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 mTMRCA_C(trees, log = None,
left = 0, right = math.inf,
gmap = Gmap(None), sft = False):
N = trees.num_samples
mtmrca_C = matrix.new_matrix(N)
tmp = 0
total_l = 0
pbar = tqdm.tqdm(total = trees.num_trees,
bar_format = '{l_bar}{bar:30}{r_bar}{bar:-30b}',
miniters = trees.num_trees // 100,
file = log)
trees_ = trees.trees()
if sft: next(trees_)
for tree in trees_:
pbar.update(1)
if tree.total_branch_length == 0: continue
l = - gmap(max(left, tree.interval[0])) + gmap(min(right, tree.interval[1]))
if l <= 0: continue
height = 0
for c in tree.nodes():
descendants = list(tree.samples(c))
n = len(descendants)
if(n == 0 or n == N): continue
t = tree.time(tree.parent(c)) - tree.time(c)
height = max(height, tree.time(tree.parent(c)))
matrix.add_square(mtmrca_C, descendants, t * l)
tmp += height * l
total_l += l
mtmrca = mat_C_to_ndarray(mtmrca_C, N)
mtmrca = tmp - mtmrca
mtmrca /= total_l
pbar.close()
return mtmrca, total_l
def d_type3(ciphertext):
alpha = utilities.get_lower()
dictList = utilities.load_dictionary('engmix.txt')
for a in range(0, 5):
for b in range(0, 5):
for c in range(0, 5):
for d in range(0, 5):
key_matrix = matrix.new_matrix(2, 2, 0)
key_matrix[0][0] = a
key_matrix[0][1] = b
key_matrix[1][0] = c
key_matrix[1][1] = d
if mod.has_mul_inv(a * d - b * c, 26):
key = ''
for i in range(2):
for j in range(2):
key += alpha[key_matrix[i][j]]
first = d_hill(ciphertext, key)
k, plain = cryptanalysis_shift(first)
if utilities.is_plaintext(plain, dictList, 0.70):
return plain, (k, key)
def test_q4():
print("-------------------------------------------")
print("Testing Q4: Matrix Library")
filename = 'q4_solution.txt'
outFile = open(filename, 'w')
print()
outFile.write('1- Testing is_vector:\n')
outFile.write('is_vector({}) = {}\n'.format([], matrix.is_vector([])))
outFile.write('is_vector({}) = {}\n'.format([10], matrix.is_vector([10])))
outFile.write('is_vector({}) = {}\n'.format([10, 20],
matrix.is_vector([10, 20])))
outFile.write('is_vector({}) = {}\n'.format(10, matrix.is_vector(10)))
outFile.write('is_vector({}) = {}\n'.format([3, 4.5],
matrix.is_vector([3, 4.5])))
outFile.write('is_vector({}) = {}\n'.format([[]], matrix.is_vector([[]])))
outFile.write('is_vector({}) = {}\n'.format([[1, 2], [3, 4]],
matrix.is_vector([[1, 2],
[3, 4]])))
outFile.write('\n')
outFile.write('2- Testing is_matrix')
A = []
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [5]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [[1, 2], [3, 4]]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [[1], [2], [3]]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [[1, 2, 3], [4, 5, 6]]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = 5
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [5.5]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
A = [[1, 2, 3], [4, 5]]
outFile.write('is_matrix({}) = {}\n'.format(A, matrix.is_matrix(A)))
outFile.write('\n')
print('3- Testing print_matrix')
A = []
print('print_matrix({})='.format(A))
matrix.print_matrix(A)
A = [10, 20, 30]
print('print_matrix({})='.format(A))
matrix.print_matrix(A)
A = [[10], [20], [30]]
print('print_matrix({})='.format(A))
matrix.print_matrix(A)
A = [[10, 20, 30], [40, 50, 60], [70, 80, 10]]
print('print_matrix({})='.format(A))
matrix.print_matrix(A)
A = [[10, 20, 30], [40, 50, 60], [70, 80]]
print('print_matrix({})='.format(A))
print(matrix.print_matrix(A))
print()
outFile.write('4/5/6- Testing size functions\n')
A = []
outFile.write('get_rowCount({}) = {}\n'.format(A,
matrix.get_rowCount(A)))
outFile.write('get_ColumnCount({}) = {}\n'.format(
A, matrix.get_columnCount(A)))
outFile.write('get_size({}) = {}\n'.format(A, matrix.get_size(A)))
outFile.write('\n')
A = [1, 2, 3]
outFile.write('get_rowCount({}) = {}\n'.format(A,
matrix.get_rowCount(A)))
outFile.write('get_ColumnCount({}) = {}\n'.format(
A, matrix.get_columnCount(A)))
outFile.write('get_size({}) = {}\n'.format(A, matrix.get_size(A)))
outFile.write('\n')
A = [[1, 2], [3, 4], [5, 6]]
outFile.write('get_rowCount({}) = {}\n'.format(A,
matrix.get_rowCount(A)))
outFile.write('get_ColumnCount({}) = {}\n'.format(
A, matrix.get_columnCount(A)))
outFile.write('get_size({}) = {}\n'.format(A, matrix.get_size(A)))
outFile.write('\n')
A = [[1, 2], [3]]
outFile.write('get_rowCount({}) = {}\n'.format(A,
matrix.get_rowCount(A)))
outFile.write('get_ColumnCount({}) = {}\n'.format(
A, matrix.get_columnCount(A)))
outFile.write('get_size({}) = {}\n'.format(A, matrix.get_size(A)))
outFile.write('\n')
outFile.write('7- Testing is_square\n')
A = []
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
A = [5]
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
A = [5, 6]
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
A = [[1, 2], [3, 4]]
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
A = [5.5]
outFile.write('is_square({}) = {}\n'.format(A, matrix.is_square(A)))
outFile.write('\n')
outFile.write('8/9/10- Testing getter functions\n')
A = [[1, 2, 3], [4, 5, 6]]
i = 0
j = 1
outFile.write('get_row({},{}) = {}\n'.format(A, i, matrix.get_row(A,
i)))
outFile.write('get_Column({},{}) = {}\n'.format(A, j,
matrix.get_column(A, j)))
outFile.write('get_element({},{},{}) = {}\n'.format(
A, i, j, matrix.get_element(A, i, j)))
outFile.write('\n')
i = 2
j = 2
outFile.write('get_row({},{}) = {}\n'.format(A, i, matrix.get_row(A,
i)))
outFile.write('get_Column({},{}) = {}\n'.format(A, j,
matrix.get_column(A, j)))
outFile.write('get_element({},{},{}) = {}\n'.format(
A, i, j, matrix.get_element(A, i, j)))
outFile.write('\n')
i = 1
j = 3
outFile.write('get_row({},{}) = {}\n'.format(A, i, matrix.get_row(A,
i)))
outFile.write('get_Column({},{}) = {}\n'.format(A, j,
matrix.get_column(A, j)))
outFile.write('get_element({},{},{}) = {}\n'.format(
A, i, j, matrix.get_element(A, i, j)))
outFile.write('\n')
A = [[1, 2, 3], []]
outFile.write('get_row({},{}) = {}\n'.format(A, i, matrix.get_row(A,
i)))
outFile.write('get_Column({},{}) = {}\n'.format(A, j,
matrix.get_column(A, j)))
outFile.write('get_element({},{},{}) = {}\n'.format(
A, i, j, matrix.get_element(A, i, j)))
outFile.write('\n')
outFile.write('11- Testing new_matrix\n')
r = 0
c = 0
pad = 0
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
c = 1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
r = 1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
r = 2
c = 1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
c = 2
r = 1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
c = 3
r = 3
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
r = -1
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
r = 3
c = -5
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
c = 5
pad = 3.5
outFile.write('new_matrix({},{},{})=\n{}\n'.format(
r, c, pad, matrix.new_matrix(r, c, pad)))
outFile.write('\n')
outFile.write('12- Testing get_I\n')
size = -1
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
size = 0
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
size = 1
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
size = 2
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
size = 3
outFile.write('get_I({}) = {}\n'.format(size, matrix.get_I(size)))
outFile.write('\n')
outFile.write('13- Testing is_identity\n')
A = [1]
outFile.write('is_identity({}) = {}\n'.format(A, matrix.is_identity(A)))
A = matrix.get_I(3)
outFile.write('is_identity({}) = {}\n'.format(A, matrix.is_identity(A)))
A = [[1, 0], [1, 1]]
outFile.write('is_identity({}) = {}\n'.format(A, matrix.is_identity(A)))
A = [[1, 0], [0, 1, 0]]
outFile.write('is_identity({}) = {}\n'.format(A, matrix.is_identity(A)))
outFile.write('\n')
outFile.write('14- Testing scalar_mul\n')
A = [[1, 2], [3, 4]]
c = 10
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
A = [1, 2, 3, 4]
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
A = []
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
A = [1, 2, 3, [4]]
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
A = [[1, 2], [3, 4]]
c = [10]
outFile.write('scalar_mul({},{}) = {}\n'.format(A, c,
matrix.scalar_mul(c, A)))
outFile.write('\n')
outFile.write('15- Testing mul\n')
A = [[1, 2], [3, 4]]
B = [[10, 20], [30, 40]]
outFile.write('mul({},{})=\n{}\n'.format(A, c, matrix.mul(A, B)))
A = [[1, 2, 3], [5, 6, 7]]
B = [[10, 20], [30, 40], [50, 60]]
outFile.write('mul({},{})= {}\n'.format(A, c, matrix.mul(A, B)))
A = [5]
B = [10]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
A = [0, 1, 2]
B = [[0], [1], [2]]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
A = [[0], 1]
B = [1, 0]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
A = [1, 0]
B = [[0], 1]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
A = [[1, 2, 3], [5, 6, 7]]
B = [[10, 20], [30, 40], [50, 60]]
outFile.write('mul({},{})= {}\n'.format(B, A, matrix.mul(B, A)))
A = [[1, 2, 3], [5, 6, 7]]
B = [[10, 20], [30, 40]]
outFile.write('mul({},{})= {}\n'.format(A, B, matrix.mul(A, B)))
outFile.write('\n')
outFile.write('16- Testing matrix_mod\n')
A = [[1, 2], [3, 4]]
m = 2
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
A = [1, 2, 3, 4]
m = 2
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
A = [[3], [5]]
m = 3
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
A = [[3], [5]]
m = 0
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
A = [3, [5]]
m = 6
outFile.write('matrix_mod({},{})= {}\n'.format(A, m,
matrix.matrix_mod(A, m)))
outFile.write('\n')
outFile.write('17- Testing det\n')
A = [[1, 2], [3, 4]]
outFile.write('det({})= {}\n'.format(A, matrix.det(A)))
A = [10]
outFile.write('det({})= {}\n'.format(A, matrix.det(A)))
A = [[1, 1, 1], [2, 2, 2], [3, 3, 3]]
outFile.write('det({})= {}\n'.format(A, matrix.det(A)))
A = [[1, 1, 1], [2, 2]]
outFile.write('det({})= {}\n'.format(A, matrix.det(A)))
outFile.write('\n')
outFile.write('18- Testing inverse\n')
A = [[1, 4], [8, 11]]
m = 26
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[4, 3], [1, 1]]
m = 5
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[1, 4], [8, 10]]
m = 26
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [1, 4, 8, 10]
m = 15
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[4, 3], [1, 1]]
m = -5
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
m = 7
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
A = [[1, 2, 3], [4, 5]]
m = 7
outFile.write('inverse({},{})= {}\n'.format(A, m, matrix.inverse(A, m)))
outFile.close()
print('Comparing q4_solution with q4_sample:')
print(utilities_A4.compare_files('q4_solution.txt', 'q4_sample.txt'))
print()
print("-------------------------------------------")
def d_hill(ciphertext, key):
plaintext = ''
base = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
if len(ciphertext) == 0:
print('Error(d_hill): invalid ciphertext')
return plaintext
if len(key) > 4:
key = key[:4]
elif len(key) < 4:
x = len(key)
count = 0
while len(key) != 4:
if count == x:
count = 0
key += key[count]
count += 1
alpha = utilities_A4.get_nonalpha(ciphertext)
text = utilities_A4.remove_nonalpha(ciphertext)
text = text.upper()
if len(text) % 2 != 0:
text += 'Q'
indx1 = 0
indx2 = 0
textMatrix = matrix.new_matrix(2, int(len(text) / 2), 0)
for i in range(len(text)):
if i % 2 == 0:
textMatrix[0][indx1] = base.find(text[i])
indx1 += 1
else:
textMatrix[1][indx2] = base.find(text[i])
indx2 += 1
keyMatrix = matrix.new_matrix(2, 2, 0)
count = 0
for i in range(2):
for j in range(2):
keyMatrix[i][j] = base.find(key[count].upper())
count += 1
inverse = matrix.inverse(keyMatrix, 26)
for i in range(int(len(text) / 2)):
a = textMatrix[0][i] * inverse[0][0] + textMatrix[1][i] * inverse[0][1]
b = textMatrix[0][i] * inverse[1][0] + textMatrix[1][i] * inverse[1][1]
plaintext += base[a % 26]
plaintext += base[b % 26]
plaintext = utilities_A4.insert_nonalpha(plaintext, alpha)
plaintext = plaintext.lower()
while plaintext[len(plaintext) - 1] == 'q':
plaintext = plaintext[:-1]
return plaintext
def new_zbuffer(width=XRES, height=YRES):
return new_matrix(width, height, float("-inf"))
def varGRM_C(trees, log = None,
rlim = 0, alim = math.inf,
left = 0, right = math.inf,
gmap = Gmap(None), g = (lambda x: 1/(x*(1-x))),
var = True, sft = False):
N = trees.num_samples
egrm_C = matrix.new_matrix(N)
if var:
egrm2_C = matrix.new_matrix(N)
tmp1 = np.zeros(N)
tmp2 = 0
total_mu = 0
pbar = tqdm.tqdm(total = trees.num_trees,
bar_format = '{l_bar}{bar:30}{r_bar}{bar:-30b}',
miniters = trees.num_trees // 100,
file = log)
trees_ = trees.trees()
if sft: next(trees_)
for tree in trees_:
pbar.update(1)
if tree.total_branch_length == 0: continue
l = - gmap(max(left, tree.interval[0])) + gmap(min(right, tree.interval[1]))
if l <= 0: continue
for c in tree.nodes():
descendants = list(tree.samples(c))
n = len(descendants)
if(n == 0 or n == N): continue
t = max(0, min(alim, tree.time(tree.parent(c))) - max(rlim, tree.time(c)))
mu = l * t * 1e-8
p = float(n/N)
matrix.add_square(egrm_C, descendants, mu * g(p))
if var:
matrix.add_square(egrm2_C, descendants, mu * np.power(g(p), 2) * np.power((1 - 2*p), 2))
tmp1[descendants] += mu * np.power(g(p), 2) * (np.power(p, 2) - 2 * np.power(p, 3))
tmp2 += mu * np.power(g(p), 2) * np.power(p, 4)
total_mu += mu
egrm = mat_C_to_ndarray(egrm_C, N)
if var:
egrm2 = mat_C_to_ndarray(egrm2_C, N)
egrm /= total_mu
if var:
egrm2 /= total_mu
tmp1 /= total_mu
tmp2 /= total_mu
egrm -= egrm.mean(axis = 0)
egrm -= egrm.mean(axis = 1, keepdims=True)
if var:
e = np.reciprocal((lambda x:x[x!=0])(np.random.poisson(lam=total_mu, size=10000)).astype("float")).mean()
vargrm = e * (egrm2 + np.tile(tmp1, (N, 1)) + np.tile(tmp1, (N, 1)).transpose() + tmp2 - np.power(egrm, 2))
else:
vargrm = None
pbar.close()
return egrm, vargrm, total_mu