2022浙江省大学生网络与信息安全初赛-Crypto复现
2022浙江省大学生网络与信息安全初赛-Crypto复现
crypto1
task.py
from random import getrandbits
FLAG = b'DASCTF{xxxxxxxxxx}'
print(len(FLAG))
class lfsr():
def __init__(self, seed, mask, length):
self.length_mask = 2 ** length - 1
self.mask = mask & self.length_mask
self.state = seed & self.length_mask
print(self.state, self.mask)
def next(self):
next_state = (self.state << 1) & self.length_mask
i = self.state & self.mask & self.length_mask
output = 0
while i != 0:
output ^= (i & 1)
i = i >> 1
next_state ^= output
self.state = next_state
return output
def getrandbit(self, nbit):
output = 0
for _ in range(nbit):
output = (output << 1) ^ self.next()
return output
seed = getrandbits(32)
mask = getrandbits(32)
box = lfsr(seed, mask, 32)
s = []
for i in FLAG:
s.append(box.getrandbit(8) ^ i)
print(s,len(s))
# [189, 81, 22, 153, 205, 197, 241, 3, 18, 128, 36, 253, 5, 200, 170, 131, 25, 71, 9, 196, 164, 161, 9, 0, 7, 123, 149, 121, 32, 122, 149, 131, 170, 252, 189, 68, 162, 164, 153, 67]
一道比较常规的LFSR密码，只是不知道mask，当然使用B-M算法加上爆破8位就可以轻松求出mask，再根据LFSR密码的特点求出flag。
我的解答
from Crypto.Util.number import *
class lfsr():
def __init__(self, seed, mask, length):
length=32
self.length_mask = 2 ** length - 1
self.mask = mask & self.length_mask
self.state = seed & self.length_mask
def next(self):
next_state = (self.state << 1) & self.length_mask
i = self.state & self.mask & self.length_mask
output = 0
while i != 0:
output ^= (i & 1)
i = i >> 1
next_state ^= output
self.state = next_state
return output
def getrandbit(self, nbit):
output = 0
for _ in range(nbit):
output = (output << 1) ^ self.next()
return output
# part1 求mask
flag=b'DASCTF{}'
s=[189, 81, 22, 153, 205, 197, 241, 3, 18, 128, 36, 253, 5, 200, 170, 131, 25, 71, 9, 196, 164, 161, 9, 0, 7, 123, 149, 121, 32, 122, 149, 131, 170, 252, 189, 68, 162, 164, 153, 67]
out=''
for i in range(7):
b=bin(flag[i]^s[i])[2:].zfill(8)
out+=b
mask_list=[]
for last in range(256):
try:
s='11111001000100000100010111011010100110011000001110001010'
lastb=bin(last)[2:].zfill(8)
s=s+lastb
M=Matrix(GF(2),32,32)
for i in range(32):
ss=s[i:i+32]
sss=list(map(int,list(ss)))
M[i]=vector(sss)
v=vector(list(map(int,list(s[-32:]))))
mask=M.solve_left(v)
st=''
for i in mask:
st+=str(i)
mask_list.append(int(st,2))
except:pass
print(mask_list)
# mask_list=[1458139876, 2252427521, 3807441478, 216380085, 3696070992, 1750340082, 331023166, 2812445596, 4256056269, 1236779887, 755392552, 776768088, 2232138609, 3149322343, 2766694892, 2589264634, 3741809440, 1950370313, 3787069494, 1797192578, 3227110059, 1436784788, 3735162392, 3760155918, 1790676666, 2773294292, 803864416, 222349197, 2279875641, 1209185879, 3266729443, 3814033278, 817319659, 1777427658, 4282506373, 2785539748, 748885264, 303986182, 2562364850, 2226048585, 3723027560, 1464600540, 3254566803, 3771586450, 2602747230, 3711590132, 2798996536, 3284245063, 3090057355, 4264956705, 2245591533, 1470020928, 792413692, 2257841053, 1423202096, 3230363703, 315411610, 1763958358, 3817291234, 204933161, 2556964654, 2778703432, 834699599, 3731928196, 2755318640, 1966572973, 1753656174, 325695906, 3261394815, 3755327932, 2222748885, 1220545739, 782119108, 3793897690, 1433477640, 3133216707, 227704081, 1446758520, 3781730986, 768924340, 4242115689, 1808548126, 3701418956, 270750674, 2268503717, 2809149696, 2599349544, 3269396653, 210563067, 1805982800, 2784426758, 2237851199, 318825708, 3713205178, 739832514, 3796571540, 3128619025, 273288860, 4270716147, 3247825629, 3726240202, 3775004644, 1216080665, 2797343094, 2577663832, 1760556576, 1475862542, 2250771535, 300907428, 3279584661, 2227671815, 2803459150, 3768879836, 787967370, 4234308539, 1766490904, 3753680114, 2550231648, 220830403, 1778411880, 3707139714, 2274195831, 830170781, 2605422608, 2756939326, 3096801113, 312840660, 1427668806, 3824050348, 1239326241, 3765841984, 2610504332, 1792201716, 3812416048, 309799752, 1451241386, 2815155922, 774231830, 3748537966, 3118637309, 1219056005, 3242678337, 806136121, 2242927779, 1962651099, 4246053919, 207508839, 332553840, 3801722632, 4294589271, 2587645876, 2271200235, 1803003596, 1462065810, 2792270826, 3282618121, 3737867094, 3138207669, 796959278, 3716266278, 2215979419, 751454302, 2770616730, 234561631, 1416605922, 278443008, 3236048249, 3788719480, 1748847804, 1225532605, 2574695876]
# part2
mask_l=[1458139876, 2252427521, 3807441478, 216380085, 3696070992, 1750340082, 331023166, 2812445596, 4256056269, 1236779887, 755392552, 776768088, 2232138609, 3149322343, 2766694892, 2589264634, 3741809440, 1950370313, 3787069494, 1797192578, 3227110059, 1436784788, 3735162392, 3760155918, 1790676666, 2773294292, 803864416, 222349197, 2279875641, 1209185879, 3266729443, 3814033278, 817319659, 1777427658, 4282506373, 2785539748, 748885264, 303986182, 2562364850, 2226048585, 3723027560, 1464600540, 3254566803, 3771586450, 2602747230, 3711590132, 2798996536, 3284245063, 3090057355, 4264956705, 2245591533, 1470020928, 792413692, 2257841053, 1423202096, 3230363703, 315411610, 1763958358, 3817291234, 204933161, 2556964654, 2778703432, 834699599, 3731928196, 2755318640, 1966572973, 1753656174, 325695906, 3261394815, 3755327932, 2222748885, 1220545739, 782119108, 3793897690, 1433477640, 3133216707, 227704081, 1446758520, 3781730986, 768924340, 4242115689, 1808548126, 3701418956, 270750674, 2268503717, 2809149696, 2599349544, 3269396653, 210563067, 1805982800, 2784426758, 2237851199, 318825708, 3713205178, 739832514, 3796571540, 3128619025, 273288860, 4270716147, 3247825629, 3726240202, 3775004644, 1216080665, 2797343094, 2577663832, 1760556576, 1475862542, 2250771535, 300907428, 3279584661, 2227671815, 2803459150, 3768879836, 787967370, 4234308539, 1766490904, 3753680114, 2550231648, 220830403, 1778411880, 3707139714, 2274195831, 830170781, 2605422608, 2756939326, 3096801113, 312840660, 1427668806, 3824050348, 1239326241, 3765841984, 2610504332, 1792201716, 3812416048, 309799752, 1451241386, 2815155922, 774231830, 3748537966, 3118637309, 1219056005, 3242678337, 806136121, 2242927779, 1962651099, 4246053919, 207508839, 332553840, 3801722632, 4294589271, 2587645876, 2271200235, 1803003596, 1462065810, 2792270826, 3282618121, 3737867094, 3138207669, 796959278, 3716266278, 2215979419, 751454302, 2770616730, 234561631, 1416605922, 278443008, 3236048249, 3788719480, 1748847804, 1225532605, 2574695876]
for mask in mask_l:
seed=int(out[:32],2)
box = lfsr(seed, mask, 32)
flag=b'DASC'
for i in range(4,len(s)):
flag+=long_to_bytes(s[i]^box.getrandbit(8))
if flag.endswith(b'}'):
print(flag)
crypto2
task.py
from Crypto.Util.number import *
import random
FLAG = b'xxx'
def leak(dp: int, dq: int):
leak_a = []
leak_b = []
for i in range(max(dp.bit_length(), dq.bit_length())):
r = random.getrandbits(32) % 2
if r == 0:
leak_a.append('1' if dp&(2**i) else '0')
leak_b.append('?')
elif r == 1:
leak_b.append('1' if dq&(2**i) else '0')
leak_a.append('?')
print('dp:', ''.join(leak_a[::-1]))
print('dq:', ''.join(leak_b[::-1]))
p = getPrime(512)
q = getPrime(512)
e = 0x10001
d = inverse(e, (p-1)*(q-1))
dp = d % (p-1)
dq = d % (q-1)
assert 55000 <= (e*dp-1)//(p-1) <= 56000
assert 49000 <= (e*dq-1)//(q-1) <= 50000
leak(dp, dq)
print('N:', p*q)
print('c:', pow(bytes_to_long(FLAG), e, p*q))
'''
dp: ??101101110001101000??????0???????1111?0??10?0??0?00?0??????01??1?00??1?011?11?0?10110????010??00?1?10?000????0??0?01??0???00??01?01?100?00110?0??0111?1???0110??00??????1?10?00?0?1????10110??0??110?0?001?????0110??00?01??11?00????000???0?????1?0???1?1??1?10????000?1??????01?10??1?0?0?11????1?00?001???1??1?????1011?0?1?????????0?1???111?01?010?0???10?00?0???00?1??1???00?10????111?0?1???11?110?0?????00110??000100?1????0???1?111010001?1?1???00?11???0?0?1?011?0??011?0???????1??0011100?1???1?1??1??00???0101???0?
dq: 10??????????????????111011?1101100????0?01??1?01?0??0?000110??10?0??11?0???0??0?0?????1110???11??0?1??0???1101?10?0??10?010??11??0??0???0?????1?00????1?110????01??110101?0??1??1?1?0000?????01?11???1?0???11110????10??1??10??0??1011???000?11000?1?001?0?00?0??0000???0?010011??1??10?1?0?1??1101?1??1???111?00?00011????1?1?000000010?1?000???0??1???1?011??0??1?100??0?00?111??1??0010???1?0?110??1???1?00100?????10??????1?1101?111?0?????????1?1?001??1??110?1?1?1???1?10???0?0111000?10???????0?100?1?10?00??111????010?1
N: 77956713622979317783761595054903981958011751094595501314491177382757729657611095418895882363723936522303701334485645032785352259197556402990449635873300021669658762637882700434079432155768745388920298118803003827231120408576526258417243630568234643852227224535788863216313553066059331134379012412201880568839
c: 6373402478226200743899445696426483055555702880465073264671889716957511631194331218010680752909232089491297245558959594952484242066243487601985639038704149982643910363538066540137001662216910771688217243126636396444036372309819771474215211720377034865803003448233174429246078453845273054750113438198122744673
'''
dp,dq在相同的位置上只知道一位，写一个DFS，然后跑一个钟头就可以出结果了吧…
我的解答
from tqdm import *
from Crypto.Util.number import *
from gmpy2 import *
ldp= '??101101110001101000??????0???????1111?0??10?0??0?00?0??????01??1?00??1?011?11?0?10110????010??00?1?10?000????0??0?01??0???00??01?01?100?00110?0??0111?1???0110??00??????1?10?00?0?1????10110??0??110?0?001?????0110??00?01??11?00????000???0?????1?0???1?1??1?10????000?1??????01?10??1?0?0?11????1?00?001???1??1?????1011?0?1?????????0?1???111?01?010?0???10?00?0???00?1??1???00?10????111?0?1???11?110?0?????00110??000100?1????0???1?111010001?1?1???00?11???0?0?1?011?0??011?0???????1??0011100?1???1?1??1??00???0101???0?'
ldq= '10??????????????????111011?1101100????0?01??1?01?0??0?000110??10?0??11?0???0??0?0?????1110???11??0?1??0???1101?10?0??10?010??11??0??0???0?????1?00????1?110????01??110101?0??1??1?1?0000?????01?11???1?0???11110????10??1??10??0??1011???000?11000?1?001?0?00?0??0000???0?010011??1??10?1?0?1??1101?1??1???111?00?00011????1?1?000000010?1?000???0??1???1?011??0??1?100??0?00?111??1??0010???1?0?110??1???1?00100?????10??????1?1101?111?0?????????1?1?001??1??110?1?1?1???1?10???0?0111000?10???????0?100?1?10?00??111????010?1'
n=77956713622979317783761595054903981958011751094595501314491177382757729657611095418895882363723936522303701334485645032785352259197556402990449635873300021669658762637882700434079432155768745388920298118803003827231120408576526258417243630568234643852227224535788863216313553066059331134379012412201880568839
c=6373402478226200743899445696426483055555702880465073264671889716957511631194331218010680752909232089491297245558959594952484242066243487601985639038704149982643910363538066540137001662216910771688217243126636396444036372309819771474215211720377034865803003448233174429246078453845273054750113438198122744673
e=65537
for k1 in tqdm(range(55295,56001)):
for k2 in range(49000,50001):
dp = [0]
dq = [0]
for i in range(len(ldp)):
tmpdp = []
tmpdq = []
for j in range(len(dp)):
if ldp[-1 - i] == '?':
for pp in range(2):
s = (e * (dp[j] + pp * 2 ** i) + k1 - 1) * (e * (dq[j] + int(ldq[-1 - i]) * 2 ** i) + k2 - 1)
if (k1 * k2 * n) % (2 ** (i + 1)) == s % (2 ** (i + 1)):
tmpdp.append(dp[j] + pp * 2 ** i)
tmpdq.append(dq[j] + int(ldq[-1 - i]) * 2 ** i)
else:
for qq in range(2):
s = (e * (dp[j] + int(ldp[-1 - i]) * 2 ** i) + k1 - 1) * (e * (dq[j] + qq * 2 ** i) + k2 - 1)
if (k1 * k2 * n) % (2 ** (i + 1)) == s % (2 ** (i + 1)):
tmpdp.append(dp[j] + int(ldp[-1 - i]) * 2 ** i)
tmpdq.append(dq[j] + qq * 2 ** i)
dp = tmpdp
dq = tmpdq
if dp:
for kk in range(len(dp)):
p=(e*dp[kk]+k1-1)//k1
if n%p==0:
print('done')
print('p=',p)
q=n//p
phi=(p-1)*(q-1)
d=invert(e,phi)
m=pow(c,d,n)
print(long_to_bytes(m))
crypto3
task.py
from secret import flag
assert flag[:7] == 'DASCTF{'
assert flag[-1] == '}'
key = random_matrix(ZZ, 5, 5)
c = 0
def encrypt(e, n):
global c
assert e > 0x10001
c = power_mod(key, e, n)
return c
def decrypt(d, n):
assert d > 0x10001
if c == 0:
print('encrypt first')
return
m = power_mod(c, d, n)
return
def init():
p = random_prime(2^512)
q = random_prime(2^512)
n = p*q
print("n=",n)
for _ in range(3):
opt = int(input('Plz input:'))
if opt == 1:
e = int(input('Plz input e:'))
print(encrypt(e, n))
elif opt == 2:
d = int(input('Plz input d:'))
print(decrypt(d, n))
elif opt == 3:
ikey = input('Plz input nums:').strip()
ikey = list(map(int, ikey.split(' ')))
assert len(ikey) == 25
ikey = Matrix(ZZ, 5, 5, ikey)
if ikey == key:
print(flag)
init()
一个共模攻击，只是这里的key是一个矩阵，还是换汤不换药。
我的解答
没有了环境就大致写一下吧，应该差不多…
from Crypto.Util.number import *
print(getPrime(20))
print(getPrime(20))
from gmpy2 import *
e1=826807
e2=951649
print(gcdext(e1,e2))
n=18333732050438948866929145722058851515599832278814638228866142488493215607530160521341920009432182233189953094579871676089611074579089540181213795407274722695030338019992429688671738485222000599102356441209929229178469898037506987407112122365135187211275050890924887844748573376316982838226378170425149995663
l1=[[ 3603171778643943992185924426311695418052593856834861763180539304487141433134173817450600777554379452178578096706008821036841113793458820608477253646230330981138640663961672722649825567727634815395649750224675526948568021011251730152216121188197672418859509674287708439891458614974289791000973500182061161709 ,10339193581153168042656824196945445568660183093130004177722671758911228957279264481535738014225677058663876752833190419087588150347268736114533020702992827033024495275498210397575432981448935613710884632618882912239893048709421380919794067821827129492296530907435316828276621328031923534186146463657305097710 ,11312885886083494534982542956798623836976535107407248204446162898868937214263700553969087347383899578179993244078266486239416008018149483921972768596353196581491818030260413634447782133587061244884743315688064102309810411642970822557428360448135452474217806956432742029219311509405301141910330798100189549095 , 1494995362986063585588059345206324048148295049219865128730951314539788637070843170815307187875169268644329133365671735371880335228645131671823490538970006197554010629938868738531950933223039245849007840736441168431793114756795338026356771275036275614865215870431831317272620605531962764275372392326244523793 , 9396631602019449363471862898275050983630437164752238861614269203476215834238623842178223262067752487689195391670708491104883804305696544647924130087587346661252042536932651629646949851480796027943748478849042068007813701559789954048118831056028029143154642762569733171460480775310882935209776707990606421351]
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]
n=18333732050438948866929145722058851515599832278814638228866142488493215607530160521341920009432182233189953094579871676089611074579089540181213795407274722695030338019992429688671738485222000599102356441209929229178469898037506987407112122365135187211275050890924887844748573376316982838226378170425149995663
c1=Matrix(ZZ,l1)
c1=c1.inverse()
c2=Matrix(ZZ,l2)
out=power_mod(c1,333735,n)*power_mod(c2,289954,n)%n
for i in range(5):
for j in range(5):
if out[i,j]>500:
out[i,j]-=n
print(out)
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