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Python implementation of the Non Overlapping Patterns cryptographic test for randomness
def non_overlapping_patterns(self, bin_data: str, pattern="000000001", num_blocks=8):
"""
Note that this description is taken from the NIST documentation [1]
[1] http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf
The focus of this test is the number of occurrences of pre-specified target strings. The purpose of this
test is to detect generators that produce too many occurrences of a given non-periodic (aperiodic) pattern.
For this test and for the Overlapping Template Matching test of Section 2.8, an m-bit window is used to
search for a specific m-bit pattern. If the pattern is not found, the window slides one bit position. If the
pattern is found, the window is reset to the bit after the found pattern, and the search resumes.
:param bin_data: a binary string
:param pattern: the pattern to match to
:return: the p-value from the test
"""
n = len(bin_data)
pattern_size = len(pattern)
block_size = math.floor(n / num_blocks)
pattern_counts = numpy.zeros(num_blocks)
# For each block in the data
for i in range(num_blocks):
block_start = i * block_size
block_end = block_start + block_size
block_data = bin_data[block_start:block_end]
# Count the number of pattern hits
j = 0
while j < block_size:
sub_block = block_data[j:j + pattern_size]
if sub_block == pattern:
pattern_counts[i] += 1
j += pattern_size
else:
j += 1
# Calculate the theoretical mean and variance
mean = (block_size - pattern_size + 1) / pow(2, pattern_size)
var = block_size * ((1 / pow(2, pattern_size)) - (((2 * pattern_size) - 1) / (pow(2, pattern_size * 2))))
# Calculate the Chi Squared statistic for these pattern matches
chi_squared = 0
for i in range(num_blocks):
chi_squared += pow(pattern_counts[i] - mean, 2.0) / var
# Calculate and return the p value statistic
p_val = spc.gammaincc(num_blocks / 2, chi_squared / 2)
return p_val
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