FFT-Based Watermark Embedding with SHA-256, Ed25519 and Reed-Solomon
Multimedia Forensics & Cryptography Project Amrita Vishwa Vidyapeetham
| Name | Roll Number |
|---|---|
| Ishwarya M | CB.SC.U4AIE24220 |
| Himavarshini K | CB.SC.U4AIE24228 |
| Meghana Kotharu | CB.SC.U4AIE24232 |
| Ranjith Raja B | CB.SC.U4AIE24250 |
- Overview
- System Architecture
- Methodology
- Implementation
- Results
- Performance Summary
- Execution Time
- Platform Information
- Conclusion
- References
The rapid growth of digital multimedia distribution has increased the risk of unauthorized duplication, tampering, and redistribution of audio content. Digital watermarking provides a mechanism to embed hidden information inside audio signals for purposes such as copyright protection, authentication, and tamper detection.
This project implements a secure audio watermarking framework that combines signal processing with modern cryptographic techniques.
The system integrates:
- SHA-256 cryptographic hashing
- Ed25519 digital signature verification
- Reed-Solomon error correction
- Spread-spectrum FFT watermark embedding
The watermark carries a cryptographically signed identity of the audio allowing both ownership verification and tamper detection.
The complete watermarking system follows a 7-stage pipeline.
Audio Input
↓
Preprocessing
↓
SHA-256 Hash Generation
↓
Ed25519 Signature
↓
Payload Construction
↓
Reed-Solomon Encoding
↓
FFT Watermark Embedding
↓
Watermarked Audio
The watermarking framework consists of two phases:
- Watermark Embedding
- Watermark Detection and Verification
The input audio signal is converted into a canonical form to ensure deterministic hashing.
Steps:
- Convert audio to mono
- Resample to 44.1 kHz
- Normalize amplitude to [-1,1]
- Divide signal into frames
Frame segmentation:
[ x_k[n] = x[n + kL] ]
Where
| Symbol | Meaning |
|---|---|
| (x[n]) | audio signal |
| (L) | frame length |
| (k) | frame index |
The canonical audio signal is converted into a byte stream and a SHA-256 hash is computed.
[ H = SHA256(audio) ]
This hash uniquely represents the audio content.
To provide authenticity, the generated hash is signed using the Ed25519 digital signature scheme.
[ S = Sign_{private}(H) ]
The signature allows any receiver to verify the authenticity of the watermark.
The watermark payload consists of the following fields.
| Field | Size |
|---|---|
| MAGIC | 4 bytes |
| VERSION | 1 byte |
| OWNER ID | 8 bytes |
| SHA-256 HASH | 32 bytes |
| ED25519 SIGNATURE | 64 bytes |
Total payload: 109 bytes
To improve robustness, the payload is encoded using Reed-Solomon RS(159,109).
| Parameter | Value |
|---|---|
| Message size | 109 bytes |
| Encoded size | 159 bytes |
| Parity symbols | 50 |
Reed-Solomon can correct up to 25 byte errors during watermark extraction.
The audio is divided into frames of length 4096 samples.
For each frame:
- Compute FFT
- Select mid-frequency band (1–8 kHz)
- Generate pseudo-random spreading sequence
- Modulate watermark bits
Embedding equation:
[ X'_k[m] = X_k[m] (1 + \alpha w_i) ]
| Symbol | Meaning |
|---|---|
| (X_k[m]) | FFT coefficient |
| (w_i) | watermark bit |
| (\alpha) | embedding strength |
Detection involves the reverse process:
- Frame synchronization
- FFT computation
- Correlation detection
- Reed-Solomon decoding
- Signature verification
Final verification:
[ Verify_{public}(S,H) = True ]
Language used: Python
Libraries used: numpy scipy librosa reedsolo pynacl matplotlib
The implementation is modular and consists of:
| Module | Function |
|---|---|
| preprocessing | audio normalization |
| hashing | SHA-256 generation |
| signature | Ed25519 signing |
| payload | payload construction |
| rs_codec | Reed-Solomon encoding |
| embedder | FFT watermark embedding |
| detector | watermark extraction |
The figure shows the waveform and frequency spectrum of the signal used during watermark embedding.
The embedding stage inserts watermark bits into mid-frequency FFT coefficients using spread-spectrum modulation.
The watermark detector extracts the embedded bits using correlation detection followed by Reed-Solomon decoding and signature verification.
The watermark is tested under various signal distortions including noise addition and synchronization shifts.
This figure summarizes watermark performance across different datasets and attack conditions.
| Dataset | Detection Result |
|---|---|
| Noise Dataset |  |
| Harvard Dataset |  |
| Collectathon Dataset | |
| Dataset | Attack Results |
|---|---|
| Noise Dataset |  |
| Harvard Dataset |  |
| Collectathon Dataset | |
| Metric | Value |
|---|---|
| SNR | > 35 dB |
| BER | < 0.02 |
| Payload | 109 bytes |
| Encoded payload | 159 bytes |
| Detection accuracy | ~97% |
| Stage | Time |
|---|---|
| Audio preprocessing | 0.21 s |
| SHA-256 hashing | 0.05 s |
| Signature generation | 0.04 s |
| Reed-Solomon encoding | 0.07 s |
| FFT embedding | 0.52 s |
| Detection | 0.48 s |
| Total time | 1.37 s |
| Parameter | Value |
|---|---|
| Platform | Laptop |
| Language | Python |
| Hardware | CPU |
| GPU | Nvidia RTX 4070 |
| Processor | Intel i9 |
| RAM | 16 GB |
| Stage | Time |
|---|---|
| Audio preprocessing | 0.21 s |
| SHA-256 hashing | 0.05 s |
| Signature generation | 0.04 s |
| Reed-Solomon encoding | 0.07 s |
| FFT embedding | 0.52 s |
| Detection | 0.48 s |
| Total time | 1.37 s |
This project demonstrates a secure and robust audio watermarking framework that integrates signal processing with modern cryptographic authentication.
The combination of FFT-based embedding, Reed-Solomon error correction, and Ed25519 digital signatures ensures:
high perceptual transparency
reliable watermark recovery
strong authenticity verification
The proposed framework can be applied in digital rights management, multimedia authentication, and secure content distribution systems.
Santin-Cruz, C., Dolecek, G. Audio Watermarking: Review, Analysis and Classification Applied Sciences, 2025
Cox, I., Miller, M., Bloom, J. Digital Watermarking and Steganography
Wu, S., Liu, J. Recent Advances in Audio Watermarking IEEE Transactions on Multimedia