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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