Untitled

To decode the message embedded using DCT-based steganography, you need to reverse the process of encoding. This involves:

1. **Reading the Image**: Load the image and extract the pixel data using `libpng`.
2. **Apply DCT**: Apply the Discrete Cosine Transform (DCT) to each 8x8 block of the image to get the frequency domain coefficients.
3. **Extract the Message**: Retrieve the embedded message from the DCT coefficients by checking the modifications (e.g., least significant bits).
4. **Reconstruct the Message**: Collect the bits extracted from each block and reconstruct the original message.

Here's an example implementation of how to decode the message embedded in a PNG image using the DCT-based method in C:

### 1. **Read the Image and Extract DCT Coefficients**

You will first need to read the PNG image into memory and apply the DCT to extract the coefficients.

### 2. **Extract the Message**

Using the same blocks you used for embedding the message, retrieve the bits of the hidden message. 

### Example Code to Decode the Message

This code assumes the message was embedded by modifying the least significant bit (LSB) of certain DCT coefficients.

#### 1. **Extract DCT Coefficients**
To extract the coefficients from the DCT-transformed image:

```c
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <png.h>
#include <string.h>

#define BLOCK_SIZE 8
#define PI 3.14159265358979323846

void perform_dct(double block[BLOCK_SIZE][BLOCK_SIZE]) {
    double temp[BLOCK_SIZE][BLOCK_SIZE];
    double alpha, beta, sum;
    int u, v, x, y;

    for (u = 0; u < BLOCK_SIZE; ++u) {
        for (v = 0; v < BLOCK_SIZE; ++v) {
            sum = 0.0;
            for (x = 0; x < BLOCK_SIZE; ++x) {
                for (y = 0; y < BLOCK_SIZE; ++y) {
                    sum += block[x][y] * 
                           cos((2 * x + 1) * u * PI / 16.0) * 
                           cos((2 * y + 1) * v * PI / 16.0);
                }
            }

            alpha = (u == 0) ? 1 / sqrt(2.0) : 1.0;
            beta = (v == 0) ? 1 / sqrt(2.0) : 1.0;
            temp[u][v] = 0.25 * alpha * beta * sum;
        }
    }

    // Copy temp back to block
    for (x = 0; x < BLOCK_SIZE; ++x) {
        for (y = 0; y < BLOCK_SIZE; ++y) {
            block[x][y] = temp[x][y];
        }
    }
}
```

#### 2. **Extract the Message**
Extract the message bits from the DCT coefficients:

```c
void extract_message(double dct_block[BLOCK_SIZE][BLOCK_SIZE], char *message, int *msg_index, int *bit_index) {
    for (int u = 0; u < BLOCK_SIZE; ++u) {
        for (int v = 0; v < BLOCK_SIZE; ++v) {
            if (*msg_index < 1024) { // Assuming a maximum of 1024 characters for simplicity
                int bit = (dct_block[u][v] > 0) ? 1 : 0; // Assuming we embedded in the LSB
                message[*msg_index] |= bit << (*bit_index);
                (*bit_index)++;
                if (*bit_index == 8) {
                    (*bit_index) = 0;
                    (*msg_index)++;
                }
            }
        }
    }
}
```

#### 3. **Process the Image to Extract Message**
Read the image and extract the message:

```c
void process_image_for_extraction(const char *input_file) {
    FILE *fp = fopen(input_file, "rb");
    if (!fp) {
        perror("File opening failed");
        return;
    }

    png_structp png = png_create_read_struct(PNG_LIBPNG_VER_STRING, NULL, NULL, NULL);
    if (!png) {
        fclose(fp);
        return;
    }

    png_infop info = png_create_info_struct(png);
    if (!info) {
        png_destroy_read_struct(&png, NULL, NULL);
        fclose(fp);
        return;
    }

    if (setjmp(png_jmpbuf(png))) {
        png_destroy_read_struct(&png, &info, NULL);
        fclose(fp);
        return;
    }

    png_init_io(png, fp);
    png_read_info(png, info);

    int width = png_get_image_width(png, info);
    int height = png_get_image_height(png, info);
    png_bytep row_pointers[height];
    for (int y = 0; y < height; y++) {
        row_pointers[y] = (png_bytep) malloc(png_get_rowbytes(png, info));
    }
    png_read_image(png, row_pointers);

    fclose(fp);

    char message[1024] = {0}; // Buffer for the message
    int msg_index = 0;
    int bit_index = 0;

    // Process each 8x8 block
    for (int i = 0; i < height; i += BLOCK_SIZE) {
        for (int j = 0; j < width; j += BLOCK_SIZE) {
            double block[BLOCK_SIZE][BLOCK_SIZE];
            for (int x = 0; x < BLOCK_SIZE; ++x) {
                for (int y = 0; y < BLOCK_SIZE; ++y) {
                    if (i + x < height && j + y < width) {
                        block[x][y] = row_pointers[i + x][j + y];
                    } else {
                        block[x][y] = 0; // Zero-padding for edge cases
                    }
                }
            }
            perform_dct(block);
            extract_message(block, message, &msg_index, &bit_index);
        }
    }

    // Null-terminate the extracted message
    message[msg_index] = '\0';
    printf("Extracted message: %s\n", message);

    // Free memory
    for (int y = 0; y < height; y++) {
        free(row_pointers[y]);
    }
    png_destroy_read_struct(&png, &info, NULL);
}
```

#### 4. **Putting It All Together**
Create a `main` function to execute the decoding process:

```c
int main() {
    const char *input_file = "output.png";

    process_image_for_extraction(input_file);

    return 0;
}
```

### Compilation
Ensure you link against `libpng` and `math` libraries when compiling:

```bash
gcc dct_steganography_decode.c -lpng -lm -o dct_steganography_decode
```

### Explanation
1. **DCT Transformation**: The DCT is applied to each 8x8 block to get the frequency coefficients.
2. **Message Extraction**: The code assumes the message bits were embedded in the DCT coefficients. It extracts these bits by checking the coefficients' values.
3. **Reconstructing the Message**: Collects bits from all blocks to reconstruct the message.

### Notes
- **Message Length**: For simplicity, this example assumes the message fits within a fixed size. For variable-length messages, include length metadata during encoding.
- **Error Handling**: The implementation lacks detailed error handling and boundary checks.
- **Steganography Limits**: The effectiveness of this approach depends on the image and the amount of data being embedded.

This example demonstrates basic DCT-based steganography decoding in a PNG image. You can expand on this with better error handling and message length encoding.