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Update crypto_hometask.py
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@golovnyakpa
golovnyakpa authored Apr 29, 2019
1 parent e9969ec commit 2ba87ff
Showing 1 changed file with 92 additions and 43 deletions.
135 changes: 92 additions & 43 deletions crypto_hometask.py
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Original file line number Diff line number Diff line change
Expand Up @@ -7,9 +7,9 @@


def anf(function):
'''
"""
Получение коэффициентов АНФ
'''
"""
buff = []
iterations = len(function)
ANF = [function[0]]
Expand All @@ -22,33 +22,33 @@ def anf(function):
return ANF


def hadamardMatrix(dimension):
'''
def hadamard_matrix(dimension):
"""
Создание мтрицы Адамара-Сильвестра соответстыующего размера
'''
"""
if dimension == 1:
return W
else:
return np.hstack((np.vstack((hadamardMatrix(dimension - 1), hadamardMatrix(dimension - 1))),
np.vstack((hadamardMatrix(dimension - 1), -hadamardMatrix(dimension - 1)))))
return np.hstack((np.vstack((hadamard_matrix(dimension - 1), hadamard_matrix(dimension - 1))),
np.vstack((hadamard_matrix(dimension - 1), -hadamard_matrix(dimension - 1)))))


def functionValue(function):
'''
def function_value(function):
"""
Получение таблиц истинности разрядных функций
'''
"""
values = [[] for _ in range(len(bin(max(function))[2:]))]
for value in function:
for function_number in range(len(bin(max(function))[2:])):
values[function_number].append(value >> function_number & 1)
return values


def generateMonoms(n):
'''
def generate_monoms(n):
"""
Генерация всех мономов в лексикографическом порядке
Функция нужна для вывода разрядных функций в виде АНФ (buildFunction)
'''
"""
monoms = ['1']
x = 1
for i in range(2 ** n - 1):
Expand All @@ -58,49 +58,49 @@ def generateMonoms(n):
mon += 'x' + str(j)
monoms.append(mon)
x += 1
return (monoms)
return monoms


def buildFunction(function):
'''
def build_function(function):
"""
Вывод значений функции в виде АНФ
'''
"""
answer = ''
num_of_bits = len(bin(max(function))[2:])
monoms = generateMonoms(num_of_bits)
monoms = generate_monoms(num_of_bits)
print_yi = "y{}"
counter = 0
for i in range(num_of_bits):
answer += print_yi.format(counter) + ' = '
coefficients = functionValue(anf(function))[i]
coefficients = function_value(anf(function))[i]
for j in range(len(function)):
if coefficients[j]:
answer += monoms[j] + ' ⊕ '
counter += 1
answer = answer[0:len(answer) - 3:]
answer += '\n'
return (answer)
return answer


def fourierSpectrum(function):
'''
def fourier_spectrum(function):
"""
Коэффициенты фурье разрядных функций
'''
values = functionValue(function)
"""
values = function_value(function)
spectrum = []
M = hadamardMatrix(int(math.log2(len(function))))
M = hadamard_matrix(int(math.log2(len(function))))
for functions in range(len(bin(max(function))[2:])):
spectrum.append(np.matmul(np.array(values[functions]).T, M).tolist())
return spectrum


def walschSpectrum(function):
'''
def walsch_spectrum(function):
"""
Коэффицинты Уолша-Адамара разрядных функций
'''
values = functionValue(function)
"""
values = function_value(function)
unit_array = np.array([1 for _ in range(len(function))])
M = hadamardMatrix(int(math.log2(len(function))))
M = hadamard_matrix(int(math.log2(len(function))))
spectrum = []
for functions in range(len(bin(max(function))[2:])):
spectrum.append(np.matmul((unit_array - 2 * np.array(values[functions])).T, M).tolist())
Expand All @@ -110,33 +110,82 @@ def walschSpectrum(function):
def strict_avalanche_effect(function):
answer = []
for k in range(4):
values = functionValue(function)[k]
values = function_value(function)[k]
temp = 0
counter = 0
for i in range(16):
for j in range(4):
if (values[temp] != values[temp ^ (2 ** j)]):
if values[temp] != values[temp ^ (2 ** j)]:
counter = counter + 1
temp = temp + 1
answer.append(counter)
return(answer)
for i in range(len(answer)):
answer[i] = answer[i] / 64
return answer


def possitions_of_ones(n):
"""
Определяет на сколько позиций надо сдвигать число циклически
вправо, чтобы получить единицу.
Ответ возвращает в виде списка
"""
answer = []
for i in range(4):
if n >> i & 1 == 1:
answer.append(i)
return answer


def bit_independence_criterion(function):
probs = strict_avalanche_effect(function)
tpl = (3, 5, 6, 9, 10, 12)
result = []
answ = []
for i in tpl:
pos = possitions_of_ones(i)
counter = 0
for j in range(16):
for k in range(4):
if function[j] >> pos[0] & 1 != function[j ^ (2 ** k)] >> pos[0] & 1 and \
function[j] >> pos[1] & 1 != function[j ^ (2 ** k)] >> pos[1] & 1:
counter += 1
answ.append(counter / 64)
if counter / 64 == probs[pos[0]] * probs[pos[1]]:
result.append('independent')
else:
result.append('dependent')
counter = 0
return result


def avalanche_effect(function):
answer = [[0, 0, 0, 0, 0] for _ in range(4)] # первый список- результаты для х4,.. Первый элемент первого списка- количество векторов, поменявших 0 координат...
"""
первый список- результаты для х4,..
Первый элемент первого списка- количество векторов, поменявших 0 координат...
"""
answer = [[0, 0, 0, 0, 0] for _ in range(4)]
for k in range(4):
for i in range(16):
counter = 0
for j in range(4):
if function[i] << j & 1 != function[i ^ (2 ** k)] << j & 1:
if function[i] >> j & 1 != function[i ^ (2 ** k)] >> j & 1:
counter += 1
answer[k][counter] += 1
return(answer)

print(functionValue(pi2))
print(buildFunction(pi2))
print(walschSpectrum(pi2))
print(fourierSpectrum(pi2))
print(int('111', 2))
sum = 0
for i in answer:
for j, k in enumerate(i):
sum += j * k
result = sum / (16 * 4)
return result


print(function_value(pi2))
print(build_function(pi2))
print(walsch_spectrum(pi2))
print(fourier_spectrum(pi2))
print(strict_avalanche_effect(pi2))
print(bin(5))
print(bit_independence_criterion(pi2))
print(avalanche_effect(pi2))
m = avalanche_effect(pi2) / 4
print(m)

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