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# Steganography with Public-Key Cryptography for borges/doc/Steganography with Public... Steganography

Jul 23, 2020

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• Steganography with Public-Key Cryptography for Videoconference

XXX CNMAC - Set/2007

Fábio Borges de Oliveira

Steganography with Public-Key Cryptography for Videoconference – p.1/26

http://www.lncc.br/~borges

• Steganography Source:

Steganography:

Steganography with Public-Key Cryptography for Videoconference – p.2/26

• Why do we need to use it?

1. The enemy could interrupt the message

2. There is the Shor’s quantum algorithm that can factor huge numbers quickly O(n3)

3. Someone might find a way to break the cryptosystem

Steganography with Public-Key Cryptography for Videoconference – p.3/26

• Symmetric

Ana BethEdna

Secure Channel

Steganography with Public-Key Cryptography for Videoconference – p.4/26

• Asymmetric

Edna Ana Beth

Steganography with Public-Key Cryptography for Videoconference – p.5/26

• RSA

ϕ = ϕ(pq) = (p − 1)(q − 1) Choose a so that gcd(a, ϕ) = 1

ab ≡ 1 mod ϕ.

xab ≡ x mod pq ∀x ∈ Z.

Steganography with Public-Key Cryptography for Videoconference – p.6/26

• Diffie-Hellman Alice chooses k with gcd(k, pq) = 1 and sends the values of k and pq. Then, Alice chooses a r, computes kr and sends the result to Bob while keeping r secret. At the same moment Bob chooses s, computes ks and sends the result to Alice while keeping s secret. So, both form the candidate exponent

a = (kr)s = (ks)r.

To verify if a is a valid RSA exponent, Alice computes gcd(a, ϕ) = 1. If a is not valid they repeat the process.

Steganography with Public-Key Cryptography for Videoconference – p.7/26

• Key agreement

Diffie-Hellman

ElGamal

Menezes-Vanstone Discrete Logarithmic Problem

Steganography with Public-Key Cryptography for Videoconference – p.8/26

• Steganography and Public-key

Steganography using public-key cryptography

cannot use a static media, like an image, but it

requires a data stream, like a dialog.

Steganography with Public-Key Cryptography for Videoconference – p.9/26

• Videoconference

We have the option to use the sound or the video

We chose the ITU-T H263 - video codec protocol

An H263 video stream contains I-frame, P-frame and B-frame

Hiding in a sequence of JPEG

Steganography with Public-Key Cryptography for Videoconference – p.10/26

• Spatial domain

For every 8 bits.

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Spatial domain

Bit position: 12345678

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Spatial domain

Bit position: 12345678

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Spatial domain

Bit position: 12345678

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Spatial domain

Bit position: 12345678

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Spatial domain

Bit position: 12345678

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Spatial domain

Bit position: 12345678

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Spatial domain

Bit position: 12345678

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Spatial domain

Bit position: 12345678

Steganography with Public-Key Cryptography for Videoconference – p.11/26

• Visual attack

Steganography with Public-Key Cryptography for Videoconference – p.12/26

• Steganographic scheme in JPEG

Steganography

Bl oc

k 8 x8

JPEG

Entropy EncoderQuantizerDCT

DequantizerInverse DCT Entropy Decoder

Image

Input

Output

Steganography with Public-Key Cryptography for Videoconference – p.13/26

• Discrete Cosine Transform (DCT)

F [m,n] = C(m)

2

C(n)

2

7 ∑

x=0

7 ∑

y=0

P [x, y] cos α cos β,

α = (2x + 1)mπ

16 ,

β = (2y + 1)nπ

16

C(k) =

{

1√ 2

for k = 0,

1 for all other values of k.

Steganography with Public-Key Cryptography for Videoconference – p.14/26

• The quantization

F ′[m,n] = F [m,n]

Q[m,n]

Steganography with Public-Key Cryptography for Videoconference – p.15/26

• Pixel matrix P

P =

0 0 0 200 200 0 0 0

0 0 200 200 200 200 0 0

0 200 200 200 200 200 200 0

200 200 200 200 200 200 200 200

200 200 200 200 200 200 200 200

0 200 200 200 200 200 200 0

0 0 200 200 200 200 0 0

0 0 0 200 200 0 0 0

Steganography with Public-Key Cryptography for Videoconference – p.16/26

• Quantization matrix Q

Q =

6 11 16 21 26 31 36 41

11 16 21 26 31 36 41 46

16 21 26 31 36 41 46 51

21 26 31 36 41 46 51 56

26 31 36 41 46 51 56 61

31 36 41 46 51 56 61 66

36 41 46 51 56 61 66 71

41 46 51 56 61 66 71 76

Steganography with Public-Key Cryptography for Videoconference – p.17/26

• Consider the matrices

A that has not suffered steganography

B that has changed in every second LSB of coefficients AC, whose modulus is greater than two

C that has changed only the second LSB of F ′[0, 2]

D that has changed the LSB of AC, whose modulus is greater than one

Steganography with Public-Key Cryptography for Videoconference – p.18/26

• Euclidian distance

|P − A| = 35.60898762 |P − B| = 200.2698180 |P − C| = 48.98979486 |P − D| = 106.5833008

Steganography with Public-Key Cryptography for Videoconference – p.19/26

• Matrix A without steganography

Steganography with Public-Key Cryptography for Videoconference – p.20/26

• Matrix B with aggressive settings

Steganography with Public-Key Cryptography for Videoconference – p.21/26

• Matrix C no aggressive settings

Steganography with Public-Key Cryptography for Videoconference – p.22/26

• Matrix D with aggressive settings

Steganography with Public-Key Cryptography for Videoconference – p.23/26

• The protocol

1. the position of the sequence of bits previously agreement to establish communication in a videoconference,

2. steganography more secure,

3. Diffie-Hellman key agreement,

4. RSA to exchange an irrational number generator,

5. strong cryptography based on irrational numbers.

Steganography with Public-Key Cryptography for Videoconference – p.24/26

• Conclusion

We have introduced a model for steganocryptography

First of all we revised the RSA, Diffie-Hellman and JPEG’s compression

Our contribution is showing the viability to embed in others LSB

It brings an extra-layer of security

Steganography with Public-Key Cryptography for Videoconference – p.25/26

• Last Slide

Thank you.

Any suggestions will be welcome.

www.lncc.br/borges Fábio Borges de Oliveira

Steganography with Public-Key Cryptography for Videoconference – p.26/26

http://www.lncc.br/~borges http://www.lncc.br/~borges

Steganography Why do we need to use it? Symmetric Asymmetric RSA Diffie-Hellman Key agreement Steganography and Public-key Videoconference Spatial domain Visual attack Steganographic scheme in JPEG Discrete Cosine Transform (DCT) The quantization Pixel matrix \$P\$ Quantization matrix \$Q\$ Consider the matrices Euclidian distance Matrix A without steganography Matrix B with aggressive settings Matrix C no aggressive settings Matrix D with aggressive settings The protocol Conclusion Last Slide

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