1. Generate the Chaotic Sequence:

• Use a chaotic map (e.g., Logistic map, Tent map, etc.) to generate the chaotic sequence. Chaotic sequences are sensitive to initial conditions and parameters, so choose your initial values and parameters carefully.
• For instance, the Logistic map is defined by the equation: xn+1=r⋅xn⋅(1−xn)x_{n+1} = r \cdot x_n \cdot (1 - x_n)xn+1​=r⋅xn​⋅(1−xn​) where rrr is the control parameter, and xnx_nxn​ is the sequence value at iteration nnn.

2. Normalize the Sequence:

• The generated chaotic sequence usually takes values in the range [0, 1] or [-1, 1]. Normalize the sequence to fit within the range of 0 to 1 if needed.

3. Convert the Sequence to a Bit Stream:

• Convert the chaotic sequence into a binary bit stream. If you need 10-bit values, you can map the normalized chaotic sequence to 10-bit integers (0 to 1023).
• For each value xnx_nxn​ in the sequence: bn=int(xn×1024)b_n = \text{int}(x_n \times 1024)bn​=int(xn​×1024) where b_n is the 10-bit representation of the chaotic sequence value.

4. Concatenate the Bit Stream:

• Concatenate the binary representation of each b_n to form a bit stream.
• Ensure that each sequence is of length 1,000,000 bits. You might need to repeat or truncate the sequence accordingly.

5. Repeat for Multiple Sequences:

• Repeat the above steps to generate multiple (e.g., 10) bit streams, each of length 1,000,000 bits, for testing.

Example in Python:--------------------------------------------------------

import numpy as np

def logistic_map(x, r, n):

sequence = []

for i in range(n):

x = r * x * (1 - x)

sequence.append(x)

return sequence

def chaotic_bit_stream(x0, r, n, bit_length):

sequence = logistic_map(x0, r, n)

bit_stream = ''

for x in sequence:

# Map to 10-bit integer

b = int(x * (2 ** bit_length))

# Convert to binary and pad to 10 bits

b_bin = format(b, f'0{bit_length}b')

bit_stream += b_bin

# Stop if we reach the desired length

if len(bit_stream) >= n:

break

return bit_stream[:n]

# Parameters

x0 = 0.7 # Initial condition

r = 3.7 # Control parameter

n = 1000000 # Length of each bit stream

bit_length = 10 # Length of bit representation

# Generate the bit stream

bit_stream = chaotic_bit_stream(x0, r, n, bit_length)

print(f"Bit Stream Length: {len(bit_stream)}")

# Repeat for multiple streams

bit_streams = [chaotic_bit_stream(x0 + i * 0.01, r, n, bit_length) for i in range(10)]