def test(input, n, M=32, Q=32):
N = int(math.floor(n/(M*Q))) #Number of blocks
if N < 38:
print(" Number of blocks must be greater than 37")
p = 0.0
return [0]*9
# Compute the reference probabilities for FM, FMM and remainder
r = M
product = 1.0
for i in range(r):
upper1 = (1.0 - (2.0**(i-Q)))
upper2 = (1.0 - (2.0**(i-M)))
lower = 1-(2.0**(i-r))
product = product * ((upper1*upper2)/lower)
FR_prob = product * (2.0**((r*(Q+M-r)) - (M*Q)))
r = M-1
product = 1.0
for i in range(r):
upper1 = (1.0 - (2.0**(i-Q)))
upper2 = (1.0 - (2.0**(i-M)))
lower = 1-(2.0**(i-r))
product = product * ((upper1*upper2)/lower)
FRM1_prob = product * (2.0**((r*(Q+M-r)) - (M*Q)))
LR_prob = 1.0 - (FR_prob + FRM1_prob)
FM = 0 # Number of full rank matrices
FMM = 0 # Number of rank -1 matrices
remainder = 0
for blknum in range(N):
block = [None] * (M*Q)
for i in range(M*Q):
block[i] = int(input[blknum*M*Q + i],2)
# Put in a matrix
matrix = gf2matrix.matrix_from_bits(M,Q,block,blknum)
rank = gf2matrix.rank(M,Q,matrix,blknum)
if rank == M: # count the result
FM += 1
elif rank == M-1:
FMM += 1
else:
remainder += 1
chisq = (((FM-(FR_prob*N))**2)/(FR_prob*N))
chisq += (((FMM-(FRM1_prob*N))**2)/(FRM1_prob*N))
chisq += (((remainder-(LR_prob*N))**2)/(LR_prob*N))
p = math.e **(-chisq/2.0)
success = (p >= 0.01)
return [n, M, Q, N, FM, FMM, chisq, p, success]
def binary_matrix_rank_test(bits, M=32, Q=32):
n = len(bits)
N = int(math.floor(n / (M * Q))) #Number of blocks
if N < 38:
print(" Number of blocks must be greater than 37")
return False, 0, None
# Compute the reference probabilities for FM, FMM and remainder
r = M
product = 1.0
for i in range(r):
upper1 = (1.0 - (2.0**(i - Q)))
upper2 = (1.0 - (2.0**(i - M)))
lower = 1 - (2.0**(i - r))
product = product * ((upper1 * upper2) / lower)
FR_prob = product * (2.0**((r * (Q + M - r)) - (M * Q)))
r = M - 1
product = 1.0
for i in range(r):
upper1 = (1.0 - (2.0**(i - Q)))
upper2 = (1.0 - (2.0**(i - M)))
lower = 1 - (2.0**(i - r))
product = product * ((upper1 * upper2) / lower)
FRM1_prob = product * (2.0**((r * (Q + M - r)) - (M * Q)))
LR_prob = 1.0 - (FR_prob + FRM1_prob)
FM = 0 # Number of full rank matrices
FMM = 0 # Number of rank -1 matrices
remainder = 0
for blknum in range(N):
block = bits[blknum * (M * Q):(blknum + 1) * (M * Q)]
# Put in a matrix
matrix = gf2matrix.matrix_from_bits(M, Q, block, blknum)
# Compute rank
rank = gf2matrix.rank(M, Q, matrix, blknum)
if rank == M: # count the result
FM += 1
elif rank == M - 1:
FMM += 1
else:
remainder += 1
chisq = (((FM - (FR_prob * N))**2) / (FR_prob * N))
chisq += (((FMM - (FRM1_prob * N))**2) / (FRM1_prob * N))
chisq += (((remainder - (LR_prob * N))**2) / (LR_prob * N))
p = math.e**(-chisq / 2.0)
success = (p >= 0.01)
return (success, p, None)