Image Cryptography and Steganography

ImageCryptography &Steganography

Master :Dr. Ghaderi

Mohammad Amin Amjadi

Winter 2015

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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 reserved

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Content

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

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ImagePreface -> Image

Image : a Matrix of Pixels

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PixelPreface -> Image -> Pixel

+

+

=

RedProperty (8 bit)

24 bit Image

GreenProperty (8 bit)

BlueProperty (8 bit)

B G RLSB MSB LSB MSB LSB MSB0000 0000 0000 0000 0000 0000

Pixel : 24 bit

LSB : Least significant bitMSB : Most significant bit

RGB Mode

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Cryptography

Goal : Security

Terms :1) Cryptography2) Encrypt3) Decrypt4) Public key Cryptography

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Cryptography

Sender : Encrypt Message Receiver : Decrypt EMessage

Preface -> Cryptography -> base scenario

SenderEncryptMessage EMessage Receiver

DecryptEMessage Message

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Cryptography

1. Change Location (reordering) 2. Mapping

Preface -> Cryptography -> base Algorithms

2 14 3

3 41 2

2 14 3

F(2)

F(1)

F(4) F(3)

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Cryptography

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

2. Public-Key Cryptographyanyone can access to the public keyonly receiver has the Private Key

Preface -> Cryptography -> Category

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Steganography

Goal : Hide Message/Data

Terms :1) DH : Data Hiding2) RDH : Reversible Data

Hiding

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Steganography

use Cover Image / Hide Message / Extract Message Sender : Hide Message inside Cover Image Receiver : Extract secret Message

Preface -> Steganography -> base scenario

SenderCover Image Cover Image(Message)Message

ReceiverCover Image(Message) Cover Image

Message

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Steganography

LSBImage quality of Cover Image

Preface -> Steganography -> base Algorithms

B G RLSB MSB LSB MSB LSB MSB0000 0000 0000 0000 0000 0000

B G RLSB MSB LSB MSB LSB MSB0000 0000 0000 0000 0000 0000

3bit of Data in any pixel of Cover Image 8bit of Data in any pixel of Cover Image

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Cryptography & SteganographyPreface -> compare Cryptography and Steganography

Encryption

Decryption

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Cryptography & SteganographyPreface -> compare Cryptography and Steganography

Cover Image (512 x 512)94 KB

LSB AlgorithmUsing Jpeg Format

Message (450 x 321)20 KB

Stego (512 x 512)37.6 KB

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EIRDH-P

Combine Cryptography & Steganography

Terms :1) EIRDH : encrypted image-

based reversible data hiding 2) EIRDH-P : encrypted image-

based reversible data hiding (EIRDH) with public key cryptography

3) Image Provider4) Hider

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EIRDH-P

1. the receiver initially sets his public / secret key pair (pk , sk)

EIRDH-P -> Schematic and Scenario -> KeyGen

ReceiverR

Data HiderH

Image ProviderP

sk

pk

pk

Send

er

Send

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EIRDH-P

2. the Image Provider picks a cover-image CI , and then uses pk and CI to generate the encrypted image EI , sends it to the hider

EIRDH-P -> Schematic and Scenario -> Image Enc

ReceiverR

Data HiderH

Image ProviderP

sk

pk

pk

Send

er

CI EIEncSe

nd

EI

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EIRDH-P

3. the Data Hider takes a message M and pk to generate the secret message SM

EIRDH-P -> Schematic and Scenario -> Message Enc

ReceiverR

Data HiderH

Image ProviderP

sk

pk

pk

Send

er

CI EI

EI

EncSe

nd

M pk Enc S

M

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EIRDH-P

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

EIRDH-P -> Schematic and Scenario -> Embedding

ReceiverR

Data HiderH

Image ProviderP

sk

pk

pk

Send

er

CI EIEncSe

nd

EI

M pk Enc S

M

Hid EIM

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EIRDH-P

5. The receiver uses EIM and sk to recover the stego-image SI

EIRDH-P -> Schematic and Scenario -> Image Dec

ReceiverR

Data HiderH

Image ProviderP

sk

pk

pk

Send

er

CI EIEncSe

nd

EI

M pk Enc S

M

Hid EIM

EIM Dec SI

Send

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EIRDH-P

6. The receiver uses SI to recover CI’ and obtain SM’

EIRDH-P -> Schematic and Scenario -> Extracting

ReceiverR

Data HiderH

Image ProviderP

sk

pk

pk

Send

er

CI EIEncSe

nd

EI

M pk Enc S

M

Hid EIM

EIM Dec SI

ExtSM’CI’Send

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EIRDH-P

7. The receiver obtains the pure message M’ by using sk to decrypt SM’

EIRDH-P -> Schematic and Scenario -> Message Dec

ReceiverR

Data HiderH

Image ProviderP

sk

pk

pk

Send

er

CI EIEncSe

nd

EI

M pk Enc S

M

Hid EIM

EIM Dec SI

ExtSM’CI’

Dec M’

Send

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EIRDH-PEIRDH-P -> Encryption Algorithm

Public key

Diffie-Hellma

nRSAPaillier

Terms :1) gcd : Greatest common divisor2) lcm : Least common multiple

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EIRDH-P

1. Choose two distinct prime numbers p and qp != qp , q : Big

EIRDH-P -> Encryption Algorithm -> RSA -> KeyGen

1. p = 61 , q = 53

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EIRDH-P

2. Compute n = pq

EIRDH-P -> Encryption Algorithm -> RSA -> KeyGen

1. p = 61 , q = 532. n = 61 x 53 = 3233

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EIRDH-P

3. Compute φ(n) = φ(p)φ(q) = (p − 1)(q − 1) = n - (p + q -1) , where φ is Euler's totient function

EIRDH-P -> Encryption Algorithm -> RSA -> KeyGen

1. p = 61 , q = 532. n = 61 x 53 = 32333. φ(n) = (61 − 1)(53 − 1) = 3120

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EIRDH-P

4. Choose an integer e such that 1 < e < φ(n) and gcd(e, φ(n)) = 1e is a prim Number on {1 to φ(n) }

EIRDH-P -> Encryption Algorithm -> RSA -> KeyGen

1. p = 61 , q = 532. n = 61 x 53 = 32333. φ(n) = (61 − 1)(53 − 1) = 31204. e = 17

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EIRDH-P

5. Determine d as d ≡ e−1 (mod φ(n))d⋅e ≡ 1 (mod φ(n))

d.e = 1 + k.φ(n)

EIRDH-P -> Encryption Algorithm -> RSA -> KeyGen

1. p = 61 , q = 532. n = 61 x 53 = 32333. φ(n) = (61 − 1)(53 − 1) = 31204. e = 175. d = 2753 17 x

2753 mod 3120 = 1

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EIRDH-P

6. public key : ( n , e )

EIRDH-P -> Encryption Algorithm -> RSA -> KeyGen

1. p = 61 , q = 532. n = 61 x 53 = 32333. φ(n) = (61 − 1)(53 − 1) = 31204. e = 175. d = 2753 17 x

2753 mod 3120 = 16. public key : ( n , e ) = ( 3233 , 17 )

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EIRDH-P

7. private key a) ( n , d )b) ( p , q ) , d mod (q-1) , d mod (p-1) , q-1 mod (p)

EIRDH-P -> Encryption Algorithm -> RSA -> KeyGen

1. p = 61 , q = 532. n = 61 x 53 = 32333. φ(n) = (61 − 1)(53 − 1) = 31204. e = 175. d = 2753 17 x

2753 mod 3120 = 16. public key : ( n , e ) = ( 3233 , 17 )7. private key : ( n , d ) = ( 3233 , 2753 )

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EIRDH-P

8. Encryptionm (Message) such that 0 ≤ m < n and gcd(m, n) = 1c : ciphertext 

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

1. p = 61 , q = 532. n = 61 x 53 = 32333. φ(n) = (61 − 1)(53 − 1) = 31204. e = 175. d = 2753 17 x

2753 mod 3120 = 16. public key : ( n , e ) = ( 3233 , 17 )7. private key : ( n , d ) = ( 3233 , 2753 )8. c(m)

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EIRDH-P

9. Decryption

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

1. p = 61 , q = 532. n = 61 x 53 = 32333. φ(n) = (61 − 1)(53 − 1) = 31204. e = 175. d = 2753 17 x

2753 mod 3120 = 16. public key : ( n , e ) = ( 3233 , 17 )7. private key : ( n , d ) = ( 3233 , 2753 )8. c(m) 9. m(c)

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EIRDH-P

1. Choose two large prime numbers p and q randomly2. Compute n = pq , 3. Select random integer g where 4. ; where 5. ( N , g ) is public key6. ( p , q , ) is private key7. where r is random such that

EIRDH-P -> Encryption Algorithm -> Paillier

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new EIRDH-P

each 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 ]]

new EIRDH-P

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new EIRDH-P

1. Receiver sets the public/secret key pair (pk, sk) as Paillier encryption

new EIRDH-P -> Algorithm -> KeyGen

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new EIRDH-P

2. Image Provider pre-processes (x,y) to compute and , and then computes and Note that d can be positive or negativeHe generates and by using pk to encrypt , Here and are the encrypted pixel pair in the encrypted imageThis step will produce EI

new EIRDH-P -> Algorithm -> Image Enc

y xCover Image

Pre Process y' x' Encrypt [[y‘]] [[x‘]]

Enc Image

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new EIRDH-P

3. Data Hider generates the secret message SM by using pk to encrypt the message M

new EIRDH-P -> Algorithm -> Message Enc

EncMpk SM

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new EIRDH-P

4. For a bit b of SM , Data Hider generates and computes and Note that is only inserted into the first encrypted pixelFinally, he generates and as a pixel pair of EIM. This step will output EIM

new EIRDH-P -> Algorithm -> Embedding

[[y‘]] [[x‘]][[y”]] [[x”]] Embed

b = 1 , ,

b = 0 , ,

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new EIRDH-P

5. Receiver uses and and sk to recover x ″ , y ″ as a pixel pair of the stego-image SI This step will finally output SI

new EIRDH-P -> Algorithm -> Image Dec

[[y”]] [[x"]] Dec y “ x “

Stego Image

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new EIRDH-P

6. If x “ and y “ are both odd or both even , Receiver extracts b = 0 and recover x’ = x” and y’ = y”if not, extracts b = 1 and recovers x’ = x”-1 and y’ = y” since b is only embedded into the first pixelReceiver can easily compute and and obtain the original pixel pair of CI by computing and At the end, this step will output SM and recovers CI

new EIRDH-P -> Algorithm -> Extracting

y” x” Extract y‘ x‘Stego Image

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new EIRDH-P

7. Receiver obtains the pure message M by using sk to decrypt SM

new EIRDH-P -> Algorithm -> Message Dec

y‘ x‘ Recover y xStego Image

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new EIRDH-Pnew EIRDH-P -> Schematic

Cover Image

Pre Process Encrypt

Enc Image

[[y‘]] [[x‘]][[y”]] [[x”]] EmbedIf bit = 1 , , If bit = 0 , ,

[[y”]] [[x"]]

Dec

y “ x “Stego Image

Extract y‘ x‘ Recover

, ,

P

H

R

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Question ?

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Thanks