def blum(p, q, m):
# your code here
if not isinstance(m, int):
print('Error(blum): Invalid value of m', end='')
return ''
if m <= 0:
print('Error(blum): Invalid value of m', end='')
return ''
if not isinstance(p, int) or not isinstance(q, int):
print('Error(blum): Invalid values of p,q', end='')
return ''
if mod.residue(p, 4) != 3 or mod.residue(q, 4) != 3:
print('Error(blum): Invalid values of p,q', end='')
return ''
n = p * q
p_file = open(primeFile, 'r')
primes = p_file.read().split('\n')
temp = n
seed = int(primes[temp - 1])
while mod.gcd(seed, n) != 1:
temp += 1
seed = int(primes[temp - 1])
bitStream = ''
x = mod.residue(seed**2, n)
for i in range(m):
x = mod.residue(x**2, n)
bitStream += str(mod.residue(x, 2))
return bitStream
def inverse(A, m):
# your code here
if not isinstance(m, int) or m <= 0:
return 'Error(inverse): invalid mod'
if not is_matrix(A):
return 'Error(inverse): invalid input'
if get_rowCount(A) == 0:
return 'Error(inverse): invalid input'
if not is_square(A):
return 'Error(inverse): matrix is not invertible'
else:
if get_rowCount(A) == 2:
if mod.gcd(det(A), m) != 1:
return 'Error(inverse): matrix is not invertible'
else:
return 'Error(inverse): Unsupported matrix size'
delta = mod.residue(det(A), m)
m_i_delta = mod.mul_inv(delta, m)
new = new_matrix(2, 2, 0)
new[0][0] = A[1][1]
new[0][1] = 0 - A[0][1]
new[1][0] = 0 - A[1][0]
new[1][1] = A[0][0]
return matrix_mod(scalar_mul(m_i_delta, new), m)
def d_hill(ciphertext, key):
# your code here
if len(ciphertext) == 0:
print('Error(d_hill): invalid ciphertext')
return ''
new_key = ''
if len(key) > 4:
new_key += key[:4]
elif len(key) == 4:
new_key += key
else:
new_key += key
counter = 0
while len(new_key) < 4:
new_key += key[counter]
counter += 1
baseString = utilities_A4.get_lower()
key_matrix = matrix.new_matrix(2, 2, 0)
count = 0
for i in range(2):
for j in range(2):
key_matrix[i][j] = baseString.index(new_key[count].lower())
count += 1
if mod.gcd(matrix.det(key_matrix), 26) != 1:
print('Error(d_hill): key is not invertible')
return ''
inverse_key_matrix = matrix.inverse(key_matrix, 26)
plaintext = ''
non_alpha = utilities_A4.get_nonalpha(ciphertext)
blocks = utilities_A4.text_to_blocks(
utilities_A4.remove_nonalpha(ciphertext), 2)
for block in blocks:
block_m = matrix.new_matrix(2, 1, 0)
block_m[0][0] = baseString.index(block[0].lower())
block_m[1][0] = baseString.index(block[1].lower())
result_m = matrix.matrix_mod(matrix.mul(inverse_key_matrix, block_m),
26)
plaintext += baseString[result_m[0][0]].lower()
plaintext += baseString[result_m[1][0]].lower()
plaintext = utilities_A4.insert_nonalpha(plaintext, non_alpha)
while plaintext[-1] == 'q':
plaintext = plaintext[:-1]
return plaintext
def test_q1():
print("-------------------------------------------")
print("Testing Q1: Modular Arithmetic Library")
filename = 'q1_solution.txt'
outFile = open(filename, 'w')
print()
outFile.write('1- Testing residue_set:\n')
outFile.write('residue_set({}) = {}\n'.format(10, mod.residue_set(10)))
outFile.write('residue_set({}) = {}\n'.format(1, mod.residue_set(1)))
outFile.write('residue_set({}) = '.format(-5))
outFile.write('{}\n'.format(mod.residue_set(-5)))
outFile.write('residue_set({}) = '.format([5]))
outFile.write('{}\n'.format(mod.residue_set([5])))
outFile.write('\n')
outFile.write('2- Testing residue:\n')
outFile.write('residue({},{}) = {}\n'.format(17, 5, mod.residue(17, 5)))
outFile.write('residue({},{}) = '.format(3.4, 5))
outFile.write('{}\n'.format(mod.residue(3.4, 5)))
outFile.write('residue({},{}) = '.format(13, -5))
outFile.write('{}\n'.format(mod.residue(13, -5)))
outFile.write('\n')
outFile.write('3- Testing is_congruent:\n')
outFile.write('is_congruent({},{},{})= {}\n'.format(
22, 33, 11, mod.is_congruent(22, 33, 11)))
outFile.write('is_congruent({},{},{}) = {}\n'.format(
7, 9, 3, mod.is_congruent(7, 9, 3)))
outFile.write('is_congruent({},{},{})= '.format(3.4, 5, 9))
outFile.write('{}\n'.format(mod.is_congruent(3.4, 5, 9)))
outFile.write('is_congruent({},{},{}) = '.format(3, 5, -9))
outFile.write('{}\n'.format(mod.is_congruent(3, 5, -9)))
outFile.write('\n')
outFile.write('4- Testing add:\n')
outFile.write('add({},{},{}) = {}\n'.format(17, 23, 7, mod.add(17, 23,
7)))
outFile.write('add({},{},{}) = {}\n'.format(-17, 23, 7,
mod.add(-17, 23, 7)))
outFile.write('add({},{},{}) = {}\n'.format(17, -23, 7,
mod.add(17, -23, 7)))
outFile.write('add({},{},{}) = '.format(9, 17, 0))
outFile.write('{}\n'.format(mod.add(9, 17, 0)))
outFile.write('add({},{},{}) = '.format([9], 17, 7))
outFile.write('{}\n'.format(mod.add([9], 17, 7)))
outFile.write('add({},{},{}) = '.format(9, 17.1, 8))
outFile.write('{}\n'.format(mod.add(9, 17.1, 8)))
outFile.write('\n')
outFile.write('5- Testing sub:\n')
outFile.write('sub({},{},{}) = {}\n'.format(17, 23, 7, mod.sub(17, 23,
7)))
outFile.write('sub({},{},{}) = {}\n'.format(-17, 23, 7,
mod.sub(-17, 23, 7)))
outFile.write('sub({},{},{}) = {}\n'.format(17, -23, 7,
mod.sub(17, -23, 7)))
outFile.write('sub({},{},{}) = '.format(9, 17, 0))
outFile.write('{}\n'.format(mod.sub(9, 17, 0)))
outFile.write('sub({},{},{}) = '.format([9], 17, 7))
outFile.write('{}\n'.format(mod.sub([9], 17, 7)))
outFile.write('sub({},{},{}) = '.format(9, 17.1, 8))
outFile.write('{}\n'.format(mod.sub(9, 17.1, 8)))
outFile.write('\n')
outFile.write('6- Testing additive inverse:\n')
outFile.write('add_inv({},{}) = {}\n'.format(3, 5, mod.add_inv(3, 5)))
outFile.write('add_inv({},{}) = {}\n'.format(6, 1, mod.add_inv(6, 1)))
outFile.write('add_inv({},{})= {}\n'.format(22, 10, mod.add_inv(22, 10)))
outFile.write('add_inv({},{}) = '.format(6, -1))
outFile.write('{}\n'.format(mod.add_inv(6, -1)))
outFile.write('add_inv({},{}) = '.format(6.2, 6))
outFile.write('{}\n'.format(mod.add_inv(6.2, 6)))
a = 4
b = 2
m = 5
result = mod.sub(a, b, m) == mod.add(a, mod.add_inv(b, m), m)
outFile.write(
'sub({0},{1},{2}) == add({0},add_inv({1},{2}),{2})? = {3}\n'.format(
a, b, m, result))
outFile.write('\n')
outFile.write('7- Testing Addition Table:\n')
outFile.write('Addition Table for mode {} =\n'.format(5))
addTab = mod.add_table(5)
for i in range(len(addTab)):
outFile.write(str(addTab[i]))
outFile.write('\n')
outFile.write('Addition Table for mode {} =\n'.format(8))
addTab = mod.add_table(8)
for i in range(len(addTab)):
outFile.write(str(addTab[i]))
outFile.write('\n')
outFile.write('Addition Table for mode {} =\n'.format(0))
outFile.write(mod.add_table(0))
outFile.write('\n')
outFile.write('\n')
outFile.write('8- Testing Subtraction Table:\n')
outFile.write('Subtraction Table for mode {} =\n'.format(5))
subTab = mod.sub_table(5)
for i in range(len(subTab)):
outFile.write(str(subTab[i]))
outFile.write('\n')
outFile.write('Subtraction Table for mode {} =\n'.format(8))
subTab = mod.sub_table(8)
for i in range(len(subTab)):
outFile.write(str(subTab[i]))
outFile.write('\n')
outFile.write('Subtraction Table for mode {} =\n'.format([5]))
outFile.write(mod.sub_table([5]))
outFile.write('\n')
outFile.write('\n')
outFile.write('9- Testing Addition Inverse Table:\n')
outFile.write('Addition Inverse Table for mode {} =\n'.format(5))
addInvTab = mod.add_inv_table(5)
outFile.write(str(addInvTab[0]))
outFile.write('\n')
outFile.write(str(addInvTab[1]))
outFile.write('\n')
outFile.write('Addition Inverse Table for mode {} =\n'.format(26))
addInvTab = mod.add_inv_table(26)
outFile.write(str(addInvTab[0]))
outFile.write('\n')
outFile.write(str(addInvTab[1]))
outFile.write('\n')
outFile.write('Addition Inverse Table for mode {} =\n'.format(-2))
outFile.write(mod.add_inv_table(-2))
outFile.write('\n')
outFile.write('\n')
outFile.write('10- Testing mul:\n')
outFile.write('mul({},{},{}) = {}\n'.format(3, 5, 5, mod.mul(3, 5, 5)))
outFile.write('mul({},{},{}) = {}\n'.format(8, 3, 7, mod.mul(8, 3, 7)))
outFile.write('mul({},{},{})= {}\n'.format(17, -3, 7, mod.mul(17, -3,
7)))
outFile.write('mul({},{},{}) = '.format(9, 17, 0))
outFile.write('{}\n'.format(mod.mul(9, 17, 0)))
outFile.write('mul({},{},{}) = '.format([9], 17, 7))
outFile.write('{}\n'.format(mod.mul([9], 17, 7)))
outFile.write('mul({},{},{}) = '.format(9, 17.1, 8))
outFile.write('{}\n'.format(mod.mul(9, 17.1, 8)))
outFile.write('\n')
outFile.write('11- Testing Multiplication Table:\n')
outFile.write('Multiplication Table for mode {} =\n'.format(4))
mulTab = mod.mul_table(4)
for i in range(len(mulTab)):
outFile.write(str(mulTab[i]))
outFile.write('\n')
outFile.write('Multiplication Table for mode {} =\n'.format(5))
mulTab = mod.mul_table(5)
for i in range(len(mulTab)):
outFile.write(str(mulTab[i]))
outFile.write('\n')
outFile.write('Multiplication Table for mode {} =\n'.format(-5))
outFile.write(mod.mul_table(-5))
outFile.write('\n')
outFile.write('\n')
outFile.write('12- Testing is_prime:\n')
outFile.write('is_prime({}) = {}\n'.format(97, mod.is_prime(97)))
outFile.write('is_prime({}) = {}\n'.format(479, mod.is_prime(479)))
outFile.write('is_prime({})= {}\n'.format(1044, mod.is_prime(1044)))
outFile.write('is_prime({}) = {}\n'.format(0, mod.is_prime(0)))
outFile.write('is_prime({}) = {}\n'.format(-17, mod.is_prime(-17)))
outFile.write('\n')
outFile.write('13- Testing gcd:\n')
outFile.write('gcd({},{}) = {}\n'.format(629, 357, mod.gcd(629, 357)))
outFile.write('gcd({},{}) = {}\n'.format(440, 700, mod.gcd(440, 700)))
outFile.write('gcd({},{}) = {}\n'.format(-30, 700, mod.gcd(-30, 700)))
outFile.write('gcd({},{}) = {}\n'.format(540, -539, mod.gcd(540, -539)))
outFile.write('gcd({},{}) = '.format(711, 0))
outFile.write(mod.gcd(711, 0))
outFile.write('\n')
outFile.write('gcd({},{}) = '.format(0, 311))
outFile.write(mod.gcd(0, 311))
outFile.write('\n')
outFile.write('gcd({},{}) = '.format([9], 27))
outFile.write(mod.gcd([9], 27))
outFile.write('\n')
outFile.write('\n')
outFile.write('14- Testing is_relatively_prime:\n')
outFile.write('is_relatively_prime({},{}) = {}\n'.format(
4, 5, mod.is_relatively_prime(4, 5)))
outFile.write('is_relatively_prime({},{})= {}\n'.format(
540, 539, mod.is_relatively_prime(540, 539)))
outFile.write('is_relatively_prime({},{}) = {}\n'.format(
18, 26, mod.is_relatively_prime(18, 26)))
outFile.write('is_relatively_prime({},{}) = {}\n'.format(
0, 26, mod.is_relatively_prime(0, 26)))
outFile.write('is_relatively_prime({},{}) = '.format([1], 26))
outFile.write(mod.is_relatively_prime([1], 26))
outFile.write('\n')
outFile.write('\n')
outFile.write('15- Testing has_mul_inv:\n')
outFile.write('has_mul_inv({},{}) = {}\n'.format(
4, 5, mod.has_mul_inv(4, 5)))
outFile.write('has_mul_inv({},{}) = {}\n'.format(17, 26,
mod.has_mul_inv(17,
26)))
outFile.write('has_mul_inv({},{}) = {}\n'.format(18, 26,
mod.has_mul_inv(18,
26)))
outFile.write('has_mul_inv({},{}) = {}\n'.format(
0, 26, mod.has_mul_inv(0, 26)))
outFile.write('has_mul_inv({},{}) = '.format([1], 26))
outFile.write(mod.has_mul_inv([1], 26))
outFile.write('\n')
outFile.write('\n')
outFile.write('16- Testing EEA:\n')
outFile.write('eea({},{}) = {}\n'.format(700, 440, mod.eea(700, 440)))
outFile.write('eea({},{}) = {}\n'.format(88, 35, mod.eea(88, 35)))
outFile.write('eea({},{}) = {}\n'.format(35, 88, mod.eea(35, 88)))
outFile.write('eea({},{}) = {}\n'.format(-88, 35, mod.eea(-88, 35)))
outFile.write('eea({},{}) = {}\n'.format(88, -35, mod.eea(88, -35)))
outFile.write('eea({},{}) = '.format(0, 777))
outFile.write(mod.eea(0, 777))
outFile.write('\n')
outFile.write('\n')
outFile.write('17- Testing mul_inv:\n')
outFile.write('mul_inv({},{}) = {}\n'.format(23, 26, mod.mul_inv(23,
26)))
outFile.write('mul_inv({},{}) = {}\n'.format(5, 6, mod.mul_inv(5, 6)))
outFile.write('mul_inv({},{}) = {}\n'.format(24, 26, mod.mul_inv(24,
26)))
outFile.write('mul_inv({},{}) = {}\n'.format(700, 440,
mod.mul_inv(700, 440)))
outFile.write('mul_inv({},{}) = {}\n'.format(0, 777,
mod.mul_inv(700, 440)))
outFile.write('mul_inv({},{}) = '.format(1, [99]))
outFile.write(mod.mul_inv(1, [99]))
outFile.write('\n')
outFile.write('mul_inv({},{}) = '.format([1], 99))
outFile.write(mod.mul_inv([1], 99))
outFile.write('\n')
outFile.write('\n')
outFile.write('18- Testing Multiplicative Inverse Table:\n')
outFile.write('Multiplicative Inverse Table for mode {} =\n'.format(5))
mulInvTab = mod.mul_inv_table(5)
outFile.write(str(mulInvTab[0]))
outFile.write('\n')
outFile.write(str(mulInvTab[1]))
outFile.write('\n')
outFile.write('Multiplicative Inverse Table for mode {} =\n'.format(26))
mulInvTab = mod.mul_inv_table(26)
outFile.write(str(mulInvTab[0]))
outFile.write('\n')
outFile.write(str(mulInvTab[1]))
outFile.write('\n')
outFile.write('Multiplicative Inverse Table for mode {} =\n'.format(-2))
outFile.write(mod.mul_inv_table(-2))
outFile.write('\n')
outFile.write('\n')
outFile.close()
print('Comparing q1_solution with q1_sample:')
print(utilities_A4.compare_files('q1_solution.txt', 'q1_sample.txt'))
print()
print("-------------------------------------------")
return
