def three():
N = mpz('720062263747350425279564435525583738338084451473999841826653057981916355690188337790423408664187663938485175264994017897083524079135686877441155132015188279331812309091996246361896836573643119174094961348524639707885238799396839230364676670221627018353299443241192173812729276147530748597302192751375739387929')
A = mul(isqrt(mul(6,N)),2)
A = add(A,1)
x = isqrt(sub(mul(A,A),mul(24,N)))
p = t_div(sub(A,x),6)
q = t_div(add(A,x),4)
if mul(p,q) == N:
print "3. " + str(p)
def three():
N = mpz(
'720062263747350425279564435525583738338084451473999841826653057981916355690188337790423408664187663938485175264994017897083524079135686877441155132015188279331812309091996246361896836573643119174094961348524639707885238799396839230364676670221627018353299443241192173812729276147530748597302192751375739387929'
)
A = mul(isqrt(mul(6, N)), 2)
A = add(A, 1)
x = isqrt(sub(mul(A, A), mul(24, N)))
p = t_div(sub(A, x), 6)
q = t_div(add(A, x), 4)
if mul(p, q) == N:
print "3. " + str(p)
def _batchgcd(xs):
tree = _product_tree(xs)
rems = tree.pop()
while tree:
LOGGER.info('Calculating batch GCDs: %10d' % (len(tree)))
xs = tree.pop()
rems = [
gmpy2.mod(rems[i // 2], gmpy2.mul(xs[i], xs[i]))
for i in range(len(xs))
]
return [gmpy2.gcd(gmpy2.t_div(r, n), n) for r, n in zip(rems, xs)]
def square_root(x, N):
square_root_x = gmpy2.powmod(x, gmpy2.t_div(N+1, 4), N)
return square_root_x
for i in range(0, TEST_N):
indexX = random.randint(0, MAX_N - 1)
indexY = random.randint(0, MAX_N - 1)
X = arr[indexX]
Y = arr[indexY]
ans = gmpy2.add(X, Y)
addition_content += generate_exp(indexX, indexY, '+')
addition_content += generate_equal(ans)
ans = gmpy2.sub(X, Y)
subtraction_content += generate_exp(indexX, indexY, '-')
subtraction_content += generate_equal(ans)
ans = gmpy2.mul(X, Y)
multiple_content += generate_exp(indexX, indexY, '*')
multiple_content += generate_equal(ans)
ans = gmpy2.t_div(X, Y)
division_content += generate_exp(indexX, indexY, '/')
division_content += generate_equal(ans)
ans = gmpy2.t_mod(X, Y)
division_content += generate_exp(indexX, indexY, '%')
division_content += generate_equal(ans)
def write_longer(test_case_name, file_name, content):
test_case = generate_test_case(test_case_name, 'Longer',
init_content + content)
output = open(file_name, 'w')
output.write(generate_header())
output.write(test_case)
output.close()
print("The number:", numtofactor)
print("has prime factors:")
print("[", end="")
def findprimefactor(numtofactor):
for primenum in primelist2M.primelist:
if (gmpy2.t_mod(numtofactor, primenum) == 0):
return (primenum)
return (0)
while (True):
if gmpy2.is_prime(numtofactor):
# We are done. All prime factors found
print(str(numtofactor) + "]")
exit(0)
primefactor = findprimefactor(numtofactor)
if (primefactor == 0):
# The remainder is not itself prime, and
# has no factors in the prime list.
# continue the 'hard way', maybe rho algorithm
print("rem=" + str(numtofactor) + "]")
exit(0)
print(str(primefactor) + ",", flush=True, end="")
numtofactor = gmpy2.t_div(numtofactor, primefactor)
#print("new num to factor = ",numtofactor)
def L(x, n):
return gmpy2.t_div(x - 1, n)
def get_random_safe_prime(start,end):
i = random.randint(start,end) # better random nunber generator
while not (gmpy2.is_prime(i) and gmpy2.is_prime(gmpy2.t_div((i-1),2))):
i +=1
return i
def divide(x, y):
return gmpy2.t_div(gmpy2.mpz(x), gmpy2.mpz(y))
2x == sqrt(4*A**2 - 4*A + 1 - 24*N)
3p == A - (x + 0.5)
6p == 2A - 2x - 1
p == 6p / 6
2q == A + (x - 0.5)
4q == 2A + 2x - 1
q = 4q / 4
"""
t0 = 4 * (A**2) - 4 * A + 1 - 24 * N
twox, is_exact = iroot(t0, 2)
if not is_exact:
print("twox is not an integer!!!")
sys.exit(1)
sixp = 2 * A - twox - 1
fourq = 2 * A + twox - 1
p = t_div(sixp, 6)
q = t_div(fourq, 4)
if (p * q) != N:
print("3: Fail check")
print("3:")
print(p.digits() if p < q else q.digits())
"""
Challenge 4.
"""
N = mpz(
'179769313486231590772930519078902473361797697894230657273430081157732675805505620686985379449212982959585501387537164015710139858647833778606925583497541085196591615128057575940752635007475935288710823649949940771895617054361149474865046711015101563940680527540071584560878577663743040086340742855278549092581'
)
C = mpz(
'22096451867410381776306561134883418017410069787892831071731839143676135600120538004282329650473509424343946219751512256465839967942889460764542040581564748988013734864120452325229320176487916666402997509188729971690526083222067771600019329260870009579993724077458967773697817571267229951148662959627934791540'
)
D.append(gmpy2.f_mod(gmpy2.mul(r, C[i]), p))
D_sum = gmpy2.mpz(0)
for i in range(0, n):
D_sum = gmpy2.add(D_sum, D[i])
D_sum = gmpy2.f_mod(D_sum, p)
#P_0 retrieves E:
sI = gmpy2.invert(s, p)
E = gmpy2.f_mod(gmpy2.mul(sI, D_sum), p)
if eval_correctness:
#Evaluate Correctness of Protocol
res = gmpy2.sub(E, gmpy2.f_mod(E, gmpy2.mul(alpha, alpha)))
res = gmpy2.t_div(res, gmpy2.mul(alpha, alpha))
correct += abs(res - plain_res)
#print("plaintext result:" + str(plain_res))
#print("protocol result:" + str(res) + "\n")
else:
#Evaluate the Attack by computing E'=E/alpha
Ep = gmpy2.t_div(E, alpha)
s_Ep = gmpy2.digits(Ep)
b0a = [
gmpy2.mul(gmpy2.mul(ai, b), alpha) for b, ai in zip(b0, a)
]
b1a = [
gmpy2.mul(gmpy2.mul(ai, b), alpha) for b, ai in zip(b1, a)
]