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TotOnline.py

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