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Image Cryptography and Steganography

Jan 25, 2017

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ImageCryptography &SteganographyMaster :Dr. GhaderiMohammad Amin Amjadi

Winter 2015

Main PaperEncrypted image-based reversible data hiding with public key cryptography from difference expansionChih-Wei Shiu , Yu-Chi Chen , Wien Hong

2015 Elsevier B.V. All rights reserved2

Content

a) Prefaceb) EIRDH-Pc) new EIRDH-P

3

ImagePreface -> Image

4Image : a Matrix of Pixels

PixelPreface -> Image -> Pixel

5

++=

RedProperty (8 bit)24 bit ImageGreenProperty (8 bit)BlueProperty (8 bit)BGRLSBMSBLSBMSBLSBMSB000000000000000000000000

Pixel : 24 bitLSB : Least significant bitMSB : Most significant bitRGB Mode

CryptographyGoal : Security

Terms :CryptographyEncryptDecryptPublic key Cryptography

6

CryptographySender: Encrypt MessageReceiver: Decrypt EMessage7Preface -> Cryptography -> base scenarioSenderEncryptMessageEMessageReceiverDecryptEMessageMessage

CryptographyChange Location (reordering)

2. Mapping8Preface -> Cryptography -> base Algorithms2143

3412

2143

F(2)F(1)F(4)F(3)

Cryptography1. Symmetric-Key Cryptographysender and receiver using same keykey is secret

2. Public-Key Cryptographyanyone can access to the public keyonly receiver has the Private Key9Preface -> Cryptography -> Category

SteganographyGoal : Hide Message/Data

Terms :DH : Data HidingRDH : Reversible Data Hiding

10

Steganographyuse Cover Image / Hide Message / Extract MessageSender: Hide Message inside Cover ImageReceiver: Extract secret Message

11Preface -> Steganography -> base scenarioSenderCover ImageCover Image(Message)MessageReceiverCover Image(Message)Cover ImageMessage

SteganographyLSBImage quality of Cover Image12Preface -> Steganography -> base AlgorithmsBGRLSBMSBLSBMSBLSBMSB000000000000000000000000

BGRLSBMSBLSBMSBLSBMSB000000000000000000000000

3bit of Data in any pixel of Cover Image8bit of Data in any pixel of Cover Image

Cryptography & Steganography13Preface -> compare Cryptography and Steganography

EncryptionDecryption

Cryptography & Steganography14Preface -> compare Cryptography and Steganography

Cover Image (512 x 512)94 KB LSB AlgorithmUsing Jpeg FormatMessage (450 x 321)20 KB Stego (512 x 512)37.6 KB

EIRDH-PCombine Cryptography & SteganographyTerms :EIRDH : encrypted image-based reversible data hiding EIRDH-P : encrypted image-based reversible data hiding (EIRDH) with public key cryptographyImage ProviderHider

15

EIRDH-P1. the receiver initially sets his public / secret key pair (pk , sk) 16EIRDH-P -> Schematic and Scenario -> KeyGenReceiverRData HiderHImage ProviderPskpkpk

SenderSend

EIRDH-P2. the Image Provider picks a cover-image CI , and then uses pk and CI to generate the encrypted image EI , sends it to the hider17EIRDH-P -> Schematic and Scenario -> Image EncReceiverRData HiderHImage ProviderPskpkpk

SenderCIEIEncSendEI

EIRDH-P3. the Data Hider takes a message M and pk to generate the secret message SM18EIRDH-P -> Schematic and Scenario -> Message EncReceiverRData HiderHImage ProviderPskpkpk

SenderCIEIEIEncSendMpkEncSM

EIRDH-P4. the Data Hider takes SM and EI to generate the encrypted image with the embedded message, EIM

19EIRDH-P -> Schematic and Scenario -> EmbeddingReceiverRData HiderHImage ProviderPskpkpk

SenderCIEIEncSendEIMpkEncSMHidEIM

EIRDH-P5. The receiver uses EIM and sk to recover the stego-image SI20EIRDH-P -> Schematic and Scenario -> Image DecReceiverRData HiderHImage ProviderPskpkpk

SenderCIEIEncSendEIMpkEncSMHidEIMEIMDecSISend

EIRDH-P6. The receiver uses SI to recover CI and obtain SM21EIRDH-P -> Schematic and Scenario -> ExtractingReceiverRData HiderHImage ProviderPskpkpk

SenderCIEIEncSendEIMpkEncSMHidEIMEIMDecSIExtSMCISend

EIRDH-P7. The receiver obtains the pure message M by using sk to decrypt SM22EIRDH-P -> Schematic and Scenario -> Message DecReceiverRData HiderHImage ProviderPskpkpk

SenderCIEIEncSendEIMpkEncSMHidEIMEIMDecSIExtSMCIDecMSend

EIRDH-P23EIRDH-P -> Encryption AlgorithmPublic keyDiffie-HellmanRSAPaillierTerms :gcd : Greatest common divisorlcm : Least common multiple

EIRDH-P1. Choose two distinctprime numberspandqp != qp , q : Big

24EIRDH-P -> Encryption Algorithm -> RSA -> KeyGenp = 61 , q = 53

EIRDH-P2. Computen=pq

25EIRDH-P -> Encryption Algorithm -> RSA -> KeyGenp = 61 , q = 53n = 61 x 53 = 3233

EIRDH-P3. Compute(n) = (p)(q) = (p 1)(q 1) =n- (p+q-1) , where isEuler's totient function

26EIRDH-P -> Encryption Algorithm -> RSA -> KeyGenp = 61 , q = 53n = 61 x 53 = 3233(n) = (61 1)(53 1) = 3120

EIRDH-P27EIRDH-P -> Encryption Algorithm -> RSA -> KeyGenp = 61 , q = 53n = 61 x 53 = 3233(n) = (61 1)(53 1) = 3120e = 17

EIRDH-P5. Determinedasde1(mod (n))de 1 (mod (n))d.e = 1 + k.(n)

28EIRDH-P -> Encryption Algorithm -> RSA -> KeyGenp = 61 , q = 53n = 61 x 53 = 3233(n) = (61 1)(53 1) = 3120e = 17d = 275317 x 2753 mod 3120 = 1

EIRDH-P6. public key : ( n , e )

29EIRDH-P -> Encryption Algorithm -> RSA -> KeyGenp = 61 , q = 53n = 61 x 53 = 3233(n) = (61 1)(53 1) = 3120e = 17d = 275317 x 2753 mod 3120 = 1public key : ( n , e ) = ( 3233 , 17 )

EIRDH-P7. private key ( n , d )b) ( p , q ) , d mod (q-1) , d mod (p-1) , q-1 mod (p)30EIRDH-P -> Encryption Algorithm -> RSA -> KeyGenp = 61 , q = 53n = 61 x 53 = 3233(n) = (61 1)(53 1) = 3120e = 17d = 275317 x 2753 mod 3120 = 1public key : ( n , e ) = ( 3233 , 17 )private key : ( n , d ) = ( 3233 , 2753 )

EIRDH-P31EIRDH-P -> Encryption Algorithm -> RSA -> Encryption

EIRDH-P32EIRDH-P -> Encryption Algorithm -> RSA -> Decryption

EIRDH-P33EIRDH-P -> Encryption Algorithm -> Paillier

new EIRDH-Peach pixel is divided into two parts : an even integer and a bit, where the summation of them is equal to the pixel value

any pixel = x + y + bit(x , y) is an even integer , x > y[[m]] = c(m) = ciphertext of m[[m1]] [[m2]] = [[ m1 + m2 ]]34new EIRDH-P

new EIRDH-P1. Receiver sets the public/secret key pair (pk, sk) as Paillier encryption35new EIRDH-P -> Algorithm -> KeyGen

new EIRDH-P36new EIRDH-P -> Algorithm -> Image Encyx

Cover ImagePre Processy'x'

Encrypt[[y]][[x]]

Enc Image

new EIRDH-P3. Data Hider generates the secret message SM by using pk to encrypt the message M37new EIRDH-P -> Algorithm -> Message EncEncMpkSM

new EIRDH-P38new EIRDH-P -> Algorithm -> Embedding[[y]][[x]]

[[y]][[x]]

Embed

new EIRDH-P39new EIRDH-P -> Algorithm -> Image Dec[[y]][[x"]]

Decy x

Stego Image

new EIRDH-P40new EIRDH-P -> Algorithm -> Extractingyx

Extractyx

Stego Image

new EIRDH-P7. Receiver obtains the pure message M by using sk to decrypt SM

41new EIRDH-P -> Algorithm -> Message Decyx

Recoveryx

Stego Image

new EIRDH-P

42new EIRDH-P -> Schematic

Cover ImagePre Process

Encrypt

Enc Image[[y]][[x]]

[[y]][[x]]

Embed[[y]][[x"]]

Decy x

Stego ImageExtractyx

Recover

PHR

Question ?43

Thanks44