In our journey through coverless steganography, we first explored CIHMSB —a method that hides data by matching message bits to the average intensity of image fragments. While perfect in its invisibility, CIHMSB faces a significant hurdle: capacity. Using only one bit per fragment limits how much data we can hide in a single image.
Today, we are looking at two advanced extensions that shatter these capacity limits: E-CIHMSB and CB-CIHMSB. By applying matrix extensions and combination theory, we can pack significantly more data into the same carrier while actually improving robustness against image attacks.
Academic Attribution 📚
This implementation and analysis are based on the 2023 research paper:
"A Robust and High-Capacity Coverless Information Hiding Based on Combination Theory" by Kurnia Anggriani, Shu-Fen Chiou, Nan-I Wu, and Min-Shiang Hwang.
DOI: https://doi.org/10.15388/23-INFOR521.
🚀 The Next Evolution: Two Powerful Extensions
The researchers identified that the original CIHMSB only embeds one bit per segment, making it inefficient for large messages. They proposed two solutions:
1. E-CIHMSB (Extended CIHMSB)
This scheme builds an "Extended Matrix". After calculating the average pixel values for all fragments in a group, it adds one extra value: the average of all those averages. This simple mathematical addition increases the bit pool for every image carrier.
2. CB-CIHMSB (Combination Theory-Based)
This is the true heavy-lifter. Instead of just adding one value, it uses combination theory to create a "Combined Matrix". If you have a group of n fragments, it calculates the averages for every possible combination of those fragments (choosing 1, 2, 3, or all n).
The capacity growth is exponential: EC = 2^n - 1. For a group of 4 fragments, you generate 15 feature values instead of just 4!
🧪 Benchmark: Performance Comparison
To see these algorithms in action, I ran a full experimental benchmark on a 512x512 carrier image using 8x8 fragments. Here are the real-world results:
1. Image Quality Assessment
As these are coverless methods, the image itself is never modified.
SSIM: 1.0 (Perfect match)
Qi: 1.0 (Optimal quality)
2. Hiding Capacity (512x512 Carrier)
| Method | Bits per Carrier | Improvement |
|---|---|---|
| Original CIHMSB | 16,384 bits | Baseline |
| E-CIHMSB | 20,480 bits | +25% |
| CB-CIHMSB | 61,440 bits | +275% |
3. Robustness Analysis (BER)
Bit Error Rate (BER) measures how many bits were lost during a transmission attack. Lower is better.
| Attack Type | E-CIHMSB BER | CB-CIHMSB BER |
|---|---|---|
| AGWN (Var 0.1) | 16.07% | 7.14% |
| SPN (Dens 0.005) | 5.36% | 1.79% |
| AF (3x3 Window) | 12.50% | 8.93% |
| JPEG (Quality 50-90) | 1.79% - 5.36% | 0.00% (Perfect) |
🔍 Why is CB-CIHMSB the Clear Winner?
Looking at the benchmark data, CB-CIHMSB is superior for two main reasons:
- Massive Capacity: It offers 275% more capacity than the original method. You can hide an entire secret document where you previously could only hide a short paragraph.
- Superior Robustness: Notice the JPEG compression results. While E-CIHMSB suffered some errors, CB-CIHMSB achieved a 0.00% Bit Error Rate. Because it averages multiple combinations of fragments, the secret features become more "stable" and resistant to pixel-level distortions like JPEG artifacts or blurring.
🎯 Conclusion
The research by Anggriani et al. proves that coverless steganography does not have to be low-capacity. By shifting from linear fragment matching to combinatorial logic, we can hide massive amounts of data with zero pixel manipulation. This makes it impossible for standard steganalysis tools to detect anything—because mathematically, there is nothing "embedded" in the pixels.
Check out the full modular Python implementation on my GitHub! https://github.com/Anjasfedo/ecihmsb_cbcihmsb