Generate an advanced python script that envelops this idea:

### Super Imaginary Digits (SID) - A Hypothetical Cryptography Algorithm

The "Super Imaginary Digits" (SID) algorithm is an advanced encryption system that leverages both imaginary numbers (complex numbers) and multi-dimensional transformations to provide high-security encryption. This system operates under the assumption of using complex-number-based transformations, making it resistant to classical approaches like brute-force attacks, as well as to quantum computing advancements.

Below is a detailed description of the SID algorithm, which incorporates multiple cryptographic techniques, including:

- **Complex number transformations**: Imaginary and real components.
- **Multi-dimensional matrices**: Transforming plaintext into complex matrix representations.
- **Elliptic curve-like transformations**: For key generation.
- **Layered encryption rounds**: Inspired by block cipher designs like AES.

### Components of SID

1. **Complex Number Encoding**:
   - Each ASCII character in the plaintext string is encoded as a complex number.
   - Real part: ASCII value of the character.
   - Imaginary part: A pseudo-random number generated based on the key (e.g., using a PRNG).

2. **Key Generation**:
   - The key is a high-dimensional vector (e.g., 128-bit, 192-bit, or 256-bit) that is used to generate pseudo-random numbers for the imaginary parts.
   - The key undergoes elliptic-curve-like transformations to generate several subkeys for multiple encryption rounds.

3. **Matrix Transformation**:
   - The complex number representations of the characters are placed into a matrix (e.g., 4x4 or 8x8, depending on the block size).
   - A series of matrix transformations are applied to the complex matrix (e.g., rotations, transpositions, and complex conjugate operations).

4. **Multi-Round Encryption**:
   - Similar to AES, SID performs multiple rounds of transformations, including:
     - **Complex Mix**: A mixing function that blends the real and imaginary components using non-linear functions (e.g., sine/cosine transformations).
     - **Complex Shift**: Shifts matrix elements based on key-dependent offsets.
     - **Complex Substitution**: Similar to S-boxes in AES, but operates on both the real and imaginary components using a complex substitution table.
     - **Key Mixing**: XOR-like operations between the matrix and subkeys.

5. **Final Transformation**:
   - After multiple rounds of transformations, the matrix is flattened back into a sequence of complex numbers.
   - The real and imaginary parts are separated, and the real parts are converted back into ASCII characters (the ciphertext).
   - The imaginary parts are used as part of an additional authentication tag (similar to a MAC), ensuring integrity.

### Pseudocode for SID Algorithm

```python
import numpy as np
import random
import cmath

# Key expansion function (elliptic curve-like)
def elliptic_key_expansion(key):
    # Placeholder for elliptic curve-like expansion of the key
    # Generates multiple subkeys from the original key
    subkeys = [key ^ (i + 1) for i in range(10)]  # Example logic
    return subkeys

# Complex Mix and Shift functions
def complex_mix(matrix, subkey):
    # Apply non-linear transformations to the complex matrix
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            real_part = np.sin(matrix[i][j].real + subkey)
            imaginary_part = np.cos(matrix[i][j].imag + subkey)
            matrix[i][j] = complex(real_part, imaginary_part)
    return matrix

def complex_shift(matrix, shift_val):
    # Shift rows and columns based on a key-derived shift value
    return np.roll(matrix, shift_val, axis=0)

# Complex Substitution function (S-box-like)
def complex_substitution(matrix):
    # Substitute real and imaginary parts based on a predefined table
    # Placeholder logic: conjugate each element
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            matrix[i][j] = np.conjugate(matrix[i][j])
    return matrix

# Encryption function
def sid_encrypt(plaintext, key):
    # Convert plaintext to complex numbers
    complex_matrix = np.zeros((4, 4), dtype=complex)
    
    # Populate matrix with complex numbers (real part: ASCII, imaginary part: PRNG)
    for i, char in enumerate(plaintext):
        row, col = divmod(i, 4)
        real_part = ord(char)
        imaginary_part = random.randint(1, 255)  # Example PRNG for imaginary part
        complex_matrix[row][col] = complex(real_part, imaginary_part)
    
    # Key expansion
    subkeys = elliptic_key_expansion(key)
    
    # Multiple rounds of encryption
    for round_num in range(10):
        complex_matrix = complex_mix(complex_matrix, subkeys[round_num])
        complex_matrix = complex_shift(complex_matrix, (round_num + 1) % 4)
        complex_matrix = complex_substitution(complex_matrix)
    
    # Convert matrix back to ciphertext
    ciphertext = ""
    for i in range(complex_matrix.shape[0]):
        for j in range(complex_matrix.shape[1]):
            ciphertext += chr(int(complex_matrix[i][j].real) % 256)  # Convert real part back to ASCII
    
    return ciphertext

# Example execution
plaintext = "HelloWorld1234"
key = 0x1A2B3C4D5E6F7A8B  # Example key
ciphertext = sid_encrypt(plaintext, key)
print(f"Ciphertext: {ciphertext}")
```

### Detailed Steps of the Algorithm

1. **Plaintext Encoding**: The input plaintext is encoded into a matrix of complex numbers, where the real part is the ASCII value of the character, and the imaginary part is a random value derived from a key-dependent PRNG.

2. **Key Expansion**: The key undergoes an elliptic curve-like expansion to generate multiple subkeys. These subkeys are used in each round of the encryption process.

3. **Rounds of Transformations**:
   - **Complex Mix**: Non-linear transformations using trigonometric functions are applied to the real and imaginary components of each complex number in the matrix.
   - **Complex Shift**: The matrix is shifted both row-wise and column-wise based on the round number and subkey.
   - **Complex Substitution**: A complex conjugate operation is applied to each matrix element to further obfuscate the data.

4. **Final Ciphertext**: After the encryption rounds, the matrix is flattened, and the real parts of the complex numbers are converted back to ASCII characters to form the ciphertext.

### Security Considerations

- **Resistance to Quantum Attacks**: By leveraging complex numbers and elliptic curve-like key expansion, SID is designed to be resistant to both classical and quantum attacks.
- **High Entropy**: The use of imaginary parts (pseudo-random numbers) adds significant entropy to the encryption process, making it difficult for attackers to predict the structure of the ciphertext.
- **Multi-dimensional Transformations**: SID operates on multi-dimensional matrices, making it more complex than traditional block ciphers.

### Conclusion

The **Super Imaginary Digits (SID)** algorithm is a theoretical encryption method that combines advanced mathematical concepts with traditional cryptographic techniques. Its use of complex numbers, matrix transformations, and elliptic curve-like key generation offers a novel approach to encryption, though its practicality and security would need rigorous testing and academic review before real-world implementation.