Data Embedding in Digital Media

Optimal Spread-Spectrum and Least-Significant-Bit Methods

Connor Weeks

Email: crweeks@knox.edu

Project Summary

• Steganography
• Digital Steganography
• Least-Significant Bit Method
• Optimal Spread Spectrum Method

OSS Algorithm Summary

Process flow showing binary data 01010001011 going through three stages:

1. Transmission
2. Embedding
3. Recovery

Math

1. Auto-Correlation Matrix
2. Calculate Eigenvectors and Values
3. Calculate S_opt and C_opt
4. Calculate A values
5. Calculate Projection Matrix

Embedding Equation

Y = SAB + TX + N

• Output Pattern
• Amplification
• Hidden bits
• Projection Matrix
• Transformed Image
• Noise

Equations:

R = TX*TX'/size(TX,2)

[Q,lambda]=eigsort(R)

S_opt = Q(1:k)

C_opt(k)=(lam(k)+sigma^2+D-sqrt((lam(k)+sigma^2+D)^2-4*lam(k)*D))/(2*lam(k))

A(k)=sqrt(D-c(k)^2*lam(k))

T=eye(L)-S*C*S'

Comparison

Optimal Spread Spectrum

• Works with lossy compression
• Harder to detect with steganalysis
• Works with additive noise

Least Significant Bit Replacement

• No bit errors (lossless compression)
• 4-12 times more storage
• No recovery key
• Computationally faster
• Less distortion

References

M. Gkizeli, D. A. Pados, and M. J. Medley, "Optimal signature design for spread-spectrum steganography," IEEE Trans. Image Process., vol. 16, pp. 391-405, Feb. 2007.

Ming Li, Ngwe Thawdar, Dimitris A. Pados, Stella N. Batalama, and Michael J. Medley, "Minimum-Distortion Data Embedding in Video Streams" IEEE ICC 2014.

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