USTC CTF 2019

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import gmpy2    
from Crypto.Util.number import getPrime, getRandomInteger    
def TonelliShanks(p, a):  # TonelliShanks算法    
if pow(a, (p - 1) // 2, p) != 1:    
    return -1    
q = p - 1    
m = 0    
while q % 2 == 0:    
    q //= 2    
    m += 1    
z = 0    
while pow(z, (p - 1) // 2, p) != p - 1:    
    z = getRandomInteger(10)    
c = pow(z, q, p)    
t = pow(a, q, p)    
r = pow(a, (q + 1) // 2, p)    
while m > 1:    
    tmp = pow(t, 1 << (m - 2), p)    
    if tmp != 1:    
        r = r * c % p    
        t = t * (c * c % p) % p    
    c = c * c % p    
    m -= 1    
return r    
    
    
def find_small_m(x, y, p):    
x2y2 = x * x + y * y    
m = x2y2 // p    
assert 0 == (x2y2 % p) and 0 == (x2y2 % m)    
while 1 < m:    
    u, v = x % m, y % m    
    if u * 2 > m:    
        u -= m    
    if v * 2 > m:    
        v -= m    
    u2v2 = u * u + v * v    
    mm = u2v2 // m    
    assert 0 == (u2v2 % m) and 0 < mm < m    
        
    x, y = (u * x + v * y) // m, (u * y - v * x) // m    
    x2y2 = x * x + y * y    
    m = x2y2 // p    
    assert 0 == (x2y2 % p) and 0 == (x2y2 % m)    
    
return x, y, m    
    
    
def get2square(r): # 这里还可以求两个数的平方和    
if r == 2:    
    return 1, 1    
assert 1 == r % 4 and gmpy2.is_prime(r)    
x0 = TonelliShanks(r, r - 1)    
assert r - 1 == pow(x0, 2, r)    
k, l, m = find_small_m(x0, 1, r)    
assert k * k + l * l == m * r    
assert 1 == m    
return k, l    
    
    
def get4square(n):    
print("n =", n)    
while True:    
    i = getRandomInteger(100)    
    j = getRandomInteger(100)    
    j ^= (i ^ j) & 0x1    
    r = n - i * i - j * j    
    if 1 == r % 4 and gmpy2.is_prime(r):    
        break    
print("r =", r)    
    
k, l = get2square(r)    
    
assert i * i + j * j + k * k + l * l == n    
print("i =", i)    
print("j =", j)    
print("k =", k)    
print("l =", l)    
return i, j, k, l    
    
    
if __name__ == '__main__':    
n = getPrime(256) * getPrime(256)    
print(get4square(n))    

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def get2square_list(n, primes):    
assert list == type(primes)    
check_product = 1    
for p in primes:    
    assert 2 == p or (1 == p % 4 and gmpy2.is_prime(p))    
    check_product *= p    
assert check_product == n    
u, v = 1, 0    
for p in primes:    
    x, y = get2square(p)    
    u, v = u * x + v * y, u * y - v * x    
assert u * u + v * v == n    
return u, v    

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λ nslookup -q=TXT xn--g28h.hack.ustclug.org    
服务器:  UnKnown    
Address:  10.3.9.5    
    
非权威应答:    
xn--g28h.hack.ustclug.org       text =    
    
    "flag{DN5_C4N_H4VE_em0ji_haha}"    

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Regex: (a*)*$    
String: aaaaaaaaaaaaaaaaaaaaaaab    

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from __future__ import division    
    
from pwn import *    
from numpy import *    
from fractions import Fraction    
    
calcList = []    
    
def genFraction(num,n=20):    
f = Fraction(num)    
a = f.numerator    
b = f.denominator    
a = a*a    
b = b*b    
for i in range(n):    
    result = a//b    
    a = a - result*b    
    #print a,b    
    a,b = b,a    
    #print a,b    
    '''    
    if result == 1:    
        break    
    '''    
    #if result > 5000:    
    #    break    
    yield result    
    if b == 0:    
        break    
        
def f(x):    
global calcList    
calcList += ["atan","sin","acos","tan"]    
return tan(arccos(sin(arctan(x))))    
    
def g(x):    
global calcList    
calcList += ["atan","cos"]    
return f(cos(arctan(x)))    
    
def test(aim):    
global calcList    
#aim = log(aim)    
#aim = 42.79781263758425 #tan(72.35711075569202)    
aim = deg2rad(aim)    
x = 0    
fList = []    
for i in genFraction(aim):    
    fList.append(i)    
print fList    
for i in range(len(fList)):    
    a = fList.pop()    
    for j in range(a):    
        x = g(x)    
    calcList += ["1/x"]    
    x = 1/x    
calcList += ["1/x"]    
x = 1/x    
calcList += ["R2D"]    
print "aim = %f" % rad2deg(aim)    
print "x = %f" % (rad2deg(x))    
#print "p = %f" % ((x*x))    
return ",".join(calcList)    
    
    
    
import json    
import requests    
    
host = "http://202.38.93.241:10024"    
    
    
def solve(x):    
return 'sin,cos,x^2' or 'magic'    
    
def test2():    
with requests.session() as sess:    
    r = sess.get(host + '/challenges')    
    X = json.loads(r.text)["msg"]    
    print(X)    
    data = {    
        "a1": test(X[0]),    
        "a2": test(X[1]),    
        "a3": test(X[2])    
    }    
    r = sess.post(host + "/submit", data=data)    
    resp = json.loads(r.text)    
    print(resp["msg"])      
    
test2()    

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x = 130095999494467643631574289251374479743427759332282644620931023932981730612064829262332840253969261363881910701276769455728130421459878658660627330362688856751252524519341435317968272275310598639991033512763704530123231772642623291899534454658707761230166809620539187116816778418242273580873637781313957589597    
y = 116513882455567447431772208851676203256471727099349255694179213039239989833646726805040167642952589899809273716764673737423792812107737304956679717082391151505476360762847773608327055926832394948293052633869637754201186227370594688119795413400655007893009882742908697688490841023621108562593724732469462968731    
z = 88688615046438957657148589794574470139777919686383514327296565433247300792803913489977671293854830459385807133302995575774658605472491904258624914486448276269854207404533062581134557448023142028865220726281791025833570337140263511960407206818858439353134327592503945131371190285416230131136007578355799517986306208039490339159501009668785839201465041101739825050371023956782364610889969860432267781626941824596468923354157981771773589236462813563647577651117020694251283103175874783965004467136515096081442018965974870665038880840823708377340101510978112755669470752689525778937276250835072011344062132449232775717960070624563850487919381138228636278647776184490240264110748648486121139328569423969642059474027527737521891542567351630545570488901368570734520954996585774666946913854038917494322793749823245652065062604226133920469926888309742466030087045251385865707151307850662127591419171619721200858496299127088429333831383287417361021420824398501423875648199373623572614151830871182111045650469239575676312393555191890749537174702485617397506191658938798937462708198240714491454507874141432982611857838173469612147092460359775924447976521509874765598726655964369735759375793871985156532139719500175158914354647101621378769238233    
n ** 10 % (x * y * y * y) == z    
求n    

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#!/usr/bin/env python3    
    
from easy_math import x as p, y as q, z as c    
from sympy.ntheory.residue_ntheory import sqrt_mod    
import sympy.ntheory.residue_ntheory    
import gmpy2    
    
    
def factor_(nn, *args, **kwargs):    
t = 0    
while nn % p == 0:    
    t += 1    
    nn //= p    
s = 0    
while nn % q == 0:    
    s += 1    
    nn //= q    
if nn != 1:    
    print(nn)    
    return None    
return {p: t, q: s}    
    
    
sympy.ntheory.residue_ntheory.factorint = factor_    
    
n = p * q ** 3    
phi = (p - 1) * (q ** 2) * (q - 1)    
root_5th_of_c = pow(c, gmpy2.invert(5, phi // 5), n)    
root_5th_of_1_all = set(pow(i, (phi // 5), n) for i in range(1, 20))    
root_5th_of_1_all = set(r for r in set(root_5th_of_1_all) if pow(r, 5, n) == 1)    
root_5th_of_c_all = [root_5th_of_c * r % n for r in root_5th_of_1_all]    
m_all = [m for r in root_5th_of_c_all for m in sqrt_mod(r, n, True)]    
print(len(m_all))    
for m in m_all:    
h = hex(m)[2:]    
if len(h) % 2 == 0 and bytes.fromhex(hex(m)[2:]).startswith(b"flag"):    
    print(bytes.fromhex(hex(m)[2:]).decode()[:32])    

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#!/usr/bin/env python3    
    
    
class UncertainBit:    
def __init__(self, value):    
    if value == 0 or value == 1 or value == None:    
        self.value = value    
    elif value == "0" or value == "1":    
        self.value = int(value)    
    elif value == "X":    
        self.value = None    
    elif isinstance(value, UncertainBit):    
        self.value = value.value    
    else:    
        raise TypeError()    
    
def __and__(self, other):    
    if self.value != None and other.value != None:    
        return UncertainBit(self.value & other.value)    
    if self.value == 0 or other.value == 0:    
        return UncertainBit(0)    
    return UncertainBit(None)    
    
def __or__(self, other):    
    if self.value != None and other.value != None:    
        return UncertainBit(self.value | other.value)    
    if self.value == 1 or other.value == 1:    
        return UncertainBit(1)    
    return UncertainBit(None)    
    
def __xor__(self, other):    
    if self.value != None and other.value != None:    
        return UncertainBit(self.value ^ other.value)    
    return UncertainBit(None)    
    
def __invert__(self):    
    if self.value is None:    
        return UncertainBit(None)    
    else:    
        return UncertainBit(1 - self.value)    
    
def __repr__(self):    
    if self.value is None:    
        return "X"    
    else:    
        return str(self.value)    
    
def combine(self, other):    
    if self.value != None and other.value != None:    
        if self.value != other.value:    
            raise ValueError()    
    if self.value != None:    
        return UncertainBit(self.value)    
    return UncertainBit(other.value)    
    
def repeat(self, n):    
    return UncertainBitVector(n, [self for _ in range(n)])    
    
    
class UncertainBitVector:    
def __init__(self, bits, value=None):    
    self.bits = bits    
    self.vec = [UncertainBit(0) for _ in range(len(self))]    
    if value is None:    
        for i in range(len(self)):    
            self[i] = None    
    elif isinstance(value, int):    
        if value.bit_length() > len(self):    
            raise ValueError()    
        for i in range(value.bit_length()):    
            self[i] = (value >> i) & 1    
    else:    
        if len(value) > len(self):    
            raise ValueError()    
        for i in range(len(value)):    
            self[i] = value[i]    
    
def __len__(self):    
    return self.bits    
    
def __getitem__(self, key):    
    if isinstance(key, int):    
        if key >= len(self):    
            return UncertainBit(0)    
        return self.vec[key]    
    elif isinstance(key, slice):    
        bv = self.vec[key]    
        return UncertainBitVector(len(bv), bv)    
    else:    
        raise TypeError()    
    
def __setitem__(self, key, value):    
    if isinstance(key, int):    
        self.vec[key] = UncertainBit(value)    
    elif isinstance(key, slice):    
        raise NotImplementedError()    
    else:    
        raise TypeError()    
    
def __and__(self, other):    
    if isinstance(other, int):    
        other = UncertainBitVector(other.bit_length(), other)    
    bits = min(len(self), len(other))    
    return UncertainBitVector(bits, [self[i] & other[i] for i in range(bits)])    
    
def __rand__(self, other):    
    return self & other    
    
def __or__(self, other):    
    if isinstance(other, int):    
        other = UncertainBitVector(other.bit_length(), other)    
    bits = max(len(self), len(other))    
    return UncertainBitVector(bits, [self[i] | other[i] for i in range(bits)])    
    
def __ror__(self, other):    
    return self & other    
    
def __xor__(self, other):    
    if isinstance(other, int):    
        other = UncertainBitVector(other.bit_length(), other)    
    bits = max(len(self), len(other))    
    return UncertainBitVector(bits, [self[i] ^ other[i] for i in range(bits)])    
    
def __rxor__(self, other):    
    return self & other    
    
def __lshift__(self, other):    
    bits = len(self) + other    
    return UncertainBitVector(bits, [0] * other + self.vec)    
    
def __rshift__(self, other):    
    bits = max(len(self) - other, 0)    
    return UncertainBitVector(bits, self.vec[other:])    
    
def __sub__(self, other):    
    if isinstance(other, int):    
        other = UncertainBitVector(other.bit_length(), other)    
    r = []    
    carry = UncertainBit(0)    
    for i in range(len(self)):    
        r.append(self[i] ^ other[i] ^ carry)    
        carry = ~((self[i] & ~other[i]) | (self[i] & ~carry) | (~other[i] & ~carry))    
    if carry.value != 0:    
        raise OverflowError()    
    return UncertainBitVector(len(self), r)    
    
def __repr__(self):    
    return "".join([str(b) for b in reversed(self.vec)])    
    
def sign_ext(self, bits):    
    if bits < len(self):    
        raise ValueError()    
    return UncertainBitVector(bits, self.vec + [self[-1]] * (bits - len(self)))    
    
def combine(self, other):    
    if len(self) != len(other):    
        raise ValueError()    
    else:    
        return UncertainBitVector(    
            len(self), [self[i].combine(other[i]) for i in range(len(self))]    
        )    
    
def all_known(self):    
    return all(self[i].value is not None for i in range(len(self)))    
    
def int_value(self):    
    if not self.all_known():    
        raise ValueError()    
    v = 0    
    for i in range(len(self)):    
        v |= self[i].value << i    
    return v    
    
    
class MTSolver:    
N = 624    
    
def __init__(self):    
    self.length = self.N * 6    
    self.mt = [UncertainBitVector(32) for _ in range(self.length)]    
    self.pos = 0    
    
def known_raw(self, pos, value):    
    self.mt[pos] = self.mt[pos].combine(value)    
    
def known_32bit(self, value):    
    if len(value) != 32:    
        raise ValueError()    
    self.known_raw(self.pos, self.untempering(value))    
    self.pos += 1    
    
def known_prime(self, begin, end, p):    
    self.known_range(begin - 1, end + 1, self.prime_to_bv(p))    
    
def known_range(self, begin, end, n):    
    bits = (end - begin).bit_length()    
    try:    
        rnd = UncertainBitVector(bits, n - begin)    
    except OverflowError:    
        rnd = UncertainBit("X").repeat(bits)    
    for i in range(bits // 32):    
        self.known_32bit(rnd[i * 32 : i * 32 + 32])    
    extra = bits % 32    
    if extra:    
        bv = UncertainBitVector(    
            32,    
            (rnd[bits // 32 * 32 :] << (32 - extra))    
            ^ UncertainBit("X").repeat(32 - extra),    
        )    
        self.known_32bit(bv)    
    
def untempering(self, y):    
    y ^= y >> 18    
    y ^= (y << 15) & 0xEFC60000    
    y ^= (    
        ((y << 7) & 0x9D2C5680)    
        ^ ((y << 14) & 0x94284000)    
        ^ ((y << 21) & 0x14200000)    
        ^ ((y << 28) & 0x10000000)    
    )    
    y ^= (y >> 11) ^ (y >> 22)    
    return y    
    
def generate(self, i):    
    y = (self.mt[i - self.N] & 0x80000000) | (self.mt[i - self.N + 1] & 0x7FFFFFFF)    
    return (    
        self.mt[i + 397 - self.N] ^ (y >> 1) ^ (0x9908B0DF & (y & 1).sign_ext(32))    
    )    
    
def do_predit(self):    
    for i in range(self.N, self.pos - 397 + self.N):    
        self.known_raw(i, self.generate(i))    
    
def prime_to_bv(self, p):    
    import sympy    
    
    pp = sympy.prevprime(p)    
    end = p - 1    
    start = pp    
    bv = UncertainBitVector(p.bit_length(), start)    
    bv = bv ^ UncertainBit("X").repeat((start ^ end).bit_length())    
    return bv    
    
def __str__(self):    
    s = []    
    for i, bv in enumerate(self.mt):    
        s.append("%s: %s %s" % (i, bv, "<<X>>" if "X" in str(bv) else ""))    
    return "\n".join(s)    
    
def get_mt_window(self):    
    return self.mt[max(self.pos - self.N, 0) : self.pos]    
    
def ready(self):    
    return self.pos >= self.N and all(bv.all_known() for bv in self.get_mt_window())    
    
def get_progress(self):    
    return sum(int(bv.all_known()) for bv in self.get_mt_window())    
    
def get_random(self):    
    if not self.ready():    
        raise ValueError()    
    import random    
    
    rnd = random.Random()    
    rnd.setstate(    
        (3, tuple(bv.int_value() for bv in self.get_mt_window()) + (self.N,), None)    
    )    
    return rnd    
    
    
if __name__ == "__main__":    
from pwn import * # pip3 install --upgrade git+https://github.com/arthaud/python3-pwntools.git    
import random    
import sympy    
    
# context.log_level = 'debug'    
    
r = remote("127.0.0.1", 10010)    
r.sendline("your token")    
r.recvuntil("Welcome")    
s = MTSolver()    
for i in range(10):    
    for j in range(10):    
        r.sendline("H")    
    for j in range(10):    
        print(i * 10 + j)    
        r.recvuntil("p = ")    
        p = int(r.recvline().strip())    
        r.recvuntil("q = ")    
        q = int(r.recvline().strip())    
        r.recvuntil("under ")    
        b = int(r.recvline().split(b" ")[0])    
    
        s.known_range(10, 1024, b)    
        bound = 2 ** b    
        s.known_prime(3, bound, p)    
        s.known_prime(3, bound, q)    
    s.do_predit()    
    print(s.get_progress(), "/ 624")    
    if s.ready():    
        break    
random.setstate(s.get_random().getstate())    
    
r.sendline("B")    
for i in range(10, 1024, 32):    
    print(i)    
    p = sympy.randprime(3, 2 ** i)    
    q = sympy.randprime(3, 2 ** i)    
    r.sendline("p = " + str(p))    
    r.sendline("q = " + str(q))    
r.interactive()    

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strings tinyELF    
please in put flag:    
correct    

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import angr    
    
proj = angr.Project("tinyELF")    
simgr = proj.factory.simgr()    
simgr.explore(find=lambda s: b"correct" in s.posix.dumps(1))    
print(simgr.found[0].posix.dumps(0))