V&NCTF 2022
V&NCTF的题目虽然很难，但是能学到很多东西，下面是看着wp的随便写写
ezmath
from Crypto.Util.number import*
import random
from secret import flag,check
from hashlib import sha256
import socketserver
import signal
import string
table = string.ascii_letters+string.digits
class Task(socketserver.BaseRequestHandler):
def _recvall(self):
BUFF_SIZE = 2048
data = b''
while True:
part = self.request.recv(BUFF_SIZE)
data += part
if len(part) < BUFF_SIZE:
break
return data.strip()
def send(self, msg, newline=True):
try:
if newline:
msg += b'\n'
self.request.sendall(msg)
except:
pass
def recv(self, prompt=b''):
self.send(prompt, newline=False)
return self._recvall()
def proof_of_work(self):
proof = (''.join([random.choice(table)for _ in range(20)])).encode()
sha = sha256(proof).hexdigest().encode()
self.send(b"[+] sha256(XXXX+" + proof[4:] + b") == " + sha )
XXXX = self.recv(prompt = b'[+] Plz Tell Me XXXX :')
if len(XXXX) != 4 or sha256(XXXX + proof[4:]).hexdigest().encode() != sha:
return False
return True
def handle(self):
proof = self.proof_of_work()
if not proof:
self.request.close()
counts = 0
signal.alarm(60)
for i in range(777):
times = getPrime(32)
self.send(b'plz give me the ' + str(times).encode() + b'th (n) that satisfying (2^n-1) % 15 == 0:')
n = int(self.recv())
a , ret = check(times,n)
if a == True:
self.send(ret.encode())
counts += 1
else:
self.send(ret.encode())
if counts == 777:
self.send(b'You get flag!')
self.send(flag)
else:
self.send(b'something wrong?')
self.request.close()
class ThreadedServer(socketserver.ThreadingMixIn, socketserver.TCPServer):
pass
class ForkedServer(socketserver.ForkingMixIn, socketserver.TCPServer):
pass
if __name__ == "__main__":
HOST, PORT = '0.0.0.0', 10001
print("HOST:POST " + HOST+":" + str(PORT))
server = ForkedServer((HOST, PORT), Task)
server.allow_reuse_address = True
server.serve_forever()
简单题目，直接枚举2模15的阶是4，故第k个满足的是4k
import hashlib
from pwn import *
from itertools import product
import string
from Crypto.Util.number import *
p=remote('node4.buuoj.cn',26276)
context.log_level = 'debug'
table = string.ascii_letters + string.digits
def proof_of_work():
rev = p.recvuntil("sha256(XXXX+")
suffix = p.recv(16).decode()
p.recvuntil(" == ")
res = p.recv(64).decode()
def f(x):
hashresult = hashlib.sha256((x+suffix).encode()).hexdigest()
if hashresult == res:
return 1
else:
return 0
prefix = util.iters.mbruteforce(f,table,4,'upto')
p.sendline(str(prefix))
proof_of_work()
for i in range(777):
p.recvuntil('me the ')
t=p.recvuntil(' ')[:-3]
t=4*int(t)
p.sendline(str(t))
p.interactive()
AreYouAdmin
from Crypto.Util.number import *
from hashlib import *
from secret import secretkey,flag,ezmath_flag
import socketserver
import os
import signal
import string
assert len(bin(secretkey)) == 169
table = string.ascii_letters+string.digits
class PseudoRandomNumbersGenerators:
def __init__(self,seed1,seed2):
self.state_a = seed1
self.state_b = seed2
self.a = getRandomNBitInteger(160)
self.b = getRandomNBitInteger(160)
self.c = getRandomNBitInteger(160)
self.M = 1 << 512
def GetNext(self):
ret = (self.state_a * self.a + self.state_b * self.b + self.c) % self.M
self.state_a = self.state_b
self.state_b = ret
return ret
def GetSomethingUseful(self,admin):
if admin == True:
return self.a,self.b,self.c
else:
return "You can't get anything here!Get out!"
def choice(self,input):
length = len(input)
tmp = self.GetNext() % length
return input[tmp]
class DigitalSignatureAlgorithm:
def __init__(self,RANDOM):
self.p = 8945295668911819059540208265461979177678201229057426412681001447446107919117765962027889488459965388254641301806100385155760254966914075104367813869235667
self.q = 4472647834455909529770104132730989588839100614528713206340500723723053959558882981013944744229982694127320650903050192577880127483457037552183906934617833
self.g = 3
self.Random = RANDOM
def verify(self, m, y, sig):
r, s = sig
if (not (1 <= r <= self.q - 1)) or (not (1 <= s <= self.q - 1)):
return False
z = bytes_to_long(sha256(m).digest())
w = inverse(s, self.q)
u1 = (z * w) % self.q
u2 = (r * w) % self.q
v = (pow(self.g, u1, self.p) * pow(y, u2, self.p)) % self.p % self.q
return r == v
def sign(self, m , x):
z = bytes_to_long(sha256(m).digest())
while 1:
k = self.Random.GetNext() % self.q
r = pow(self.g , k, self.p) % self.q
s = (inverse(k, self.q) * (z + x * r)) % self.q
if (s != 0) and (r != 0) :
return (r, s)
RANDOM = PseudoRandomNumbersGenerators(getPrime(120),getPrime(120))
DSA = DigitalSignatureAlgorithm(RANDOM)
x = secretkey
y = pow(DSA.g,x,DSA.p)
MENU = br'''
[S]ign.
[V]erify(or get flag).
[I]dentify.
[E]xit.
'''
class Task(socketserver.BaseRequestHandler):
def _recvall(self):
BUFF_SIZE = 2048
data = b''
while True:
part = self.request.recv(BUFF_SIZE)
data += part
if len(part) < BUFF_SIZE:
break
return data.strip()
def send(self, msg, newline=True):
try:
if newline:
msg += b'\n'
self.request.sendall(msg)
except:
pass
def recv(self, prompt=b''):
self.send(prompt, newline=False)
return self._recvall()
def proof_of_work(self):
proof = (''.join([RANDOM.choice(table)for _ in range(20)])).encode()
sha = sha256(proof).hexdigest().encode()
self.send(b"[+] sha256(XXXX+" + proof[4:] + b") == " + sha )
XXXX = self.recv(prompt = b'[+] Plz Tell Me XXXX :')
if len(XXXX) != 4 or sha256(XXXX + proof[4:]).hexdigest().encode() != sha:
return False
return True
def sign(self):
m0 = b'dawn'
m1 = b'whisper'
m2 = b'want flag'
sign0 = DSA.sign(m0,x)
sign1 = DSA.sign(m1,x)
sign2 = DSA.sign(m2,x)
self.send(b'sign of (dawn) is: ' + str(sign0).encode())
self.send(b'sign of (whisper) is: ' + str(sign1).encode())
self.send(b'sign of (want flag) is: ' + str(sign2).encode())
def identify(self):
rec_key = self.recv(b'flag of ezmath is :')
ret = RANDOM.GetSomethingUseful(rec_key == ezmath_flag)
self.send(str(ret).encode())
def verify(self):
msg = self.recv(b'msg:')
r = int(self.recv(b'r:'))
s = int(self.recv(b's:'))
sig = (r,s)
if msg == b"I'm Admin.Plz give me flag!":
if DSA.verify(msg,y,sig):
self.send(b'Yes Sir!Thank you Sir!')
return flag
else:
self.send(b'Who are U?Get out!')
return False
else:
if DSA.verify(msg,y,sig):
self.send(b'Yeah!You sign successfully!')
return os.urandom(32)
def handle(self):
proof = self.proof_of_work()
if not proof:
self.request.close()
signal.alarm(60)
chance = 0
while 1:
self.send(MENU)
option = self.recv(b'\n==plz give me your option==\n[IN]:')
if option == b'S':
if chance == 0:
self.sign()
chance += 1
else:
self.send(b'ERROR! You only have one time!')
elif option == b'V':
ret = self.verify()
if ret :
self.send(b'Your Flag is :' + ret)
break
elif option == b'I':
self.identify()
else:
break
self.request.close()
class ThreadedServer(socketserver.ThreadingMixIn, socketserver.TCPServer):
pass
class ForkedServer(socketserver.ForkingMixIn, socketserver.TCPServer):
pass
if __name__ == "__main__":
HOST, PORT = '0.0.0.0', 10004
print("HOST:POST " + HOST+":" + str(PORT))
server = ForkedServer((HOST, PORT), Task)
server.allow_reuse_address = True
server.serve_forever()
题目条件就是给了三次签名和魔改LCG的生成系数
然后我就想着去构造格，真不明白我当时为什么总想着SVP规约出一个长达256bits的向量，还是tcl
后面问了下大佬，可以通过CVP解决，之前陇原战疫有接触过一次，不是很熟悉
这里借这个机会深入了解一下
Babai's Algorithm
很明显的我们在平面直角坐标系里解决CVP问题是简单的，只需对目标向量坐标取整即可，那么为什么CVP问题会是NP-hard问题呢
这里引入Hadamard ratio
对于n维的格的一组基v1,···,vn 记H(v1,···,vn)=\((\frac{det(L)}{||v1||||v2||···||v~n~||})^{\frac{1}{n}}∈(0,1)\)
我们利用哈达马比率来刻画一组基的正交程度
H~1时我们称其为好基，H~0时我们称其为坏基
babai算法的思想就是利用LLL算法规约出一组好基，并利用取整的思想求最近向量
babai的代码实现(reversed这个地方没太明白，以后问问)
def babai(A, w):
A = A.LLL()
G = A.gram_schmidt()[0]
t = w
for i in reversed(range(A.nrows())):
c = ((t * G[i]) / (G[i] * G[i])).round()
t -= A[i] * c
return w - t
我们根据条件得出四个同余式
s1k1=h1+xr1 mod(q)
s2k2=h2+xr2 mod(q)
s3k3=h3+xr3 mod(q)
k3=ak1+bk2+c mod(M)
梳理一下我们未知的量是k1,k2,k3,x
调整一下同余式
我们考虑构造格\(\left[\begin{matrix}s_1&&&-a\\&s_2&&-b\\&&s_3&1\\r_1&r_2&r_3&\\q&&&\\&q&&\\&&q&\\&&&M\end{matrix}\right]\)
我们希望规约后能够得到\([\begin{matrix}h_1&h_2&h_3&c\end{matrix}]\)首先注意到h都在256bits的量级，c在160bits的量级，基本不能通过SVP解决，故只能考虑CVP
于是我们需要对格进行扩充
\(\left[\begin{matrix}s_1&&&-a&1/λ_1&&&&\\&s_2&&-b&&1/λ_2&&&\\&&s_3&1&&&1/λ_3&\\r_1&r_2&r_3&&&&&1/λ_4\\q&&&\\&q&&\\&&q&\\&&&M\end{matrix}\right]\)
将其调整为8×8的矩阵，其中λ我们是可以根据需求进行调整的
于是我们希望规约后可以得到\([\begin{matrix}h_1&h_2&h_3&c&\frac{k_1}{λ_1}&\frac{k_2}{λ_2}&\frac{k_3}{λ_3}&-\frac{x}{λ_4}\end{matrix}]\)
其中k平均大概在511bits的样子(注意到最开始的几个低bits的数在sha256的验证时用掉了)
x的话题目给了在167bits的量级上
于是我们令λ1-3=2511,λ4=2167
用babai算法找\([\begin{matrix}h_1&h_2&h_3&c&1&1&1&-1\end{matrix}]\)的最近向量
由于同一个端口数据相同，我就没有写交互了
h1=59321673573909906265288710676456384358157017247524812933609264006321909880946
h2=84344567394273297492826058854936847520759247638820383794017833480152249569966
h3=31915758673949819228460572288910607244566306546872092881831612333627535673163
s1=2313608943027490945436746972423511365879999330988549095095132120714394465148082634131163512272345999596881490464359543365542617220829797786792240343115038
s2=969838527803859562171399332746979221088434685014925682789858498898550675886955557222288015549413071909933836811563263353311430176281676138272351592417782
s3=2705895714477901863092933739898228254114437223114721094423380479182263285235889280492479840081206911882012812956517058692673774491305322039721568384262796
r1=2648168993951468948635423727912213456286832390117660198247386119008267054780100804475308964094224973917725846851433949296444053774254373994933506863614902
r2=1641581589246292967706310483596963882929119604760421080209223001054553185925721220826880872464819666195439769525050420483288240083859929318309030945071425
r3=2047344748363132977442661413765298431089316641404391668494489079071777863130943485327993372769474260007190838259780861912416677386811473551434746276919523
a=1288778668095346346053418256124506514548392096659
b=817117072486370525439624349682018381752585029841
c=1387869140496615611625076357881819669517224075919
p = 8945295668911819059540208265461979177678201229057426412681001447446107919117765962027889488459965388254641301806100385155760254966914075104367813869235667
q = 4472647834455909529770104132730989588839100614528713206340500723723053959558882981013944744229982694127320650903050192577880127483457037552183906934617833
M=1<<512
kk=1<<511
xx=1<<167
def babai(A, w):
A = A.LLL()
G = A.gram_schmidt()[0]
t = w
for i in reversed(range(A.nrows())):
c = ((t * G[i]) / (G[i] * G[i])).round()
t -= A[i] * c
return w - t
L=Matrix(QQ,[[s1,0,0,-a,1/kk,0,0,0],
[0,s2,0,-b,0,1/kk,0,0],
[0,0,s3,1,0,0,1/kk,0],
[r1,r2,r3,0,0,0,0,1/xx],
[q,0,0,0,0,0,0,0],
[0,q,0,0,0,0,0,0],
[0,0,q,0,0,0,0,0],
[0,0,0,M,0,0,0,0]])
v=vector(QQ,[h1,h2,h3,c,1,1,1,-1])
vv=babai(L,v)
print(vv)
x=vv[7]*xx
print(x)
from hashlib import sha256
import gmpy2
from Crypto.Util.number import bytes_to_long
p = 8945295668911819059540208265461979177678201229057426412681001447446107919117765962027889488459965388254641301806100385155760254966914075104367813869235667
q = 4472647834455909529770104132730989588839100614528713206340500723723053959558882981013944744229982694127320650903050192577880127483457037552183906934617833
g=3
msg=b"I'm Admin.Plz give me flag!"
x=99681635728635879538940784529297431947697608270113
print(x.bit_length())
def sign(m, x):
z = bytes_to_long(sha256(m).digest())
k=2022
r = pow(g, k, p) % q
s = (gmpy2.invert(k, q) * (z + x * r)) % q
if (s != 0) and (r != 0):
return (r, s)
print(sign(msg,x))
babyPHE
hint:babyphe 给个hint 快速幂的消耗
from Crypto.Util.number import*
import random
class CryptoSystem:
def __init__(self,kbit) :
self.k_bit = kbit
self.p_bit = self.k_bit//2
self.q_bit = self.k_bit - self.p_bit
self.gen_alice_key()
def gen_alice_key(self):
while 1:
p = getPrime(self.p_bit)
p_tmp = (p-1)//2
if isPrime(p_tmp):
break
while 1:
q = getPrime(self.q_bit)
q_tmp = (q-1)//2
if isPrime(q_tmp):
break
N = p * q
while 1:
g = random.randrange(N*N)
if (pow(g,p_tmp * q_tmp,N*N) - 1) % N == 0 and \
(pow(g,p_tmp * q_tmp,N*N) - 1) // N >= 1 and \
(pow(g,p_tmp * q_tmp,N*N) - 1) // N <= N - 1:
break
self.alice_pub = (N,g)
self.alice_sec = (p,q)
def gen_other_key(self):
N,g = self.alice_pub
a = random.randrange(N*N)
h = pow(g,a,N*N)
pub = h
sec = a
return pub,sec
def other_encrypt(self,pk,m):
N,g = self.alice_pub
r = random.randrange(N*N)
A = pow(g,r,N*N)
B = (pow(pk,r,N*N) * (1 + m * N)) % (N * N)
return A,B
def Add(self,dataCipher1,dataCipher2):
N , g = self.alice_pub
A1,B1 = dataCipher1
A2,B2 = dataCipher2
B = (B1*B2) % (N*N)
return (A1,A2,B)
What do you want to get?
[1]the pk list
[2]Alice Public Parameters
[3]Mixed Flag
[4]exit
SERVER <INPUT>: 1
[~]My pk_list is:
[1322842566065856798965165348078862357662198978947230709254526492285633103717144968735233037057635982712449886088094071707373492828329816403406086925271118810344041229312732672575513454776879004607034599714440192959516462346178676822793054022355340273220895758465252657627533580580661259224576036836899300361602939684184409146605413303645375209063407283788834371731645965734210815674655141937633174952825964571184358064898432155429127042537390331662523018090768538304757528325737029530914511997095609887140188315159519726941243145154982311426980770893222512421681100895613703769217217726796485797389777578427706351431, 1929353920719299187661308157981749306000287810274985728139426214822581195090665401749753846077249277129639243707822757055941082464616169391698813564752296766917445328390119101887079278115873441407801269666064184707573218538829473509387530062976418264787144789530314562024653164934843854581804048249892522951148405452048197467260971792040669602533612092283424644152035305528153991413104737633877324819675765337058593912363038132773480442939092315660329419364524776069424287921244597238072942644562723590311132742006220424699393681291317394377782898447415333917160012108428733209008198177742632631879274165624277481851, 2789011373470240533905631892024296570906678296635752216220081790321204618235380094204993170523863943409640177956225417067840314617943182599260568907798576069406172968452018144820358899764046320473076086697805329140694534284547901328504085789250614483796435793917853203275245694757472744115420469760429645812640609868625658899893385756019985012438222660060690915389700165285949020489881437563281013841781250607647190620114790531723711706881018137164963096418632285359393453886085197112836853795501737185507901528886916379304576807819903178457247637148399648414584715050473645451454849514269920884716122913229594738752, 8944887367617587241442393229883580834740342304462111105224025291430611321546396102859687333969359524930738537937019013829384606176130513825457156561590666892656705555749481830166659743707548225210121902143969013444405319894625585668596912347789701976651629049271616876141532892390115295041834392608002822127929010500807946326595393217920014219030212857645423747224881557529221103453754309642068857884385938458625120451502032936317586320054048545222493315098707459226052260059007544536679036212141093443337050020955677617422530969961597220552901351308324088233175574555360591700985283581991040305739566382858380007428, 4397583564610423253499843461668397587635466857732498334676375533511290617079510457503762044490728238057694987978886639696168812864700076791908544778388891874223240097159332439061591837526459605271437124176402469035387238812282824293798762114991886550968552873900950500579121111075038947153723573424753662964020656383407389945413094698336805849701462154602561757363428980638610186902374298570018733098337050825688853874037287219878049002782016236313417300752658640951783183554558075556909424245130397476445117448915568396749223181152049295802355315026409054042717276851919403986477022829837140433933944675291372701186, 1887024557812390859587427679482183732847546004970185587894674995710637541577988021282086719881808142878304006798878288881586175207328098796364980971344261196626251002434715710053431197448244191714456166010179613555563774449838465354540108151902674835883336359438359335789619289783630973892862795355598386473633599846961468826660481787403864011853875011153240424154600064584435939126646722766878200900632739799123128975043646600429503490785669792258905940031301822731688276652795642091651576954347376088562802150248176635532850763237619932687425335901131629912404948543484891756530792238399773172947496813143007946734]
What do you want to get?
[1]the pk list
[2]Alice Public Parameters
[3]Mixed Flag
[4]exit
SERVER <INPUT>: 2
[~]Alice public_parameters is
(99432570713451062672092617212319674009128734021066252368974800380230695323011362021233083666801384874016217174138172838324478923078565331451675890131482611143922160917396923797235440250981885284277138989238227045468313350149185634986094994817254420199118748807731778875073713159130977981056629225363484612477, 3968529370264936315920184477746788220647053714090169783299608119529824310904496486702826831189864895901209648545829990235312934722991437418299346170024807755247754432133360178045395401174982549914108473260518839316780908593318455968053014605561504763936320319823824648449367236939727402970530941741756355440144535524693269860226342989569545529027400537822905839372506033736360929447563246349881828685681190426611634101046071883134662542428054340117879442277375242419725749540743809427149381516979587301032095071523792619805416206328411405597400382193217814410409605898798472988157572731575592931542612306878517511455)
What do you want to get?
[1]the pk list
[2]Alice Public Parameters
[3]Mixed Flag
[4]exit
SERVER <INPUT>: 3
[~]What you want is the flag!
[(8629971888291975347213791416269354663615597341449778464247397219745286182369049868780117508051847999960298596024452522313329959950925171599359898743763042054503440417555174526249829160862494674723813461791740628652379407441970707977460111090664195622293993068339178752253267336919360579659595380424128716331274966011720520402081818339785138564100448828785381210446654549751563770054480276370471933784135979318211388960544875452302901572290613486671118837737952929707183938688557203481397969599355299594458247427664016117339384449186175616507581548517338060151198448327302002598499596140923762164185685397703246525017, 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(2382704819350988648204939926259922012821070196393254466517927977328047779007630655554783102909445420233334603414269830021827909871784463842733412228018177538280291666226870925572366499683051585600821733321248692261413823782180369786281108496129071519528138126973685857158738633931510584076135644438451418512008698435996783365565980823146754387114607644836143562871251037131100844233499210456295742002818248405955542240031209179401171271988182498301048707975128420754563407337516505117424026601497057408173728989963923392569169720608288778589977299331468798591689742966007919372616963939427942973022672206407915356894, 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3603233069921949635850852842102780282250188557063111749359701863158964441251898915819927526832514804676814118399988368079794874992149765916759224281185627030856640018562907911112504000563096016700256240666273611941320289178055416603630913077176567643353181182220432293206255187929971213857584642985361915813306867425294385269330460752200900341331665528445829353168856397102607628243111558263291982908278855340763809937944911956507459341371522547886786433534425538866644727624245702953159357318705462680438481025308981427064201053009152196210535434082336140957273740170206132676978454465699712662183230838620576397771), (2507489313693027727447823694213947097758893725637064080783076417422312360728871796716507607648204050957058352447513001293923638548755061814481143157280185982134248529705643296490203782611775648931232850380043060019259802341855745407723808559404538235550140640847652196525197728216863601181861238447111155134874873220188560494260693812235297043755237290506736697473642464212381153314464150028542768640544348115479388781714169932337684281395098898295048720991373671433770742876559915120975993663066370466552784425304512344074776338296352164911126588429313182901480992761403886230939719560496866577975131579057233980418, 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1980172577526976953208467529900525783074696095931646996510173485588725995089661024536807562115058145311072178324244275386472867798089304656532882034354969245827559132434491283213041279414052179349423545284449349791764442814795484489622913236952945004885237471927992708071668392107252909374174486979848725181384806622865162901189364378882337523881706060196311538634436782157680819223656846784628557021576760718204769640388889532408106414067642872013172395542468221843563481648375218787976310106718686529056130227939362903825973551762087339318300140188516130629026785777810412625331595370234139359970280877739798474389), (7769230445155201113494537348459352387708612203054561299606903286112936921859421067127410781913677713423158049411013804288570673695825855969822168904613465090290306226978616894321879293271162132061470408070909310151619998411378202847228354918571965001390588172776972224778839119169450173333867054090477937647516598663804457249106382500709364775634358601371251459877683379682809903658838902783963786177719437968604142810768329151307435649733153348164028321577077681431486645592176232620214087883116496965071120567845561936056520916949714662519666931982850792755106900551200428113854794154127442081282902169286650571401, 1575094877701795854498774908638903522669421051531573312093667127284544685427913301822137233349330103439966188241901781657995508053590393431112660182478894250834736190200611323499178795811947949448699368341885262244922319233898608781419619210833188270769502178623446319852515092097374376230284979030896357428170209276025068117869920819506765819887277035215331513588698837794510471067850530536430462916048677656769292228807520578503908679844209663943585309414158448052732725558692228885890997143173078704774290593538094709155128226553159420350131695351485888673216532336279540226705255688328040783577052756207587006270, 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(1575094877701795854498774908638903522669421051531573312093667127284544685427913301822137233349330103439966188241901781657995508053590393431112660182478894250834736190200611323499178795811947949448699368341885262244922319233898608781419619210833188270769502178623446319852515092097374376230284979030896357428170209276025068117869920819506765819887277035215331513588698837794510471067850530536430462916048677656769292228807520578503908679844209663943585309414158448052732725558692228885890997143173078704774290593538094709155128226553159420350131695351485888673216532336279540226705255688328040783577052756207587006270, 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1518486070937095431267728249967625462615084214873519869724691145931391888893984408735020316869577560635376392428533320137999061224646280418013600820687411977047143852240859128701565827810521684321783327786465208897593862389568908868890826199105669712761247928108093008056596587483514169117862021972656609656939975812867444210967581049993172306174305541579882729780098039933312778734112663231561634590403753870449301486897270821771001471591549309582677751258104686430351246789904546466436576979978832001105662418364938101412232320509104886209874169009281768978468363614092630860981345300448240861393056424955085865425)]
What do you want to get?
[1]the pk list
[2]Alice Public Parameters
[3]Mixed Flag
[4]exit
SERVER <INPUT>: 4
还给了个附件是6个数组记录了某个参数的变化
总的来说这道题有点遗憾，给了提示后我猜到应该和侧信道攻击有关，查到了一个相似的描述电压变化的，但是最后不知道为什么还是算不出结果，复现的时候我按一模一样的操作重做了一遍就出了。。。😢
import gmpy2
from Crypto.Util.number import *
n,g=(99432570713451062672092617212319674009128734021066252368974800380230695323011362021233083666801384874016217174138172838324478923078565331451675890131482611143922160917396923797235440250981885284277138989238227045468313350149185634986094994817254420199118748807731778875073713159130977981056629225363484612477, 3968529370264936315920184477746788220647053714090169783299608119529824310904496486702826831189864895901209648545829990235312934722991437418299346170024807755247754432133360178045395401174982549914108473260518839316780908593318455968053014605561504763936320319823824648449367236939727402970530941741756355440144535524693269860226342989569545529027400537822905839372506033736360929447563246349881828685681190426611634101046071883134662542428054340117879442277375242419725749540743809427149381516979587301032095071523792619805416206328411405597400382193217814410409605898798472988157572731575592931542612306878517511455)
energy=[[166, 171, 75, 63, 194, 190, 165, 80, 194, 164, 90, 74, 198, 182, 88, 89, 179, 89, 193, 70, 61, 74, 187, 175, 171, 73, 84, 91, 199, 189, 62, 160, 174, 175, 96, 77, 175, 167, 94, 69, 173, 69, 88, 60, 183, 99, 164, 98, 91, 185, 174, 69, 80, 160, 90, 79, 91, 81, 71, 77, 89, 180, 62, 185, 171, 89, 164, 160, 180, 96, 160, 99, 190, 76, 178, 86, 90, 70, 91, 76, 165, 199, 88, 169, 76, 72, 64, 77, 172, 98, 65, 88, 89, 69, 81, 172, 193, 195, 193, 160, 179, 89, 168, 95, 79, 83, 67, 160, 187, 88, 60, 165, 187, 171, 194, 162, 82, 91, 199, 93, 85, 164, 93, 93, 61, 163, 180, 80, 173, 165, 182, 183, 90, 186, 62, 85, 90, 63, 183, 78, 77, 184, 80, 61, 193, 195, 166, 80, 70, 96, 178, 182, 91, 62, 189, 167, 80, 83, 192, 75, 73, 92, 178, 75, 67, 162, 66, 83, 161, 179, 94, 84, 82, 72, 199, 80, 96, 65, 186, 94, 186, 95, 199, 189, 182, 99, 94, 172, 185, 99, 89, 194, 165, 188, 70, 169, 198, 184, 70, 84, 191, 174, 162, 194, 188, 160, 180, 189, 83, 191, 171, 182, 70, 84, 174, 68, 171, 162, 75, 94, 96, 180, 83, 70, 192, 161, 67, 70, 62, 98, 178, 196, 190, 196, 167, 82, 75, 89, 195, 187, 87, 160, 182, 90, 193, 192, 180, 68, 83, 85, 185, 197, 163, 178, 92, 65, 167, 91, 196, 197, 184, 60, 169, 186, 181, 84, 64, 190, 183, 191, 72, 68, 99, 80, 193, 180, 79, 76, 191, 190, 184, 187, 75, 184, 92, 183, 90, 69, 164, 180, 166, 169, 196, 175, 179, 181, 192, 178, 193, 81, 183, 170, 66, 60, 175, 195, 77, 170, 164, 94, 75, 193, 197, 85, 78, 196, 86, 164, 176, 97, 171, 73, 70, 65, 82, 92, 76, 165, 75, 61, 91, 176, 198, 167, 164, 178, 186, 63, 76, 194, 90, 62, 162, 173, 68, 190, 71, 163, 70, 178, 194, 97, 68, 170, 162, 187, 177, 60, 190, 76, 176, 183, 176, 71, 71, 61, 66, 75, 195, 164, 189, 74, 180, 169, 99, 190, 162, 66, 163, 66, 81, 175, 165, 195, 88, 88, 187, 170, 77, 90, 190, 72, 80, 177, 84, 193, 96, 69, 99, 181, 90, 161, 80, 69, 69, 85, 90, 68, 198, 174, 64, 161, 91, 169, 194, 174, 184, 61, 97, 180, 80, 199, 192, 88, 172, 88, 187, 63, 168, 81, 65, 184, 168, 178, 189, 163, 68, 184, 189, 98, 194, 162, 196, 186, 77, 185, 80, 84, 169, 79, 66, 68, 81, 89, 72, 182, 67, 88, 82, 182, 80, 68, 65, 90, 171, 177, 65, 95, 70, 60, 180, 79, 170, 76, 193, 173, 168, 173, 93, 171, 190, 87, 74, 161, 189, 165, 69, 160, 180, 91, 167, 188, 184, 73, 82, 79, 86, 164, 78, 178, 166, 165, 163, 189, 71, 85, 191, 180, 79, 60, 198, 60, 186, 167, 178, 175, 79, 90, 65, 181, 168, 75, 63, 97, 96, 197, 192, 73, 86, 69, 189, 68, 186, 177, 92, 179, 185, 189, 193, 186, 161, 98, 79, 167, 81, 77, 84, 194, 169, 67, 164, 195, 176, 162, 199, 168, 177, 66, 189, 69, 62, 76, 191, 190, 97, 92, 79, 74, 92, 181, 174, 61, 68, 65, 83, 186, 61, 163, 93, 60, 163, 190, 86, 91, 173, 63, 190, 72, 190, 168, 189, 191, 92, 175, 90, 170, 175, 94, 81, 75, 74, 195, 92, 198, 167, 98, 73, 190, 174, 161, 75, 77, 84, 79, 190, 88, 80, 68, 68, 90, 174, 190, 186, 62, 178, 66, 194, 97, 186, 172, 68, 177, 62, 197, 171, 170, 179, 88, 96, 96, 169, 84, 62, 60, 69, 187, 96, 87, 94, 65, 195, 174, 87, 94, 80, 73, 168, 195, 98, 82, 198, 92, 80, 174, 186, 160, 168, 177, 192, 188, 67, 193, 191, 193, 174, 67, 174, 194, 88, 82, 197, 76, 61, 188, 189, 175, 177, 81, 68, 69, 83, 88, 179, 88, 87, 190, 64, 91, 169, 190, 84, 65, 166, 76, 171, 92, 192, 98, 81, 65, 178, 166, 66, 195, 174, 161, 189, 188, 62, 160, 96, 66, 93, 178, 166, 79, 96, 193, 84, 192, 180, 163, 190, 98, 165, 81, 166, 85, 193, 81, 79, 72, 187, 196, 90, 62, 171, 93, 89, 160, 98, 80, 194, 88, 179, 65, 87, 186, 163, 92, 73, 189, 61, 86, 166, 187, 70, 93, 185, 173, 161, 90, 184, 199, 189, 173, 191, 179, 164, 174, 60, 69, 192, 176, 170, 198, 164, 185, 63, 75, 188, 189, 173, 88, 61, 184, 68, 71, 165, 163, 79, 189, 185, 61, 98, 77, 65, 172, 190, 175, 174, 78, 173, 193, 160, 162, 171, 91, 182, 193, 98, 187, 160, 190, 197, 90, 89, 98, 161, 67, 80, 61, 171, 168, 173, 89, 193, 196, 84, 96, 185, 179, 177, 196, 63, 161, 176, 80, 63, 66, 68, 75, 179, 74, 171, 66, 174, 176, 75, 162, 96, 76, 86, 193, 93, 192, 72, 82, 74, 194, 92, 190, 84, 170, 86, 195, 168, 174, 78, 186, 169, 75, 196, 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175, 64, 174, 87, 87, 72, 75, 165, 70, 170, 195, 188, 65, 84, 171, 97, 75, 79, 172, 165, 94, 164, 178, 90, 71, 168, 161, 71, 195, 66, 94, 188, 60, 98, 170, 76, 161, 198, 75, 187, 193, 60, 82, 95, 178, 74, 194, 177, 164, 73, 82, 176, 186, 83, 162, 60, 63, 84, 89, 75, 194, 167, 74, 68, 67, 169, 160, 96, 67, 197, 82, 170, 177, 197, 181, 94, 83, 81, 75, 161, 96, 184, 91, 177, 193, 174, 161, 90, 166, 182, 85, 67, 68, 87, 77, 79, 76, 61, 163, 63, 65, 183, 86, 181, 74, 172, 69, 167, 194, 93, 68, 195, 174, 184, 60, 64, 168, 63, 80, 190, 80, 186, 183, 64, 163, 84, 161, 167, 77, 75, 161, 171, 164, 162, 99, 69, 169, 84, 191, 70, 191, 61, 82, 190, 63, 191, 94, 64, 195, 182, 165, 185, 198, 160, 193, 189, 87, 176, 162, 178, 89, 71, 90, 160, 180, 184, 167, 81, 177, 80, 178, 197, 85, 93, 181, 72, 191, 62, 164, 97, 86, 175, 79, 177, 171, 74, 91, 165, 186, 172, 190, 188, 166, 196, 96, 65, 81, 74, 82, 60, 76, 77, 67, 63, 172, 169, 80, 198, 85, 98, 176, 77, 180, 194, 185, 81, 67, 69, 63, 72, 95, 97, 177, 163, 94, 78, 91, 183, 98, 67, 94, 74, 196, 161, 76, 72, 171, 78, 71, 83, 71, 60, 66, 95, 89, 197, 94, 189, 73, 81, 61, 60, 186, 72, 62, 178, 181, 166, 81, 64, 83, 82, 99, 164, 88, 176, 176, 83, 80, 197, 96, 186, 167, 181, 97, 191, 71, 189, 177, 178, 161, 189, 192, 199, 188, 83, 163, 70, 88, 197, 67, 179, 75, 70, 187, 186, 82, 75, 79, 174, 196, 99, 70, 163, 164, 62, 195, 178, 76, 62, 171, 177, 75, 165, 170, 90, 174, 79, 178, 197, 98, 191, 174, 65, 89, 174, 166, 73, 199, 83, 75, 165, 172, 163, 88, 72, 161, 80, 167, 172, 177, 94, 73, 175, 183, 183, 161, 89, 174, 180, 162, 82, 165, 177, 177, 76, 182, 195, 62, 177, 184, 67, 93, 61, 191, 77, 88, 175, 163, 99, 79, 97, 80, 88, 176, 76, 181, 80, 170, 160, 185, 167, 61, 170, 90, 162, 78, 197, 73, 192, 99, 63, 170, 82, 191, 95, 66, 84, 168, 187, 198, 178, 70, 83, 168, 172, 174, 187, 180, 196, 175, 63, 88, 181, 183, 184, 171, 94, 179, 175, 61, 162, 197, 189, 82, 175, 86, 76, 183, 169, 69, 169, 170, 163, 79, 81, 86, 161, 94, 194, 77, 183, 191, 169, 83, 99, 180, 95, 183, 188, 180, 167, 77, 75, 169, 161, 85, 161, 173, 67, 199, 162, 65, 169, 72, 169, 177, 83, 164, 170, 93, 77, 181, 174, 69, 189, 95, 166, 179, 73, 169, 160, 183, 181, 193, 88, 73, 182, 192, 90, 189]]
sec=[]
for i in range(len(energy)):
t=energy[i]
s=''
for j in range(len(t)):
if t[j]>130:
s+='1'
else:
s+='0'
sec.append(int(s,2))
c=[(8629971888291975347213791416269354663615597341449778464247397219745286182369049868780117508051847999960298596024452522313329959950925171599359898743763042054503440417555174526249829160862494674723813461791740628652379407441970707977460111090664195622293993068339178752253267336919360579659595380424128716331274966011720520402081818339785138564100448828785381210446654549751563770054480276370471933784135979318211388960544875452302901572290613486671118837737952929707183938688557203481397969599355299594458247427664016117339384449186175616507581548517338060151198448327302002598499596140923762164185685397703246525017, 2382704819350988648204939926259922012821070196393254466517927977328047779007630655554783102909445420233334603414269830021827909871784463842733412228018177538280291666226870925572366499683051585600821733321248692261413823782180369786281108496129071519528138126973685857158738633931510584076135644438451418512008698435996783365565980823146754387114607644836143562871251037131100844233499210456295742002818248405955542240031209179401171271988182498301048707975128420754563407337516505117424026601497057408173728989963923392569169720608288778589977299331468798591689742966007919372616963939427942973022672206407915356894, 7720313960516556678241507800313698506319294922044337939798672519899373894106710230654330788343477820100945131225868724604111187104961165449671731600123366694979688433519949770849824359157765719319384499326446776281094391789559201066092080637825695308899163795101674215619537911161758825346990604246201908242641998141131720545547223028612859544467335764381503082373878441543065709211578323452814290911656080720587522044520123114130521964539949874597280324605268358583300909472806691738357290060135813749592500883291268752974739510309885861678540543885454291467441449775481576475597779098977264432915191026950037121271), (2382704819350988648204939926259922012821070196393254466517927977328047779007630655554783102909445420233334603414269830021827909871784463842733412228018177538280291666226870925572366499683051585600821733321248692261413823782180369786281108496129071519528138126973685857158738633931510584076135644438451418512008698435996783365565980823146754387114607644836143562871251037131100844233499210456295742002818248405955542240031209179401171271988182498301048707975128420754563407337516505117424026601497057408173728989963923392569169720608288778589977299331468798591689742966007919372616963939427942973022672206407915356894, 2507489313693027727447823694213947097758893725637064080783076417422312360728871796716507607648204050957058352447513001293923638548755061814481143157280185982134248529705643296490203782611775648931232850380043060019259802341855745407723808559404538235550140640847652196525197728216863601181861238447111155134874873220188560494260693812235297043755237290506736697473642464212381153314464150028542768640544348115479388781714169932337684281395098898295048720991373671433770742876559915120975993663066370466552784425304512344074776338296352164911126588429313182901480992761403886230939719560496866577975131579057233980418, 3603233069921949635850852842102780282250188557063111749359701863158964441251898915819927526832514804676814118399988368079794874992149765916759224281185627030856640018562907911112504000563096016700256240666273611941320289178055416603630913077176567643353181182220432293206255187929971213857584642985361915813306867425294385269330460752200900341331665528445829353168856397102607628243111558263291982908278855340763809937944911956507459341371522547886786433534425538866644727624245702953159357318705462680438481025308981427064201053009152196210535434082336140957273740170206132676978454465699712662183230838620576397771), (2507489313693027727447823694213947097758893725637064080783076417422312360728871796716507607648204050957058352447513001293923638548755061814481143157280185982134248529705643296490203782611775648931232850380043060019259802341855745407723808559404538235550140640847652196525197728216863601181861238447111155134874873220188560494260693812235297043755237290506736697473642464212381153314464150028542768640544348115479388781714169932337684281395098898295048720991373671433770742876559915120975993663066370466552784425304512344074776338296352164911126588429313182901480992761403886230939719560496866577975131579057233980418, 7769230445155201113494537348459352387708612203054561299606903286112936921859421067127410781913677713423158049411013804288570673695825855969822168904613465090290306226978616894321879293271162132061470408070909310151619998411378202847228354918571965001390588172776972224778839119169450173333867054090477937647516598663804457249106382500709364775634358601371251459877683379682809903658838902783963786177719437968604142810768329151307435649733153348164028321577077681431486645592176232620214087883116496965071120567845561936056520916949714662519666931982850792755106900551200428113854794154127442081282902169286650571401, 1980172577526976953208467529900525783074696095931646996510173485588725995089661024536807562115058145311072178324244275386472867798089304656532882034354969245827559132434491283213041279414052179349423545284449349791764442814795484489622913236952945004885237471927992708071668392107252909374174486979848725181384806622865162901189364378882337523881706060196311538634436782157680819223656846784628557021576760718204769640388889532408106414067642872013172395542468221843563481648375218787976310106718686529056130227939362903825973551762087339318300140188516130629026785777810412625331595370234139359970280877739798474389), (7769230445155201113494537348459352387708612203054561299606903286112936921859421067127410781913677713423158049411013804288570673695825855969822168904613465090290306226978616894321879293271162132061470408070909310151619998411378202847228354918571965001390588172776972224778839119169450173333867054090477937647516598663804457249106382500709364775634358601371251459877683379682809903658838902783963786177719437968604142810768329151307435649733153348164028321577077681431486645592176232620214087883116496965071120567845561936056520916949714662519666931982850792755106900551200428113854794154127442081282902169286650571401, 1575094877701795854498774908638903522669421051531573312093667127284544685427913301822137233349330103439966188241901781657995508053590393431112660182478894250834736190200611323499178795811947949448699368341885262244922319233898608781419619210833188270769502178623446319852515092097374376230284979030896357428170209276025068117869920819506765819887277035215331513588698837794510471067850530536430462916048677656769292228807520578503908679844209663943585309414158448052732725558692228885890997143173078704774290593538094709155128226553159420350131695351485888673216532336279540226705255688328040783577052756207587006270, 6610352931587720854451143899633952315748731096581247094289941806600249309199110458686226240414159314916443802659936796194501937130258325721955971712271359425220780891458718764787684248492736828049383593460850257630134166697516000923586434837108552164118408207483861356227241654737966362556299121885909952085344055245123817034374630986706235981670472671656419267459375338043531055577663540904728281161038164044605649226826294253565008079171696929526279467128593521303305237010056264278316607644578180995774851856042734859960770608950180509999278132547381198060859308178075010227172861725398283857061313337363575325263), (1575094877701795854498774908638903522669421051531573312093667127284544685427913301822137233349330103439966188241901781657995508053590393431112660182478894250834736190200611323499178795811947949448699368341885262244922319233898608781419619210833188270769502178623446319852515092097374376230284979030896357428170209276025068117869920819506765819887277035215331513588698837794510471067850530536430462916048677656769292228807520578503908679844209663943585309414158448052732725558692228885890997143173078704774290593538094709155128226553159420350131695351485888673216532336279540226705255688328040783577052756207587006270, 2899196346496640651515578300741477267252027393819388234592692441244872565455171075206663782801019182310445822694710022355107834170061256021528233984226982722687848721193571620263169761625920013511824364907813108870230498313614430769087521400686949128276439718637571413546438066894526733998540267545169908267918034044567676900418717621781005337988884902642672158843440942895072083594499934345701806316446232804191200045145796718350218780127702500537329430739697477802056514649362531623994574050100569446437453774196354144878113348032018382822752357224093912706852592549799275481078987386652273745516181324786938308335, 1518486070937095431267728249967625462615084214873519869724691145931391888893984408735020316869577560635376392428533320137999061224646280418013600820687411977047143852240859128701565827810521684321783327786465208897593862389568908868890826199105669712761247928108093008056596587483514169117862021972656609656939975812867444210967581049993172306174305541579882729780098039933312778734112663231561634590403753870449301486897270821771001471591549309582677751258104686430351246789904546466436576979978832001105662418364938101412232320509104886209874169009281768978468363614092630860981345300448240861393056424955085865425)]
m=[bytes_to_long(b'vnctf')]
for i in range(len(c)):
cc=c[i][2]
pri1=pow(c[i][0],sec[i],n**2)
pri2=pow(c[i][1],sec[i+1],n**2)
pri=gmpy2.invert(pri1*pri2,n**2)
mm=((cc*pri-1)%(n**2))//n
mm-=m[i]
m.append(mm)
for i in range(len(m)):
print(str(long_to_bytes(m[i]))[2:-1],end='')
还有一道AES和ocb模式的比赛的时候没看，以后找机会复现吧
总的来说还要加油呀，不会的东西还是太多了
浙公网安备 33010602011771号