def aks_test(n):
"""
Implement the AKS primality test.
"""
get_context().precision = bit_length(n)
# Check if n is a perfect power. If so, return composite.
if is_power(n):
return "composite"
# Find the smallest r such that the multiplicative order of n modulo r
# is greater than log(n, 2)^2
r = get_r(n)
# If 1 < gcd(a, n) < n for some a <= r, return composite
for a in range(1, r):
if gcd(a, n) > 1 and gcd(a, n) < n:
return "composite"
# If n <= r, return prime
if n <= r:
return "prime"
# Check if (x + a)^n mod (x^r - 1, n) != (x^n + a) mod (x^r - 1, n)
if False in ray.get([
is_congruent.remote(a, n, r)
for a in range(1, mpz(floor(sqrt(phi(r)) * log2(n))))
]):
return "composite"
return "prime"
def check(self, i):
#区间大小
diff = self.right - self.left
#新的左右区间
curleft = self.left + diff * self.lp1[i]
curright = self.left + diff * self.rp1[i]
#读取的数转化为小数
decimal = gmpy2.mpfr(self.cur / self.log10)
decimal = decimal - gmpy2.floor(decimal)
#判断是否满足要求
if curleft > decimal:
return False
if curright < decimal:
return False
#更新区间
self.left = curleft
self.right = curright
#通过decimal计算新的cur，抛弃掉cur前导多余数字，cur维持为整数防止精度缺失
self.cur = decimal*self.log10
self.cur = gmpy2.rint_round(self.cur)
return True
def bits_in_number(number):
"""
Returns number of bits in the given number
:param number: long number
"""
if number == 0:
return 0
return gmpy2.mpz(gmpy2.floor(gmpy2.log2(number)) + 1)
def find_limits():
# create an empty dictionary
limits = {}
for planet in xrange(1, 10):
# read date files, one per planet
file_in = open('VSOP2013p' + str(planet) + '.dat')
# create a list with the header position and values for variables planet, var, power
elenco = [(s[0], s[1].split()) for s in enumerate(file_in)
if "VSOP" in s[1]]
file_in.close()
# extend the dictionary with a subdictionary for each planet
limits[planet] = {}
for var in xrange(1, 7):
# extend the dictionary with a subdictionary for each variable
limits[planet][var] = {}
for power in xrange(0, 21):
# extend the dictionary with a subdictionary for each power
limits[planet][var][power] = {}
for threshold in xrange(0, 21):
# extend the dictionary with a two values tuple (min and max)
# for each sensibility threshold
# and for each item in list assign (0,0) to the tuple
limits[planet][var][power][threshold] = (0, 0)
# create a tuple with range limits for each planet, variable, power
for i in xrange(len(elenco)):
start = int(elenco[i][0]) + 1
planet = int(elenco[i][1][1])
var = int(elenco[i][1][2])
power = int(elenco[i][1][3])
end = int(elenco[i][1][4]) + start
# load a file chunk for each voice in list and find extreme value for each threshold
file_in = open('VSOP2013p' + str(planet) + '.dat')
segmento = islice(file_in, start, end)
for j, k in enumerate(segmento):
cursor = j
line = k.split()
Sb = float(line[-4])
Se = int(line[-3])
S = Sb * 10**Se
Cb = float(line[-2])
Ce = int(line[-1])
C = Cb * 10**Ce
ro = gmp.sqrt(S * S + C * C)
threshold = -int(gmp.floor(gmp.log10(ro)))
limits[planet][var][power][threshold] = (start, start + cursor)
file_in.close()
for planet in xrange(1, 10):
for var in xrange(1, 7):
for power in xrange(0, 21):
for threshold in xrange(1, 21):
prec_ = limits[planet][var][power][threshold - 1]
subs_ = limits[planet][var][power][threshold]
if subs_ == (0, 0) and prec_ != 0:
limits[planet][var][power][threshold] = limits[planet][
var][power][threshold - 1]
return limits
def find_sqrt(N):
n =gmpy2.floor(
gmpy2.sqrt(
gmpy2.mpfr(N,precision = len(str(N))+50 )
)
)
n = gmpy2.mpz(n)
for i in xrange(-2**10,2**20,1):
#print (n+i)**2>N
if (n+i)**2>N:
print 'found'
return n+i
assert False,'bla'
def format(num):
s = ''
si = ''
if num < GSConst.c[0]:
num = -num
si = '-'
num1 = mpz(floor(num))
while 1:
s = str(num1 % 10) + s
num1 -= num1 % 10
num1 /= 10
if num1 <= 0:
break
s += '.'
num1 = num - floor(num)
for i in range(100):
num1 *= 10
s += str(mpz(floor(num1)))
num1 -= floor(num1)
s = si + s
return s
def format(num):
s = ''
si = ''
if num < GSConst.c[0]:
num = -num
si = '-'
num1 = mpz(floor(num))
while 1:
s = str(num1 % 10) + s
num1 -= num1 % 10
num1 /= 10
if num1 <= 0:
break
s += '.'
num1 = num - floor(num)
for i in range(100):
num1 *= 10
s += str(mpz(floor(num1)))
num1 -= floor(num1)
s = si + s
return s
def ex3():
N = mpz(
720062263747350425279564435525583738338084451473999841826653057981916355690188337790423408664187663938485175264994017897083524079135686877441155132015188279331812309091996246361896836573643119174094961348524639707885238799396839230364676670221627018353299443241192173812729276147530748597302192751375739387929
)
sqrt_6N = sqrt(6 * N)
sqrt_6N_decimal = sqrt_6N % 1
if sqrt_6N_decimal < 0.5:
A = floor(sqrt_6N) + 0.5
else:
A = ceil(sqrt_6N)
x = sqrt(A**2 - 6 * N)
# P = 3 * p
# Q = 2 * q
P = A - x
p = mpz(P / 3)
print(p)
def naive(number):
if number == 2:
return True
if number % 2 == 0 or number < 2:
return False
i = 3
rooted = gmpy2.floor(gmpy2.sqrt(number))
print rooted
while i <= rooted:
if number % i == 0:
return False
i += 2
if i % 10000000 == 1:
print i
return True
def lsb_oracle(public_key, ciphertext, oracle):
# type: (RSAKey, RSACiphertext, Callable[[RSACiphertext], bool]) -> RSAPlaintext
r"""
The Least Significant Bit Oracle attack is a simpler variation on
Bleichenbacher.
It assumes a decryption oracle :math:`LSB(\dot)` that accepts ciphertexts and returns the
least significant or parity bit of the decrypted plaintext.
"""
mult = powmod(2, public_key.e, public_key.n)
t = (ciphertext * mult) % public_key.n
lower = mpfr(0)
upper = mpfr(public_key.n)
for i in range(public_key.n.bit_length()):
possible_plaintext = (lower + upper) / 2
if not oracle(int(t)):
upper = possible_plaintext # plaintext is in the lower half
else:
lower = possible_plaintext # plaintext is in the upper half
t = (t * mult) % public_key.n
return mpz(floor(upper))
err=0
try:
p=remote('programming.pwn2win.party','9004',ssl=1)
except:
err=err+1
if err>10 : break
continue
s=''
t=0
while 1:
s=''
s=p.recv()
if s.startswith('CTF-BR{') or s == 'WRONG ANSWER': break
if 'WRONG' in s: break
n1= gmpy2.mpz(s)
n=gmpy2.floor((gmpy2.sqrt(n1)-1)/2)
print 'n='+str(n)
n2=(2*n+1)*(2*n+1)
d=n1-n2
print 'd='+str(d)
v1=2*n+1
v2=2*n+1+2*(n+1)
v3=2*n+1+4*(n+1)
v4=2*n+1+4*(n+1)+2*(n+1)+1
x=0
y=0
if d<v1:
x=n+1
y=d-n
elif d<v2:
x=n+1-(d-v1)
from gmpy2 import mpz, isqrt, floor
data = open('a.txt', 'r').read().split('\n')
T = int(data.pop(0))
for t in range(T):
(r, ml) = map(mpz, data.pop(0).split(' '))
a = mpz('2')
b = mpz(2 * r - 1)
c = mpz(-1 * ml)
ans = int(floor((isqrt(mpz(b * b - 4.0 * a * c)) - b) / (2.0 * a)))
print 'Case #' + str(t + 1) + ": " + str(ans)
def getexponent(self):
return int(gmpy2.floor(self.log().val))
err = 0
try:
p = remote('programming.pwn2win.party', '9004', ssl=1)
except:
err = err + 1
if err > 10: break
continue
s = ''
t = 0
while 1:
s = ''
s = p.recv()
if s.startswith('CTF-BR{') or s == 'WRONG ANSWER': break
if 'WRONG' in s: break
n1 = gmpy2.mpz(s)
n = gmpy2.floor((gmpy2.sqrt(n1) - 1) / 2)
print 'n=' + str(n)
n2 = (2 * n + 1) * (2 * n + 1)
d = n1 - n2
print 'd=' + str(d)
v1 = 2 * n + 1
v2 = 2 * n + 1 + 2 * (n + 1)
v3 = 2 * n + 1 + 4 * (n + 1)
v4 = 2 * n + 1 + 4 * (n + 1) + 2 * (n + 1) + 1
x = 0
y = 0
if d < v1:
x = n + 1
y = d - n
elif d < v2:
x = n + 1 - (d - v1)
def is_prime_by_AKS(n):
"""
使用AKS算法确定n是否是一个素数
True:n是素数
False:n是合数
"""
def __is_integer__(n):
"""
判断一个数是否是整数
"""
i = gmpy2.mpz(n)
f = n - i
return not f
def __phi__(n):
"""
欧拉函数，测试小于n并与n互素的个数
"""
res = gmpy2.mpz(n)
a = gmpy2.mpz(n)
for i in range(2, a + 1):
if a % i == 0:
res = res // i * (i - 1)
while a % i == 0:
a //= i
if a > 1:
res = res // a * (a - 1)
return res
def __gcd__(a, b):
"""
计算a b的最大公约数
"""
if b == 0:
return a
return __gcd__(gmpy2.mpz(b), gmpy2.mpz(a) % gmpy2.mpz(b))
print("步骤1, 确定%d是否是纯次幂" % n)
for b in range(2, gmpy2.mpz(gmpy2.floor(gmpy2.log2(n))) + 1):
a = n**(1 / b)
if __is_integer__(a):
return False
print("步骤2，找到一个最小的r，符合o_r(%d) > (log%d)^2" % (n, n))
maxk = gmpy2.mpz(gmpy2.floor(gmpy2.log2(n)**2))
maxr = max(3, gmpy2.mpz(gmpy2.ceil(gmpy2.log2(n)**5)))
nextR = True
r = 0
for r in range(2, maxr):
if nextR == False:
break
nextR = False
for k in range(1, maxk + 1):
if nextR == True:
break
nextR = (gmpy2.mpz(n**k % r) == 0) or (gmpy2.mpz(n**k % r) == 1)
r = r - 1 # 循环多增加了一层
print("r = %d" % r)
print("步骤3，如果 1 < gcd(a, %d) < %d，对于一些 a <= %d, 输出合数" % (n, n, r))
for a in range(r, 1, -1):
g = __gcd__(a, n)
if g > 1 and g < n:
return False
print("步骤4，如果n=%d <= r=%d，输出素数" % (n, r))
if n <= r:
return True
print("步骤5")
print("遍历a从1到\sqrt{\phi(r=%d)}logn=%d" % (r, n))
print("如果(X+a)^%d != X^%d+a mod {X^%d-1, %d}$输出合数" % (n, n, r, n))
# 构造P = (X+a)^n mod (X^r-1)
print("构造多项式(X+a)^%d,并且进行二项式展开" % n)
X = multi_ysymbols('X')
a = multi_ysymbols('a')
X_a_n_expand = binomial_expand(ypolynomial1(X, a), n)
print(X_a_n_expand)
X.pow(r)
reduce_poly = ypolynomial1(X, ysymbol(value=-1.0))
print("构造消减多项式 %s" % reduce_poly)
print("进行运算 (X+a)^%d mod (X^%d-1)" % (n, r))
r_equ = ypolynomial_mod(X_a_n_expand, reduce_poly)
print("得到余式: %s" % r_equ)
print("进行运算'余式' mod %d 得到式(A)" % n)
A = ypolynomial_reduce(r_equ, n)
print("A = %s" % A)
print("B = x^%d+a mod x^%d-1" % (n, r))
B = ypolynomial1(multi_ysymbols('X', power=31), a)
B = ypolynomial_mod(B, reduce_poly)
print("B = %s" % B)
C = ypolynomial_sub(A, B)
print("C = A - B = %s" % C)
maxa = math.floor(math.sqrt(__phi__(r)) * math.log2(n))
print("遍历a = 1 to %d" % maxa)
print("检查每个'%s = 0 (mod %d)'" % (C, n))
for a in range(1, maxa + 1):
print("检查a = %d" % a)
C.set_variables_value(a=a)
v = C.eval()
if v % n != 0:
return False
print("步骤6 输出素数")
return True
def getexponent(self):
return int(gmpy2.floor(self.log().val))
#!/usr/bin/env python3 # Calculates floor(2**256/pi), and encodes the result as base64. # Intended to be used as a SHA256 hash where I don't have a preimage up my sleeve. # Originally by Ryan Castellucci. Python3 port, pi sourcing, and base64 output added by Jeremy Rand. import codecs, gmpy2 # precision in bits gmpy2.get_context().precision = 1024 # 1000 digits of pi from https://www.angio.net/pi/digits/1000.txt (first HTTPS result in Startpage results for "digits of pi") # (retrieved 2017 May 13.) pi_str = '3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198' pi_mpfr = gmpy2.mpfr(pi_str) fraction = gmpy2.floor(2**256 / pi_mpfr) hx = hex(int(fraction))[2:66] #print(hx) b64 = codecs.encode(codecs.decode(hx, "hex"), "base64").decode() print(b64)
#!/usr/bin/env python2
import sys, os
import math
import gmpy2
# Cases
t = int(sys.stdin.readline())
gmpy2.get_context().precision=150
for case in xrange(t):
r, t = map(int, sys.stdin.readline().rstrip('\n').split())
delta = (2*r-1)**2 + 8*t
result = 0
if delta < 0:
result = 0
else:
result = int(gmpy2.floor((-(2*r-1)+gmpy2.sqrt(delta))/4))
print "Case #%d: %d" % (case+1, result)
