Further enhance and add in some layering with enhancements.

```
import numpy as np
import random
import cmath

# Key expansion function (elliptic curve-like)
def elliptic_key_expansion(key):
    """
    Performs an elliptic curve-like expansion of the key to generate multiple subkeys.
    This is a placeholder implementation for demonstration purposes.
    """
    subkeys = []
    # Example of key expansion logic: bitwise rotations and XOR operations
    for i in range(10):
        # Rotate key bits
        rotated_key = ((key << (i + 1)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) | (key >> (128 - (i + 1)))
        # XOR with a prime number sequence
        subkey = rotated_key ^ (0x9E3779B97F4A7C15 * (i + 1))
        subkey = subkey & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF  # Ensure subkey is 128-bit
        subkeys.append(subkey)
    return subkeys

# Complex Mix function
def complex_mix(matrix, subkey):
    """
    Applies non-linear transformations to the complex matrix using trigonometric functions.
    """
    key_real = (subkey >> 64) & 0xFFFFFFFFFFFFFFFF
    key_imag = subkey & 0xFFFFFFFFFFFFFFFF
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            real_part = np.sin(matrix[i][j].real + key_real)
            imaginary_part = np.cos(matrix[i][j].imag + key_imag)
            matrix[i][j] = complex(real_part, imaginary_part)
    return matrix

# Complex Shift function
def complex_shift(matrix, shift_val):
    """
    Shifts rows and columns of the matrix based on a key-derived shift value.
    """
    # Shift rows
    matrix = np.roll(matrix, shift=shift_val, axis=0)
    # Shift columns
    matrix = np.roll(matrix, shift=shift_val, axis=1)
    return matrix

# Complex Substitution function (S-box-like)
def complex_substitution(matrix):
    """
    Substitutes real and imaginary parts based on a predefined complex substitution table.
    For demonstration, we'll invert the values.
    """
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            real_part = 1 / matrix[i][j].real if matrix[i][j].real != 0 else 0
            imaginary_part = 1 / matrix[i][j].imag if matrix[i][j].imag != 0 else 0
            matrix[i][j] = complex(real_part, imaginary_part)
    return matrix

# Key Mixing function
def key_mixing(matrix, subkey):
    """
    Mixes the matrix with the subkey using XOR-like operations.
    """
    key_real = (subkey >> 64) & 0xFFFFFFFFFFFFFFFF
    key_imag = subkey & 0xFFFFFFFFFFFFFFFF
    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            real_part = matrix[i][j].real ^ key_real
            imaginary_part = matrix[i][j].imag ^ key_imag
            matrix[i][j] = complex(real_part, imaginary_part)
    return matrix

# Encryption function
def sid_encrypt(plaintext, key):
    """
    Encrypts the given plaintext using the SID algorithm with the provided key.
    """
    # Determine block size (e.g., 4x4 matrix)
    block_size = 4
    total_chars = block_size * block_size
    # Pad plaintext to fit the block size
    if len(plaintext) < total_chars:
        plaintext += ' ' * (total_chars - len(plaintext))
    elif len(plaintext) > total_chars:
        raise ValueError(f"Plaintext length should be {total_chars} characters.")
    
    # Convert plaintext to complex numbers
    complex_matrix = np.zeros((block_size, block_size), dtype=complex)
    
    # Seed the random number generator with the key for reproducibility
    random.seed(key)
    # Populate matrix with complex numbers (real part: ASCII, imaginary part: PRNG)
    for i, char in enumerate(plaintext):
        row, col = divmod(i, block_size)
        real_part = ord(char)
        imaginary_part = random.randint(1, 255)  # 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) % block_size)
        complex_matrix = complex_substitution(complex_matrix)
        complex_matrix = key_mixing(complex_matrix, subkeys[round_num])
    
    # Convert matrix back to ciphertext
    ciphertext = ""
    auth_tag = ""
    for i in range(complex_matrix.shape[0]):
        for j in range(complex_matrix.shape[1]):
            # Real part to ASCII character (modulo 256 to fit into byte range)
            real_value = int(abs(complex_matrix[i][j].real)) % 256
            ciphertext += chr(real_value)
            # Imaginary part to create an authentication tag
            imag_value = int(abs(complex_matrix[i][j].imag)) % 256
            auth_tag += chr(imag_value)
    
    return ciphertext, auth_tag

# Example execution
if __name__ == "__main__":
    plaintext = "HelloWorld1234 "  # 16 characters to fit into 4x4 matrix
    key_text = "0x1A2B3C4D5E6F7A8B9C0D1E2F3A4B5C6"  # Example 128-bit key
    key = int(key_text, 16)
    ciphertext, auth_tag = sid_encrypt(plaintext, key)
    print(f"Plaintext: {plaintext}")
    print(f"Key: {key_text}")
    print(f"Ciphertext: {ciphertext}")
    print(f"Auth Tag: {auth_tag}")