED HISTOGRAM SHIFTING IN ENCRYPTED IMAGES …Lossless and Adjustable Data Hiding inEncrypted Images with Public -Key Cryptography [3]. In the lossless organization, the ciphert

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