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from math import log as log
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from numpy import zeros as zeros
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from math import fabs as fabs
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from math import floor as floor
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from math import sqrt as sqrt
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from scipy.special import erfc as erfc
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from scipy.special import gammaincc as gammaincc
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class TotOnline:
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@staticmethod
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def monobit_test(binary_data:str):
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length_of_bit_string = len(binary_data)
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# Variable for S(n)
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count = 0
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# Iterate each bit in the string and compute for S(n)
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for bit in binary_data:
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if bit == '0':
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# If bit is 0, then -1 from the S(n)
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count -= 1
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elif bit == '1':
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# If bit is 1, then +1 to the S(n)
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count += 1
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# Compute the test statistic
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sObs = count / sqrt(length_of_bit_string)
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# Compute p-Value
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p_value = erfc(fabs(sObs) / sqrt(2))
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# return a p_value and randomness result
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return (p_value, (p_value >= 0.01))
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@staticmethod
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def block_frequency(binary_data:str, block_size=128):
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length_of_bit_string = len(binary_data)
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if length_of_bit_string < block_size:
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block_size = length_of_bit_string
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# Compute the number of blocks based on the input given. Discard the remainder
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number_of_blocks = floor(length_of_bit_string / block_size)
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if number_of_blocks == 1:
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# For block size M=1, this test degenerates to test 1, the Frequency (Monobit) test.
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return TotOnline.monobit_test(binary_data[0:block_size])
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# Initialized variables
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block_start = 0
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block_end = block_size
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proportion_sum = 0.0
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# Create a for loop to process each block
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for counter in range(number_of_blocks):
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# Partition the input sequence and get the data for block
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block_data = binary_data[block_start:block_end]
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# Determine the proportion 蟺i of ones in each M-bit
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one_count = 0
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for bit in block_data:
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if bit == '1':
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one_count += 1
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# compute π
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pi = one_count / block_size
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# Compute Σ(πi -½)^2.
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proportion_sum += pow(pi - 0.5, 2.0)
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# Next Block
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block_start += block_size
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block_end += block_size
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# Compute 4M Σ(πi -½)^2.
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result = 4.0 * block_size * proportion_sum
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# Compute P-Value
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p_value = gammaincc(number_of_blocks / 2, result / 2)
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return (p_value, (p_value >= 0.01))
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@staticmethod
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def approximate_entropy_test(binary_data:str, pattern_length=10):
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length_of_binary_data = len(binary_data)
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# Augment the n-bit sequence to create n overlapping m-bit sequences by appending m-1 bits
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# from the beginning of the sequence to the end of the sequence.
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# NOTE: documentation says m-1 bits but that doesnt make sense, or work.
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binary_data += binary_data[:pattern_length + 1:]
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# Get max length one patterns for m, m-1, m-2
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max_pattern = ''
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for i in range(pattern_length + 2):
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max_pattern += '1'
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# Keep track of each pattern's frequency (how often it appears)
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vobs_01 = zeros(int(max_pattern[0:pattern_length:], 2) + 1)
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vobs_02 = zeros(int(max_pattern[0:pattern_length + 1:], 2) + 1)
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for i in range(length_of_binary_data):
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# Work out what pattern is observed
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vobs_01[int(binary_data[i:i + pattern_length:], 2)] += 1
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vobs_02[int(binary_data[i:i + pattern_length + 1:], 2)] += 1
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# Calculate the test statistics and p values
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vobs = [vobs_01, vobs_02]
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sums = zeros(2)
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for i in range(2):
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for j in range(len(vobs[i])):
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if vobs[i][j] > 0:
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sums[i] += vobs[i][j] * log(vobs[i][j] / length_of_binary_data)
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sums /= length_of_binary_data
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ape = sums[0] - sums[1]
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xObs = 2.0 * length_of_binary_data * (log(2) - ape)
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p_value = gammaincc(pow(2, pattern_length - 1), xObs / 2.0)
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return (p_value, (p_value >= 0.01))
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@staticmethod
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def run_test(binary_data:str):
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one_count = 0
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vObs = 0
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length_of_binary_data = len(binary_data)
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# Predefined tau = 2 / sqrt(n)
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tau = 2 / sqrt(length_of_binary_data)
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# Step 1 - Compute the pre-test proportion πof ones in the input sequence: π = Σjεj / n
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one_count = binary_data.count('1')
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pi = one_count / length_of_binary_data
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# Step 2 - If it can be shown that absolute value of (π - 0.5) is greater than or equal to tau
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# then the run test need not be performed.
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if abs(pi - 0.5) >= tau:
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return (0.0000)
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else:
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# Step 3 - Compute vObs
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for item in range(1, length_of_binary_data):
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if binary_data[item] != binary_data[item - 1]:
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vObs += 1
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vObs += 1
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# Step 4 - Compute p_value = erfc((|vObs − 2nπ * (1−π)|)/(2 * sqrt(2n) * π * (1−π)))
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p_value = erfc(abs(vObs - (2 * (length_of_binary_data) * pi * (1 - pi))) / (2 * sqrt(2 * length_of_binary_data) * pi * (1 - pi)))
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return (p_value, (p_value > 0.01))
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@staticmethod
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def longest_one_block_test(binary_data:str):
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length_of_binary_data = len(binary_data)
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# print('Length of binary string: ', length_of_binary_data)
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# Initialized k, m. n, pi and v_values
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if length_of_binary_data < 128:
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# Not enough data to run this test
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return (0.00000, 'Error: Not enough data to run this test')
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elif length_of_binary_data < 6272:
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k = 3
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m = 8
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v_values = [1, 2, 3, 4]
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pi_values = [0.2148, 0.3672, 0.2305, 0.1875]
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elif length_of_binary_data < 750000:
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k = 5
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m = 128
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v_values = [4, 5, 6, 7, 8, 9]
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pi_values = [0.1174, 0.2430, 0.2493, 0.1752, 0.1027, 0.1124]
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else:
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# If length_of_bit_string > 750000
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k = 6
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m = 10000
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v_values = [10, 11, 12, 13, 14, 15, 16]
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pi_values = [0.0882, 0.2092, 0.2483, 0.1933, 0.1208, 0.0675, 0.0727]
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number_of_blocks = floor(length_of_binary_data / m)
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block_start = 0
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block_end = m
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xObs = 0
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# This will intialized an array with a number of 0 you specified.
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frequencies = zeros(k + 1)
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# print('Number of Blocks: ', number_of_blocks)
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for count in range(number_of_blocks):
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block_data = binary_data[block_start:block_end]
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max_run_count = 0
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run_count = 0
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# This will count the number of ones in the block
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for bit in block_data:
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if bit == '1':
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run_count += 1
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max_run_count = max(max_run_count, run_count)
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else:
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max_run_count = max(max_run_count, run_count)
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run_count = 0
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max(max_run_count, run_count)
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#print('Block Data: ', block_data, '. Run Count: ', max_run_count)
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if max_run_count < v_values[0]:
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frequencies[0] += 1
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for j in range(k):
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if max_run_count == v_values[j]:
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frequencies[j] += 1
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if max_run_count > v_values[k - 1]:
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frequencies[k] += 1
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block_start += m
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block_end += m
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# print("Frequencies: ", frequencies)
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# Compute xObs
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for count in range(len(frequencies)):
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xObs += pow((frequencies[count] - (number_of_blocks * pi_values[count])), 2.0) / (
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number_of_blocks * pi_values[count])
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p_value = gammaincc(float(k / 2), float(xObs / 2))
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return (p_value, (p_value > 0.01))
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