随机数检测（四）- 累加和检测、近似熵检测、线性复杂度检测、Maurer通用统计检测、离散傅里叶检测
- 3.12 累加和检测方法
- 3.13 近似熵检测方法
- 3.14 线性复杂度检测
- 3.15 Maurer通用统计检测
- 3.16 离散傅里叶检测方法
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3.12 累加和检测方法
累加和检测方法如下图。
以下实现代码供参考。
def cusum(epsilon:bitarray, direction):
n = int(len(epsilon))
X = [0]*n
S = [0]*n
epsilonList = epsilon.tolist()
for i in range(n):
X[i]=2*epsilonList[i]-1
if direction == 0:#forward cumum
S[0] = X[0]
SMax = abs(S[0])
for i in range(1,n):
S[i] = S[i-1]+X[i]
if abs(S[i]) > SMax:
SMax = abs(S[i])
else:#backward cusunm
S[0] = X[n-1]
SMax = abs(S[n-1])
for i in range(1,n):
S[i] = S[i-1]+X[n-1-i]
if abs(S[i]) > SMax:
SMax = abs(S[i])
sum1 = 0.0
for i in range(int((1-(n/SMax))/4), int(((n/SMax)-1)/4)):
sum1 += norm.cdf((4*i + 1)*SMax/sqrt(n)) - norm.cdf((4*i - 1)*SMax/sqrt(n))
sum2 = 0.0
for i in range(int((-3-(n/SMax))/4), int(((n/SMax)-1)/4)):
sum2 += norm.cdf((4*i + 3)*SMax/sqrt(n)) - norm.cdf((4*i + 1)*SMax/sqrt(n))
pvalue = 1.0 - sum1 + sum2
qvalue = pvalue
return {'p':pvalue, 'q':qvalue}
3.13 近似熵检测方法
近似熵检测方法如下图。
以下实现代码供参考。
def getselfCorrelationM(len):
if len < 100000000:
m = [2,5]
else:
m = [5,7]
return m
def alterOffsetBit(m, offset, listSub:list):
ret = []
listSub[offset] = 0
if offset == (m-1):
ret.append(listSub.copy())
else:
ret += (alterOffsetBit(m, offset+1, listSub))
listSub[offset] = 1
if offset == (m-1):
ret.append(listSub.copy())
else:
ret += (alterOffsetBit(m, offset+1, listSub))
return ret
def seedSequence(m):
sequencelist = [0]*m
return alterOffsetBit(m, 0, sequencelist)
def getPhyN(epsilonList:list, mlen):
n = len(epsilonList)
prefixM = epsilonList[:mlen-1:1]
epsilonList += prefixM
Vm = getV(epsilonList, mlen)
C = [Vm[i]/n for i in range(2**mlen)]
phy_mlist = [C[i]*math.log(C[i],math.e) for i in range(2**mlen)]
return sum(phy_mlist)
def getV(epsilonList:list, mlen):
seedList = seedSequence(mlen)
V = [0] * (2**mlen)
for i in range(len(epsilonList)-mlen+1):
seedindex = seedList.index(epsilonList[i:i+mlen:1])
V[seedindex] += 1
return V
def approximateEntropy(epsilon:bitarray,m):
n = int(len(epsilon))
epsilonList = epsilon.tolist()
apen_m = getPhyN(epsilonList, m) - getPhyN(epsilonList, m+1)
V = 2.0*n*(math.log(2,math.e) - apen_m)
pvalue = scipy.special.gammaincc(2**(m-1), V/2)
qvalue = pvalue
return {'p':pvalue, 'q':qvalue}
3.14 线性复杂度检测
线性复杂度检测方法如下图。
以下实现代码供参考。
def linearComplexity(len):
if len < 100000000:
m = [500,1000]
else:
m = [5000]
return m
def Berlekamp_Massey_algorithm(sequence):
N = len(sequence)
s = sequence[:]
for k in range(N):
if s[k] == 1:
break
f = set([k + 1, 0])
l = k + 1
g = set([0])
a = k
b = 0
for n in range(k + 1, N):
d = 0
for ele in f:
d ^= s[ele + n - l]
if d == 0:
b += 1
else:
if 2 * l > n:
f ^= set([a - b + ele for ele in g])
b += 1
else:
temp = f.copy()
f = set([b - a + ele for ele in f]) ^ g
l = n + 1 - l
g = temp
a = b
b = n - l + 1
return l#(print_poly(f), l)
def getV(epsilonList:list, N:int, M:int):
V = [0]*7
mean = M/2.0 + (9.0+1)/36.0 - 1.0/(2**M) * (M/3.0 + 2.0/9.0)
temp = [0]*M
for ii in range(N):
B_ = [0]*M
C = [0]*M
T = [0]*M
P = [0]*M
# print('loop N', ii)
L = 0
m = -1
d = 0
C[0] = 1
B_[0] = 1
for N_ in range(M):
d = epsilonList[ii*M+N_]
for i in range(1,L+1):
d += C[i] * epsilonList[ii*M+N_-i]
d = d%2
if d == 1:
T = C.copy()
P = temp.copy()
for j in range(M):
if B_[j] == 1:
P[j+N_-m] = 1
for i in range(M):
C[i] = (C[i] + P[i])%2
if L <= int(N_/2) :
L = N_ + 1 - L
m = N_
B_ = T.copy()
T_ = (L - mean) + 2.0/9.0
if T_ <= -2.5:
V[0]+=1
elif T_ > -2.5 and T_ <= -1.5:
V[1]+=1
elif T_ > -1.5 and T_ <= -0.5:
V[2]+=1
elif T_ > -0.5 and T_ <= 0.5:
V[3]+=1
elif T_ > 0.5 and T_ <= 1.5:
V[4]+=1
elif T_ > 1.5 and T_ <= 2.5:
V[5]+=1
else:
V[6]+=1
return V
def linearComplexity(epsilon:bitarray,m):
n = len(epsilon)
N = int(len(epsilon)/m)
epsilonList = epsilon.tolist()
L = [ Berlekamp_Massey_algorithm(epsilonList[i*m:(i+1)*m]) for i in range(N)]
mu = (m/2) + (9 + (-1)**(m+1))/36 - (m/3 + 2/9)/(2**m)
T = [((-1)**m)*(L[i] - mu) + 2/9 for i in range(N)]
V = [0]*7
for i in range(N):
if T[i] <= -2.5:
V[0] += 1
elif T[i] <= -1.5 and T[i] > -2.5:
V[1] += 1
elif T[i] <= -0.5 and T[i] > -1.5:
V[2] += 1
elif T[i] <= 0.5 and T[i] > -0.5:
V[3] += 1
elif T[i] <= 1.5 and T[i] > 0.5:
V[4] += 1
elif T[i] <= 2.5 and T[i] > 1.5:
V[5] += 1
elif T[i] > 2.5:
V[6] += 1
pi = [0.010417, 0.03125, 0.12500, 0.5000, 0.25000, 0.06250, 0.020833]
resultV = [((V[i] - N*pi[i])**2)/(N*pi[i]) for i in range(7)]
pvalue = scipy.special.gammaincc(3, sum(resultV)/2)
qvalue = pvalue
return {'p':pvalue, 'q':qvalue}
3.15 Maurer通用统计检测
Maurer通用统计检测方法如下图。
以下实现代码供参考。
expected_value = [0, 0, 0, 0, 0, 0, 5.2177052, 6.1962507, 7.1836656,
8.1764248, 9.1723243, 10.170032, 11.168765,
12.168070, 13.167693, 14.167488, 15.167379]
variance = [ 0, 0, 0, 0, 0, 0, 2.954, 3.125, 3.238, 3.311, 3.356, 3.384,
3.401, 3.410, 3.416, 3.419, 3.421 ]
def getLQ(n:int):
if n >= 1000000:
return (7,1280)
else:
return (7,1280)
def universal(epsilon:bitarray, L):
n = len(epsilon)
# (L,Q) = getLQ(n)
Q = 10*(2**L)
K = int(n/L)-Q
p = 2**L
c = 0.7 - 0.8/L + (4 + 32/L)*(K**(-3/L))/15
sigma = c * sqrt(variance[L]/K)
sqrt2 = sqrt(2)
sum = 0.0
T = [0]*p
for i in range(1,Q+1):
decRep = 0
for j in range(L):
decRep = (decRep << 1) + epsilon[(i-1)*L + j]
T[decRep] = i
for i in range(Q+1, Q+K+1):
decRep = 0
for j in range(L):
decRep = (decRep << 1) + epsilon[(i-1)*L + j]
sum += np.log2(i - T[decRep])
T[decRep] = i
phi =(sum/K)
V = (phi-expected_value[L])/sigma
pvalue = math.erfc(abs(V)/sqrt2)
qvalue = math.erfc(V/sqrt2)/2
return {'p':pvalue, 'q':qvalue}
3.16 离散傅里叶检测方法
离散傅里叶检测方法如下图。
以下实现代码供参考。
def discreteFourierTransform(epsilon:bitarray):
n = len(epsilon)
X = [2*epsilon[i]-1 for i in range(n)]
f = np.fft.fft(X)
m = [abs(i) for i in f[0:int(n/2)]]
count = 0
upperBound = sqrt(2.995732274*n)
for i in range(int(n/2)):
if m[i] < upperBound:
count +=1
N_l = count
N_o = int(0.95*n/2.0)
d = (N_l - N_o)/sqrt(n/3.8*0.95*0.05)
pvalue = math.erfc(abs(d)/sqrt(2))
qvalue = math.erfc(d/sqrt(2))/2
