NewStarCTF 2023 公开赛道 WEEK5|CRYPTO WP

last_signin

from Crypto.Util.number import *
flag = b'?'

e = 65537
p, q = getPrime(1024), getPrime(1024)
N = p * q
gift = p&(2**923-2**101)
m = bytes_to_long(flag)
c = pow(m, e, N)

print("N = ",N)
print("gift = ",gift)
print("c = ",c)

"""
N =  12055968471523053394851394038007091122809367392467691213651520944038861796011063965460456285088011754895260428814358599592032865236006733879843493164411907032292051539754520574395252298997379020268868972160297893871261713263196092380416876697472160104980015554834798949155917292189278888914003846758687215559958506116359394743135211950575060201887025032694825084104792059271584351889134811543088404952977137809673880602946974798597506721906751835019855063462460686036567578835477249909061675845157443679947730585880392110482301750827802213877643649659069945187353987713717145709188790427572582689339643628659515017749
p0 =  70561167908564543355630347620333350122607189772353278860674786406663564556557177660954135010748189302104288155939269204559421198595262277064601483770331017282701354382190472661583444774920297367889959312517009682740631673940840597651219956142053575328811350770919852725338374144
c =  2475592349689790551418951263467994503430959303317734266333382586608208775837696436139830443942890900333873206031844146782184712381952753718848109663188245101226538043101790881285270927795075893680615586053680077455901334861085349972222680322067952811365366282026756737185263105621695146050695385626656638309577087933457566501579308954739543321367741463532413790712419879733217017821099916866490928476372772542254929459218259301608413811969763001504245717637231198848196348656878611788843380115493744125520080930068318479606464623896240289381601711908759450672519228864487153103141218567551083147171385920693325876018
"""

参考：D^3CTF 官方Write Up-Crypto-Bivariate

exp:

#sage#
N =  12055968471523053394851394038007091122809367392467691213651520944038861796011063965460456285088011754895260428814358599592032865236006733879843493164411907032292051539754520574395252298997379020268868972160297893871261713263196092380416876697472160104980015554834798949155917292189278888914003846758687215559958506116359394743135211950575060201887025032694825084104792059271584351889134811543088404952977137809673880602946974798597506721906751835019855063462460686036567578835477249909061675845157443679947730585880392110482301750827802213877643649659069945187353987713717145709188790427572582689339643628659515017749
p0 =  70561167908564543355630347620333350122607189772353278860674786406663564556557177660954135010748189302104288155939269204559421198595262277064601483770331017282701354382190472661583444774920297367889959312517009682740631673940840597651219956142053575328811350770919852725338374144
c =  2475592349689790551418951263467994503430959303317734266333382586608208775837696436139830443942890900333873206031844146782184712381952753718848109663188245101226538043101790881285270927795075893680615586053680077455901334861085349972222680322067952811365366282026756737185263105621695146050695385626656638309577087933457566501579308954739543321367741463532413790712419879733217017821099916866490928476372772542254929459218259301608413811969763001504245717637231198848196348656878611788843380115493744125520080930068318479606464623896240289381601711908759450672519228864487153103141218567551083147171385920693325876018

def bivariate(pol, XX, YY, kk=4):
    N = pol.parent().characteristic()

    f = pol.change_ring(ZZ)
    PR, (x, y) = f.parent().objgens()

    idx = [(k - i, i) for k in range(kk + 1) for i in range(k + 1)]
    monomials = list(map(lambda t: PR(x ** t[0] * y ** t[1]), idx))
    # collect the shift-polynomials
    g = []
    for h, i in idx:
        if h == 0:
            g.append(y ** h * x ** i * N)
        else:
            g.append(y ** (h - 1) * x ** i * f)

    # construct lattice basis
    M = Matrix(ZZ, len(g))
    for row in range(M.nrows()):
        for col in range(M.ncols()):
            h, i = idx[col]
            M[row, col] = g[row][h, i] * XX ** h * YY ** i

    # LLL
    B = M.LLL()

    PX = PolynomialRing(ZZ, 'xs')
    xs = PX.gen()
    PY = PolynomialRing(ZZ, 'ys')
    ys = PY.gen()

    # Transform LLL-reduced vectors to polynomials
    H = [(i, PR(0)) for i in range(B.nrows())]
    H = dict(H)
    for i in range(B.nrows()):
        for j in range(B.ncols()):
            H[i] += PR((monomials[j] * B[i, j]) / monomials[j](XX, YY))

    # Find the root
    poly1 = H[0].resultant(H[1], y).subs(x=xs)
    poly2 = H[0].resultant(H[2], y).subs(x=xs)
    poly = gcd(poly1, poly2)
    x_root = poly.roots()[0][0]

    poly1 = H[0].resultant(H[1], x).subs(y=ys)
    poly2 = H[0].resultant(H[2], x).subs(y=ys)
    poly = gcd(poly1, poly2)
    y_root = poly.roots()[0][0]

    return x_root, y_root

PR = PolynomialRing(Zmod(N), names='x,y')
x, y = PR.gens()
pol = 2 ** 923 * x + y + p0

x, y = bivariate(pol, 2 ** 101, 2 ** 101)
p = 2 ** 923 * x + y + p0
q = N // p
print(p)
print(q)
#p = 128316995030969915324601380638393686940451314028029847288048482890311391444850912731036515693294185876094548175445535907681477441597112946116144447110741965169166242532652418536974280062421433117597771884350348782061336417186073214602745554392782563801452571827824278044551188124531752043347553290530270395447
#q = 93954572959047928343011750832384121004425708514797352779274995744988621009506935222019019171047965401245311260375453924225343494879356560534244565490966730992944825873075214193169703861204568164588812686254102717072093288624081316906954278209584119401170082334613277995260895181460040974631476760070669352467

from Crypto.Util.number import *
p = 128316995030969915324601380638393686940451314028029847288048482890311391444850912731036515693294185876094548175445535907681477441597112946116144447110741965169166242532652418536974280062421433117597771884350348782061336417186073214602745554392782563801452571827824278044551188124531752043347553290530270395447
q = 93954572959047928343011750832384121004425708514797352779274995744988621009506935222019019171047965401245311260375453924225343494879356560534244565490966730992944825873075214193169703861204568164588812686254102717072093288624081316906954278209584119401170082334613277995260895181460040974631476760070669352467
c = 2475592349689790551418951263467994503430959303317734266333382586608208775837696436139830443942890900333873206031844146782184712381952753718848109663188245101226538043101790881285270927795075893680615586053680077455901334861085349972222680322067952811365366282026756737185263105621695146050695385626656638309577087933457566501579308954739543321367741463532413790712419879733217017821099916866490928476372772542254929459218259301608413811969763001504245717637231198848196348656878611788843380115493744125520080930068318479606464623896240289381601711908759450672519228864487153103141218567551083147171385920693325876018
n = p * q
e=65537
d = inverse(e, (p - 1)*(q - 1))
m = int(pow(c, d, n))
print(long_to_bytes(m))
#flag{although_11ts_norma11_tis_still_stay_dsadsa}

School of CRC32

import secrets
from secret import flag
import zlib

ROUND = 100

LENGTH = 20

print('Extreme hard CRC32 challenge')
print('ARE YOU READY')

for i in range(ROUND):
    print('ROUND', i, '!'*int(i/75 + 1))

    target = secrets.randbits(32)

    print('Here is my CRC32 value: ', hex(target))

    dat = input('Show me some data > ')
    raw = bytes.fromhex(dat)

    if zlib.crc32(raw) == target and len(raw) == LENGTH:
        print("GREAT")
    else:
        print("OH NO")
        exit()

print("Congratulation! Here is your flag")
print(flag)

考点：crc32的逆向（碰撞），参考：https://pypi.org/project/crcsolver/

exp:

from Crypto.Util.number import *
import crcsolver
import zlib
from pwn import *

sh = remote("IP",端口号)
for i in range(100):
    data = sh.recvuntil(b"Here is my CRC32 value:")
    c = eval(sh.recvline().decode())
    m = crcsolver.solve(b'_'*20, range(8*20), c, zlib.crc32) #关键代码
    message = hex(bytes_to_long(m))[2:].zfill(40)  #传给服务器的数据需要是16进制形式，而且需填充满40位才行，否则会报错。
    sh.sendlineafter(b"Show me some data >",message)
sh.interactive()