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Steganography with Public-KeyCryptography for Videoconference

XXX CNMAC - Set/2007

Fábio Borges de Oliveira

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

SteganographySource:

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 thatcan factor huge numbers quickly O(n3)

3. Someone might find a way to break thecryptosystem

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

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

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

To verify if a is a valid RSA exponent, Alicecomputes gcd(a, ϕ) = 1. If a is not valid theyrepeat the process.

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

Key agreement

Diffie-Hellman

ElGamal

Menezes-VanstoneDiscrete 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 thevideo

We chose the ITU-T H263 - video codecprotocol

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

Block 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 ofcoefficients AC, whose modulus is greaterthan two

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

D that has changed the LSB of AC, whosemodulus 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

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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 previouslyagreement to establish communication in avideoconference,

2. steganography more secure,

3. Diffie-Hellman key agreement,

4. RSA to exchange an irrational numbergenerator,

5. strong cryptography based on irrationalnumbers.

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

Conclusion

We have introduced a model forsteganocryptography

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

Our contribution is showing the viability toembed 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/borgesFábio Borges de Oliveira

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