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Python implementation of the Binary Matrix Rank cryptographic test for randomness
def matrix_rank(self, bin_data: str, q=32):
"""
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 the test is the rank of disjoint sub-matrices of the entire sequence. The purpose of this test is
to check for linear dependence among fixed length sub strings of the original sequence. Note that this test
also appears in the DIEHARD battery of tests.
:param bin_data: a binary string
:return: the p-value from the test
"""
shape = (q, q)
n = len(bin_data)
block_size = int(q * q)
num_m = math.floor(n / (q * q))
block_start, block_end = 0, block_size
# print(q, n, num_m, block_size)
if num_m > 0:
max_ranks = [0, 0, 0]
for im in range(num_m):
block_data = bin_data[block_start:block_end]
block = numpy.zeros(len(block_data))
for i in range(len(block_data)):
if block_data[i] == '1':
block[i] = 1.0
m = block.reshape(shape)
ranker = BinaryMatrix(m, q, q)
rank = ranker.compute_rank()
# print(rank)
if rank == q:
max_ranks[0] += 1
elif rank == (q - 1):
max_ranks[1] += 1
else:
max_ranks[2] += 1
# Update index trackers
block_start += block_size
block_end += block_size
piks = [1.0, 0.0, 0.0]
for x in range(1, 50):
piks[0] *= 1 - (1.0 / (2 ** x))
piks[1] = 2 * piks[0]
piks[2] = 1 - piks[0] - piks[1]
chi = 0.0
for i in range(len(piks)):
chi += pow((max_ranks[i] - piks[i] * num_m), 2.0) / (piks[i] * num_m)
p_val = math.exp(-chi / 2)
return p_val
else:
return -1.0
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