2023极客大挑战WP
WEEK1
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题目描述：
Bibo...Hello! 你好! こんにちは! Привет! 5359437b48656c6c6f5f576f726c645f43727970746f5f6269626f6269626f7d… Hmm... Something goes wrong with my grettings bot.
做题流程：
hex解码
proof_of_work
题目描述：
题目链接：nc 59.110.20.54:5526 Build your own function to solve proof_of_work!
做题流程：
爆破sha256
exp：
from string import *
from hashlib import *
from string import *
import sys
c_sha256 = '49827ac949fbba5a07aa8ca286c2ec23175cd8d1f88fbe4821d7a304da3bec4b'
sh = sha1()
dict = ascii_letters + digits
print(dict)
k = []
print(ascii_letters)
for i in dict:
print(i)
for j in dict:
for k in dict:
for x in dict:
c_ascii = i + j + k + x + 'avhfc4wnKN3c6lYj'
z = sha256(c_ascii.encode()).hexdigest()
if z == c_sha256:
print(z)
print(c_ascii)
sys.exit(1)
# print(c_ascii)SimpleRSA
题目描述：
So simple RSA! Wait... Are you kidding me? https://en.wikipedia.org/wiki/RSA_(cryptosystem)
from Crypto.Util.number import *
from gmpy2 import *
p = 24724324630507415330944861660078769085865178656494256140070836181271808964994457686409910764936630391300708451701526900994412268365698217113884698394658886249353179639767806926527103624836198494439742123128823109527320850165486500517304731554371680236789357527395416607541627295126502440202040826686102479225702795427693781581584928770373613126894936500089282093366117940069743670997994742595407158340397268147325612840109162997306902492023078425623839297511182053658542877738887677835528624045235391227122453939459585542485427063193993069301141720316104612551340923656979591045138487394366671477460626997125944456537
c = 510345661718450375632304764819724223824018609359964259503762283253350010161515190912152623604019093266967095847334388281390406831587663253164256543905694021952211220652820225527413861208452760215767828927039893435528572148282529198773772864255061213208279999011194952146362748485103032149806538140693537361755210176698895104708379400806511907719904867068865970241208806615061055047254026118016836750283966478103987375361826198930529462261013324904522014804502582865716441828895047550041401172127129749969507853355531197814919603963664646220505672302543085959372679395717892060245461464861507164276442140407308832537707450729432224150754603518526288767105682399190438680085925078051459448618725871249563011864525585870188123725554411655044152994826056900502298772802133526591794328224932405680583757307064395792317383571866619582974377344736930271554160701478385763426091091686496788999588340419226785217028504684542197970387916262126278955278523452903043316452825738030645100271595942652498852506660789605846309602343932245435421425673058238785509280366229754404949219663043627431437755087855502139890639468481922788973821783957766433857773771229298328019250652625289700950165414584983487319078090573179470893450632419467111117341472
e = 65537
d = invert(e, p - 1)
print(long_to_bytes(powmod(c, d, p)))做题流程：
发现p有2048位，m远小于p，直接用p做rsa解密
from Crypto.Util.number import *
from gmpy2 import *
p = 24724324630507415330944861660078769085865178656494256140070836181271808964994457686409910764936630391300708451701526900994412268365698217113884698394658886249353179639767806926527103624836198494439742123128823109527320850165486500517304731554371680236789357527395416607541627295126502440202040826686102479225702795427693781581584928770373613126894936500089282093366117940069743670997994742595407158340397268147325612840109162997306902492023078425623839297511182053658542877738887677835528624045235391227122453939459585542485427063193993069301141720316104612551340923656979591045138487394366671477460626997125944456537
c = 510345661718450375632304764819724223824018609359964259503762283253350010161515190912152623604019093266967095847334388281390406831587663253164256543905694021952211220652820225527413861208452760215767828927039893435528572148282529198773772864255061213208279999011194952146362748485103032149806538140693537361755210176698895104708379400806511907719904867068865970241208806615061055047254026118016836750283966478103987375361826198930529462261013324904522014804502582865716441828895047550041401172127129749969507853355531197814919603963664646220505672302543085959372679395717892060245461464861507164276442140407308832537707450729432224150754603518526288767105682399190438680085925078051459448618725871249563011864525585870188123725554411655044152994826056900502298772802133526591794328224932405680583757307064395792317383571866619582974377344736930271554160701478385763426091091686496788999588340419226785217028504684542197970387916262126278955278523452903043316452825738030645100271595942652498852506660789605846309602343932245435421425673058238785509280366229754404949219663043627431437755087855502139890639468481922788973821783957766433857773771229298328019250652625289700950165414584983487319078090573179470893450632419467111117341472
e = 65537
d = invert(e, p - 1)
print(long_to_bytes(powmod(c, d, p)))OTPTwice
题目描述：
I invented a new symmetric cryptosystem, and I believe you will never break it!
from pwn import xor
from os import urandom
flag = b"SYC{Al3XEI_FAKE_FLAG}"
# step0: key generation & distribution
def s0(msg):
k1,k2 = [urandom(len(msg)) for _ in "__"]
return k1,k2
#
# step1: Alice encrypt M, and send it to Bob
def s1(msg,k1):
c1 = xor(msg,k1)
return c1
# step2: Bob encrypt c1, and send it to Alice
def s2(msg,k2):
c2 = xor(msg,k2)
return c2
# step3: Alice decrypt c2, and send it to Bob.
def s3(msg,k1):
c3 = xor(msg,k1)
return c3
# step4: Bob decrypt c3, get M.
def s4(msg,k2):
m_ = xor(msg,k2)
return m_
def encrypt(msg,k1,k2):
c1 = s1(msg,k1)
c2 = s2(c1,k2)
c3 = s3(c2,k1)
m_ = s4(c3,k2)
assert msg == m_
# Here's what hacker Eve got:
def encrypt_(msg,k1,k2):
c1 = s1(msg,k1)
c2 = s2(c1,k2)
c3 = s3(c2,k1)
m_ = s4(c3,k2)
if HACK == True:
print(c1)
print(c2)
print(c3)
k1,k2 = s0(flag)
encrypt_(flag,k1,k2)
'''
b'\xdbi\xab\x8d\xfb0\xd3\xfe!\xf8Xpy\x80w\x8c\x87\xb9'
b'o\xb0%\xfb\xdb\x0e\r\x04\xde\xd1\x9a\x08w\xda4\x0f\x0cR'
b'\xe7\x80\xcd\ria\xb2\xca\x89\x1a\x9d;|#3\xf7\xbb\x96'
'''做题流程：
通过xor即可还原key，出m
from Crypto.Util.number import *
from gmpy2 import *
c1 = bytes_to_long(b'\xdbi\xab\x8d\xfb0\xd3\xfe!\xf8Xpy\x80w\x8c\x87\xb9')
c2 = bytes_to_long(b'o\xb0%\xfb\xdb\x0e\r\x04\xde\xd1\x9a\x08w\xda4\x0f\x0cR')
c3 = bytes_to_long(b'\xe7\x80\xcd\ria\xb2\xca\x89\x1a\x9d;|#3\xf7\xbb\x96')
k1 = c2 ^ c3
k2 = c1 ^ c2
m_ = c3 ^ k2
print(long_to_bytes(m_))OldAlgorithm
题目描述：
An old algorithm but widely used nowadays.
from Crypto.Util.number import *
import os
flag = b"SYC{Al3XEI_FAKE_FLAG}"
pad = lambda msg,padlen: msg+os.urandom(padlen-len(msg))
flag = pad(flag,32)
print(len(flag))
p = [getPrime(16) for _ in range(32)]
c = [bytes_to_long(flag)%i for i in p]
print('p=',p)
print('c=',c)
'''
p= [58657, 47093, 47963, 41213, 57653, 56923, 41809, 49639, 44417, 38639, 39857, 53609, 55621, 41729, 60497, 44647, 39703, 55117, 44111, 57131, 37747, 63419, 63703, 64007, 46349, 39241, 39313, 44909, 40763, 46727, 34057, 56333]
c= [36086, 4005, 3350, 23179, 34246, 5145, 32490, 16348, 13001, 13628, 7742, 46317, 50824, 23718, 32995, 7640, 10590, 46897, 39245, 16633, 31488, 36547, 42136, 52782, 31929, 34747, 29026, 18748, 6634, 9700, 8126, 5197]
'''做题流程：
发现多组c，p，一眼crt
from Crypto.Util.number import *
from gmpy2 import *
p= [58657, 47093, 47963, 41213, 57653, 56923, 41809, 49639, 44417, 38639, 39857, 53609, 55621, 41729, 60497, 44647, 39703, 55117, 44111, 57131, 37747, 63419, 63703, 64007, 46349, 39241, 39313, 44909, 40763, 46727, 34057, 56333]
c= [36086, 4005, 3350, 23179, 34246, 5145, 32490, 16348, 13001, 13628, 7742, 46317, 50824, 23718, 32995, 7640, 10590, 46897, 39245, 16633, 31488, 36547, 42136, 52782, 31929, 34747, 29026, 18748, 6634, 9700, 8126, 5197]
func = crt(c, p)
print(long_to_bytes(func))easy_classic
题目描述：
非常好套娃，使我的古典旋转
做题流程：
好玩，爱玩
第一层：凯撒
第二层：栅栏
第三层：base64
第四层：与熊论禅
第五层：key为base100，加密为playfair
SYC{classical_1s_fun}WEEK2
PolyRSA
题目描述：
Harder RSA. Check it out!
import gmpy2
from Crypto.Util.number import *
flag = b"SYC{Al3XEI_FAKE_FLAG}"
p,q = [getPrime(2048) for _ in "__"]
e1,e2 = [getPrime(17) for _ in "__"]
e = 65537
n = p*q
c1 = gmpy2.powmod(2*p + 3*q,e1,n)
c2 = gmpy2.powmod(5*p + 7*q,e2,n)
c = gmpy2.powmod(bytes_to_long(flag),e,n)
print("e1=",e1)
print("e2=",e2)
print("c1=",c1)
print("c2=",c2)
print("c=",c)
print("n=",n)
#e1= 113717
#e2= 80737
#c1= 97528398828294138945371018405777243725957112272614466238005409057342884425132214761228537249844134865481148636534134025535106624840957740753950100180978607132333109806554009969378392835952544552269685553539656827070349532458156758965322477969141073720173165958341043159560928836304172136610929023123638981560836183245954461041167802574206323129671965436040047358250847178930436773249800969192016749684095882580749559014647942135761757750292281205876241566597813517452803933496218995755905344070203047797893640399372627351254542342772576533524820435965479881620338366838326652599102311019884528903481310690767832417584600334987458835108576322111553947045733143836419313427495888019352323209000292825566986863770366023326755116931788018138432898323148059980463407567431417724940484236335082696026821105627826117901730695680967455710434307270501190258033004471156993017301443803372029004817834317756597444195146024630164820841200575179112295902020141040090350486764038633257871003899386340004440642516190842086462237559715130631205046041819931656962904630367121414263911179041905140516402771368603623318492074423223885367923228718341206283572152570049573607906130786276734660847733952210105659707746969830132429975090175091281363770357
#c2= 353128571201645377052005694809874806643786163076931670184196149901625274899734977100920488129375537186771931435883114557320913415191396857882995726660784707377672210953334914418470453787964899846194872721616628198368241044602144880543115393715025896206210152190007408112767478800650578941849344868081146624444817544806046188600685873402369145450593575618922226415069043442295774369567389939040265656574664538667552522329712111984168798829635080641332045614585247317991581514218486004191829362787750803153463482021229058714990823658655863245025037102127138472397462755776598314247771125981017814912049441827643898478473451005083533693951329544115861795587564408860828213753948427321483082041546722974666875065831843384005041800692983406353922680299538080900818930589336142421748023025830846906503542594380663429947801329079870530727382679634952272644949425079242992486832995962516376820051495641486546631849426876810933393153871774796182078367277299340503872124124714036499367887886486264658590613431293656417255355575602576047502506125375605713228912611320198066713358654181533335650785578352716562937038768171269136647529849805172492594142026261051266577821582011917001752590659862613307646536049830151262848916867223615064832279222
#c= 375617816311787295279632219241669262704366237192565344884527300748210925539528834207344757670998995567820735715933908541800125317082581328287816628816752542104514363629022246620070560324071543077301256917337165566677142545053272381990573611757629429857842709092285442319141751484248315990593292618113678910350875156232952525787082482638460259354559904243062546518553607882194808191571131590524874275187750985821420412987586148770397073003186510357920710387377990379862185266175190503647626248057084923516190642292152259727446111686043531725993433395002330208067534104745851308178560234372373476331387737629284961288204368572750848248186692623500372605736825205759172773503283282321274793846281079650686871355211691681512637459986684769598186821524093789286661348936784712071312135814683041839882338235290487868969391040389837253093468883093296547473466050960563347060307256735803099039921213839491129726807647623542881247210251994139130146519265086673883077644185971830004165931626986486648581644383717994174627681147696341976767364316172091139507445131410662391699728189797082878876950386933926807186382619331901457205957462337191923354433435013338037399565519987793880572723211669459895193009710035003369626116024630678400746946356
#n= 728002565949733279371529990942440022467681592757835980552797682116929657292509059813629423038094227544032071413317330087468458736175902373398210691802243764786251764982802000867437756347830992118278032311046807282193498960587170291978547754942295932606784354258945168927044376692224049202979158068158842475322825884209352566494900083765571037783472505580851500043517614314755340168507097558967372661966013776090657685241689631615245294004694287660685274079979318342939473469143729494106686592347327776078649315612768988028622890242005700892937828732613800620455225438339852445425046832904615827786856105112781009995862999853122308496903885748394541643702103368974605177097553007573113536089894913967154637055293769061726082740854619536748297829779639633209710676774371525146758917646731487495135734759201537358734170552231657257498090553682791418003138924472103077035355223367678622115314235119493397080290540006942708439607767313672671274857069053688258983103863067394473084183472609906612056828326916114024662795812611685559034285371151973580240723680736227737324052391721149957542711415812665358477474058103338801398214688403784213100455466705770532894531602252798634923125974783427678469124261634518543957766622712661056594132089做题流程：
$$\left\{ \begin{array}{rcl} {c_1}^{e_2}\equiv (2p+3q)^{e_1e_2}&(mod\ n)\\ {c_2}^{e_1}\equiv (5p+7q)^{e_1e_2}&(mod\ n)\\ \end{array} \right. $$
二项式展开化简：
$$\left\{ \begin{array}{rcl} {c_1}^{e_2}\equiv (2p)^{e_1e_2}+(3q)^{e_1e_2}&(mod\ n)\\ {c_2}^{e_1}\equiv (5p)^{e_1e_2}+(7q)^{e_1e_2}&(mod\ n)\\ \end{array} \right. $$
令$\left\{ \begin{array}{rcl} a=2^{e_1e_2}&(mod\ n)\\ b=3^{e_1e_2}&(mod\ n)\\ c=5^{e_1e_2}&(mod\ n)\\ d=7^{e_1e_2}&(mod\ n)\\ \end{array} \right. $
则有：
$$\left\{ \begin{array}{rcl} {c_1}^{e_2}\equiv a*p^{e_1e_2}+b*q^{e_1e_2}\ (mod\ n)\\ {c_2}^{e_1}\equiv c*p^{e_1e_2}+d*q^{e_1e_2}\ (mod\ n)\\ \end{array} \right. $$
将$式1*d-式2*b$得
$$(ad-bc)p^{e_1e_2}\equiv d*{c_1}^{e_2}-b*{c_2}^{e_1}\ (mod n)$$
所以：
$$p^{e_1e_2}\equiv {(ad-bc)}^{-1}(d*{c_1}^{e_2}-b*{c_2}^{e_1})\ (mod n)$$
$$p=gcd(p^{e_1e_2},n)$$
接着普通rsa
Exp:
from Crypto.Util.number import *
from gmpy2 import *
e1 = 113717
e2 = 80737
c1 = 97528398828294138945371018405777243725957112272614466238005409057342884425132214761228537249844134865481148636534134025535106624840957740753950100180978607132333109806554009969378392835952544552269685553539656827070349532458156758965322477969141073720173165958341043159560928836304172136610929023123638981560836183245954461041167802574206323129671965436040047358250847178930436773249800969192016749684095882580749559014647942135761757750292281205876241566597813517452803933496218995755905344070203047797893640399372627351254542342772576533524820435965479881620338366838326652599102311019884528903481310690767832417584600334987458835108576322111553947045733143836419313427495888019352323209000292825566986863770366023326755116931788018138432898323148059980463407567431417724940484236335082696026821105627826117901730695680967455710434307270501190258033004471156993017301443803372029004817834317756597444195146024630164820841200575179112295902020141040090350486764038633257871003899386340004440642516190842086462237559715130631205046041819931656962904630367121414263911179041905140516402771368603623318492074423223885367923228718341206283572152570049573607906130786276734660847733952210105659707746969830132429975090175091281363770357
c2 = 353128571201645377052005694809874806643786163076931670184196149901625274899734977100920488129375537186771931435883114557320913415191396857882995726660784707377672210953334914418470453787964899846194872721616628198368241044602144880543115393715025896206210152190007408112767478800650578941849344868081146624444817544806046188600685873402369145450593575618922226415069043442295774369567389939040265656574664538667552522329712111984168798829635080641332045614585247317991581514218486004191829362787750803153463482021229058714990823658655863245025037102127138472397462755776598314247771125981017814912049441827643898478473451005083533693951329544115861795587564408860828213753948427321483082041546722974666875065831843384005041800692983406353922680299538080900818930589336142421748023025830846906503542594380663429947801329079870530727382679634952272644949425079242992486832995962516376820051495641486546631849426876810933393153871774796182078367277299340503872124124714036499367887886486264658590613431293656417255355575602576047502506125375605713228912611320198066713358654181533335650785578352716562937038768171269136647529849805172492594142026261051266577821582011917001752590659862613307646536049830151262848916867223615064832279222
cc = 375617816311787295279632219241669262704366237192565344884527300748210925539528834207344757670998995567820735715933908541800125317082581328287816628816752542104514363629022246620070560324071543077301256917337165566677142545053272381990573611757629429857842709092285442319141751484248315990593292618113678910350875156232952525787082482638460259354559904243062546518553607882194808191571131590524874275187750985821420412987586148770397073003186510357920710387377990379862185266175190503647626248057084923516190642292152259727446111686043531725993433395002330208067534104745851308178560234372373476331387737629284961288204368572750848248186692623500372605736825205759172773503283282321274793846281079650686871355211691681512637459986684769598186821524093789286661348936784712071312135814683041839882338235290487868969391040389837253093468883093296547473466050960563347060307256735803099039921213839491129726807647623542881247210251994139130146519265086673883077644185971830004165931626986486648581644383717994174627681147696341976767364316172091139507445131410662391699728189797082878876950386933926807186382619331901457205957462337191923354433435013338037399565519987793880572723211669459895193009710035003369626116024630678400746946356
n = 728002565949733279371529990942440022467681592757835980552797682116929657292509059813629423038094227544032071413317330087468458736175902373398210691802243764786251764982802000867437756347830992118278032311046807282193498960587170291978547754942295932606784354258945168927044376692224049202979158068158842475322825884209352566494900083765571037783472505580851500043517614314755340168507097558967372661966013776090657685241689631615245294004694287660685274079979318342939473469143729494106686592347327776078649315612768988028622890242005700892937828732613800620455225438339852445425046832904615827786856105112781009995862999853122308496903885748394541643702103368974605177097553007573113536089894913967154637055293769061726082740854619536748297829779639633209710676774371525146758917646731487495135734759201537358734170552231657257498090553682791418003138924472103077035355223367678622115314235119493397080290540006942708439607767313672671274857069053688258983103863067394473084183472609906612056828326916114024662795812611685559034285371151973580240723680736227737324052391721149957542711415812665358477474058103338801398214688403784213100455466705770532894531602252798634923125974783427678469124261634518543957766622712661056594132089
e = 65537
ee = e1 * e2
a = powmod(2, ee, n)
b = powmod(3, ee, n)
c = powmod(5, ee, n)
d = powmod(7, ee, n)
t = a * d - b * c
inv_t = invert(t, n)
pp = inv_t * (d * powmod(c1, e2, n) - b * powmod(c2, e1, n)) % n
p = gcd(pp, n)
assert isPrime(p)
q = n // p
assert isPrime(q)
print(q)
phi = (p - 1) * (q - 1)
dd = invert(e, phi)
m = powmod(cc, dd, n)
print(long_to_bytes(m))Fi1nd_th3_x'
题目描述：
听说在那个大陆有位叫jrl777的旅行者......Cryptoer穿越到了提瓦特就要拿出真本事！
做题流程：
文本不知道有什么用
一个CRT就解决了，迷惑（
考点应该是不互素情况下的CRT
Exp:
from Crypto.Util.number import *
from gmpy2 import *
p = 13014610351521460822156239705430709078128228907778181478242620569429327799535062679140131416771915929573454741755415612880788196172134695027201422226050343
q = 12772373441651008681294250861077909144300908972709561019514945881228862913558543752401850710742410181542277593157992764354184262443612041344749961361188667
r = 12128188838358065666687296689425460086282352520167544115899775800918383085863282204525519245937988837403739683061218279585168168892037039644924073220678419
dp = 116715737414908163105708802733763596338775040866822719131764691930369001776551671725363881836568414327815420649861207859100479999650414099346914809923964116101517432576562641857767638396325944526867458624878906968552835814078216316470330511385701105459053294771612727181278955929391807414985165924450505855941
dq = 44209639124029393930247375993629669338749966042856653556428540234515804939791650065905841618344611216577807325504984178760405516121845853248373571704473449826683120387747977520655432396578361308033763778324817416507993263234206797363191089863381905902638111246229641698709383653501799974217118168526572365797
dr = 60735172709413093730902464873458655487237612458970735840670987186877666190533417038325630420791294593669609785154204677845781980482700493870590706892523016041087206844082222225206703139282240453277802870868459288354322845410191061009582969848870045522383447751431300627611762289800656277924903605593069856921
c = 93063188325241977486352111369210103514669725591157371105152980481620575818945846725056329712195176948376321676112726029400835578531311113991944495646259750817465291340479809938094295621728828133981781064352306623727112813796314947081857025012662546178066873083689559924412320123824601550896063037191589471066773464829226873338699012924080583389032903142107586722373131642720522453842444615499672193051587154108368643495983197891525747653618742702589711752256009
n = p * q * r
phi = (p - 1) * (q - 1) * (r - 1)
d=crt([dp, dq, dr],[phi // (p - 1),phi // (q - 1),phi // (r - 1)])
m = powmod(c,d,n)
print(long_to_bytes(m))Simple3DES
题目描述：
nc 59.110.20.54:23333 https://blog.csdn.net/Mr_wzc/article/details/121713518
from Crypto.Cipher import DES3
from Crypto.Util.number import *
import os
import random
import string
import hashlib
xor = lambda a,b: bytes([a[i % len(a)] ^ b[i % len(b)] for i in range(max(len(a), len(b)))])
pad = lambda msg,padlen: msg+chr((padlen-(len(msg)%padlen))).encode()*(padlen-(len(msg)%padlen))
flag = os.environ.get("FLAG", "SYC{Al3XEI_FAKE_FLAG}").encode()
sec = os.urandom(8)
banner = '|'*70
DEBUG = False
def proof_of_work():
if DEBUG:
return True
proof = ''.join([random.choice(string.ascii_letters+string.digits) for _ in range(20)])
digest = hashlib.sha256(proof.encode()).hexdigest()
print("sha256(XXXX+%s) == %s" % (proof[4:], digest))
x = input("Give me XXXX: ")
if len(x)!=4 or hashlib.sha256((x+proof[4:]).encode()).hexdigest() != digest:
return False
print("Right!")
return True
def enc(msg,key):
try:
key = long_to_bytes(key)
msg = xor(long_to_bytes(msg),sec)
des = DES3.new(key,DES3.MODE_ECB)
ct = xor(des.encrypt(pad(msg,8)),sec)
return bytes_to_long(ct)
except Exception as e:
print(e)
return Exception
def service():
cnt = 0
if not proof_of_work():
exit()
print(banner)
print('Simple DES Encryption Service')
print(banner)
while cnt<2:
print('1. Encrypt\n2. Get encrypted flag.')
choice = int(input('> '))
if choice == 1:
print('Input msg:')
msg = int(input('> ').strip())
print('Input key:')
key = int(input('> ').strip())
print(enc(msg,key))
elif choice == 2:
print('Input key:')
key = int(input('> ').strip())
print(enc(bytes_to_long(flag),key))
else:
exit()
cnt+=1
print(banner)
print('Bye!')
exit()
try:
service()
except Exception:
print("Something goes wrong...\n")
print(banner+'\n')
exit()做题流程：
看到这个pad，想到随便传个8位，则明文和sec异或得到的就是一个8位，被被填充后成16位则最后8位都是\x08，发现经过3des后末尾八位都是固定的，我们用密钥把任意一个8位＋8位\x00加密，发现末尾8位都是一串固定的数，将这个8位与输出异或即可得到sec，得到sec再逆着走边加密流程即可得到flag
Exp:
from Crypto.Util.number import *
from Crypto.Cipher import DES3
from gmpy2 import *
import random
import string
import hashlib
import os
xor = lambda a,b: bytes([a[i % len(a)] ^ b[i % len(b)] for i in range(max(len(a), len(b)))])
pad = lambda msg,padlen: msg+chr((padlen-(len(msg)%padlen))).encode()*(padlen-(len(msg)%padlen))
key = b'1234567812345677'
msg = b'\x15|\x07\x172\xfe\xc5\xe5'
print(len(msg))
sec = os.urandom(8)
print(len(sec))
des = DES3.new(key,DES3.MODE_ECB)
print(pad(sec, 8))
print(des.encrypt(pad(sec, 8)))
ct = xor(des.encrypt(pad(sec, 8)),sec)
print(len(ct))
z = (long_to_bytes(130827495204001562781583811333231577670))
print(xor(z, msg))
sec = b'\x9f\x07\xe7\x88\x17\x8fO\xa3'
print(len(sec))
z = (long_to_bytes(3635303539058369704084970711745626839589893640907549430077))
m = (xor(z, sec))
m = des.decrypt(m)
print(xor(m, sec))JPGDiff
题目描述：
图片中的字符串即为flag
做题流程：
推256256走法，将图片弯曲成一个256256的图片（人懒，用的CryptoCTF2023的生成函数）
from PIL import Image
def sox(n, d):
x, y, t = 0, 0, d
for s in range(n - 1):
u = 1 & t // 2
v = 1 & t ^ u
x, y = spin(2**s, x, y, u, v)
x += 2**s * u
y += 2**s * v
t = t // 4
return x, y
def spin(n, x, y, u, v):
if v == 0:
if u == 1:
x = n - 1 - x
y = n - 1 - y
x, y = y, x
return x, y
def get_path_sequence(n):
path_sequence = []
for d in range(n**2):
x, y = sox(n, d)
path_sequence.append((x, y))
return path_sequence
raw = Image.open("/home/nightmare/Cryp/geek_chanllenge/ct.png")
new_image = Image.new("RGB", (256,256), "white")
images = []
for i in range(0,65536):
region = raw.crop((0,i,1,i+1))
images.append(region)
path = []
path = get_path_sequence(256)
for i in range(len(path)):
new_image.paste(images[i],(path[i][0],path[i][1]))
new_image.save("/home/nightmare/Cryp/geek_chanllenge/out.png")翻转一下，得到图片
Energetic_Carcano
题目描述：
nc 59.110.20.54:8763 https://en.wikipedia.org/wiki/Elliptic-curve_cryptography
# from sage.all import *
import os
import random
import string
import hashlib
from Crypto.Util.number import *
DEBUG = True
banner = '|'*70
flag = os.environ.get("FLAG", b"SYC{Al3XEI_FAKE_FLAG}").encode()
pbits = 120
abp = "abp"
def proof_of_work():
if DEBUG:
return True
proof = ''.join([random.choice(string.ascii_letters+string.digits) for _ in range(20)])
digest = hashlib.sha256(proof.encode()).hexdigest()
print("sha256(XXXX+%s) == %s" % (proof[4:], digest))
x = input("Give me XXXX: ")
if len(x)!=4 or hashlib.sha256((x+proof[4:]).encode()).hexdigest() != digest:
return False
print("Right!")
return True
def check(a,b,p,turn,ans):
if DEBUG:
return True
try:
if turn == "a":
return int(a) == ans
if turn == "b":
return int(b) == ans
if turn == "p":
return int(p) == ans
except Exception:
exit()
try:
if not proof_of_work():
exit()
print(banner)
print('\nHi Crypto-ers! AL3XEI here. I know you are excellent at math, so I prepared a game for u.')
print('In the equation y^2 = x^3+ a*x + b (mod p), 4 points are given. Plz give me the right a, b or p to contine the game.')
print('Good Luck!\n')
print(banner+'\n')
for i in range(10):
turn = random.choice(abp)
p = getPrime(pbits)
a,b = [next_prime(random.randint(2,p)) for _ in "ab"]
curve = EllipticCurve(GF(p),[a,b])
pts = [curve.random_point() for _ in range(4)]
pts = [(_[0], _[1]) for _ in pts]
for _ in pts:
print(_,end=" ")
print('\nGive me '+turn+" :")
ans = int(input('> '))
if check(a,b,p,turn,ans):
print("Good! Next challenge->\n")
print(banner+'\n')
pbits+=5
continue
else:
print("Something goes wrong...\n")
print(banner+'\n')
exit()
print('Congrats! Your flag is:',flag)
except Exception:
print("Something goes wrong...\n")
print(banner+'\n')
exit() 做题流程：
有原式子：
$$y^2=x^3+ax+b\ (mod p)$$
知道四个点，x和y已知
$$ \left\{\begin{array}{rcl}{y_1}^2-{x_1}^3＝ax_1+b\ (mod\ p) \\ {y_2}^2-{x_2}^3＝ ax_2+b\ (mod\ p)\\ {y_3}^2-{x_3}^3＝ ax_3+b\ (mod\ p)\\ {y_4}^2-{x_4}^3＝ ax_4+b\ (mod\ p)\\ \end{array} \right. $$ 式2-式1和式3-式1联立得 $$\left\{ \begin{array}{rcl} ({y_2}^2-{x_2}^3)-({y_1}^2-{x_1}^3)＝ ax_2-ax_1\ (mod\ p)\\ ({y_3}^2-{x_3}^3)-({y_1}^2-{x_1}^3)＝ ax_3-ax_1\ (mod\ p)\\ \end{array} \right. $$ 令 $({y_2}^2-{x_2}^3)-({y_1}^2-{x_1}^3)=t_1$ , $({y_3}^2-{x_3}^3)-({y_1}^2-{x_1}^3)=t_2$ 则有： $$\left\{\begin{array}{rcl}t_1＝a(x_2-x_1)(mod p)\\ t_2＝a(x_3-x_1) (mod p)\\ \end{array}\right. $$
将式5 $(x_3-x_1)$，式6 $(x_2-x_1)$，相减可得到：
$$t_1*(x_3-x_1)-t_2(x_2-x_1)=0\ (mod p)$$
这样我们即可求出kp，分解后得到p，根据式5求出a，再根据原式求出b
Exp:
from Crypto.Util.number import *
from functools import reduce
from gmpy2 import *
pts = [[9919887393477746178534175105516135467884408832173, 19958266120603700511875407508208280666242793356852],[3595522573583061314509664626455857557236490082950, 7844818469778389188067619619555050311084508661624],[19012115773786761225750188806634440613045262597955, 33081986637027085345095605616372809095234468671967],[34196017632168655637054726684559122319589088633467, 33150136169196868045901637529474922917121632432058]]
xx = []
yy = []
for pt in pts:
xx.append(pt[0] ** 3)
yy.append(pt[1] ** 2)
f = []
for x in range(len(pts)):
f.append(yy[x] - yy[0] - (xx[x] - xx[0]))
# print(f)
p = f[1] * (pts[2][0] - pts[0][0]) - f[2] * (pts[1][0] - pts[0][0])
p1 = f[3] * (pts[2][0] - pts[0][0]) - f[2] * (pts[3][0] - pts[0][0])
print(gcd(p,p1))
p = 35926127419138943502466980597080965242987634950823
print(p.bit_length())
assert isPrime(p)
inv = invert(pts[1][0] - pts[0][0], p)
a = (f[1] * inv) % p
print(a)
b = (yy[1] - xx[1] - a * pts[1][0]) % p
print(b)
Just need One
题目描述：
题目链接：nc 59.110.20.54:2613 One bullet to kill all Outlaws.
import os
import random
import string
import hashlib
flag = os.environ.get("FLAG", b"SYC{Al3XEI_FAKE_FLAG}")
DEBUG = False
banner = '|'*70
if DEBUG:
print("==DEBUG MODE==")
def proof_of_work():
if DEBUG:
return True
proof = ''.join([random.choice(string.ascii_letters+string.digits) for _ in range(20)])
digest = hashlib.sha256(proof.encode()).hexdigest()
print("sha256(XXXX+%s) == %s" % (proof[4:], digest))
x = input("Give me XXXX: ")
if len(x)!=4 or hashlib.sha256((x+proof[4:]).encode()).hexdigest() != digest:
return False
print("Right!")
return True
try:
if not proof_of_work():
exit()
print(banner)
parms = [random.getrandbits(32) for _ in range(128)]
res = res = int(input('Give me x calculating f(x) :\n> '))
if res >= 2**32:
print("Give me something smaller.\n")
print(banner+'\n')
exit()
cnt = 0
for _ in range(128):
cnt += pow(res,_)*parms[_]
print(cnt)
ans = input('Give me Coefficients :\n> ')
ans = [int(_) for _ in ans.split(",")]
if ans == parms:
print('Congrats! Your flag is:',flag)
else:
exit()
except Exception:
print("Something goes wrong...\n")
print(banner+'\n')
exit() 做题流程：
每一个随机数有32位，正常只需要x取2^32就能够使得每组系数互不干扰，组成一个$$\overline{a_0a_1a_2...a_n}$$的二进制数，但题目限制了。我们可以想到x传-2^32，将得到的结果取绝对值，效果是类似的，只是每个的奇次幂的最低位会少1，偶次幂的数要用2^32减去，这样我们就可以得到全部系数
由于懒得写交互，所以。。。
exp：
st = 2 ** 32
print(st)
f = 175110518470050214311252208588439497233859974965843301573501150665105370885160932732266664106894635769347686910638085239904480094492658846059636249060430246503662967313895029621524454404153167719468689989026081151299490589243124365354471312558228639710222850879091900838412736214856057475205489122589865518469465813833850258524613215593668851547025232903349052899457691500393609804421428126021357281586324058308332941103714584366378427332509333316091374742966486591321245048957767182630317606854985994814985728860404082674626469535091912244027690957063979237769162558978220671124629145227531716385828491939130328762969373260692120133304770046361957730804573737550194784956854802153210176261676477520184939283281851793173711909264376089655413313757049962215085196884638283727053130393809491633549317643797654799739907743650478878803810420222850065785495908199760719703304402447147992885462581136660381797268526563537319402991265099090205951380228863538262567329997046302680663223606385029584869529614437282799927770669536355795512010240094506162690330618811758684527784885432204861343484107321006464765901128403864624500882456479620901930927911105148561126202224552724777210945131303939541175114958582099164318448840447020045997403836
f = bin(f)
print(f)
s = str(f).replace('0b','00')
chunk_size = 64
chunks = [s[i:i + chunk_size] for i in range(0, len(s), chunk_size)]
a_list = []
for chunk in reversed(chunks):
c1 = chunk[:32]
c2 = chunk[32:]
t1 = int(c1, 2) + 1
t2 = st - int(c2, 2)
a_list.append(str(t2))
a_list.append(str(t1))
print(",".join(a_list))WEEK3
Diligent_Liszt
题目描述：
https://en.wikipedia.org/wiki/Discrete_logarithm
做题流程：
一眼p，q，r光滑，Pohlig–Hellman直接嗦(la佬脚本真好用）
def babystep_giantstep(g, y, p, q=None):
if q is None:
q = p - 1
m = int(q**0.5 + 0.5)
# Baby step
table = {}
gr = 1 # g^r
for r in range(m):
table[gr] = r
gr = (gr * g) % p
# Giant step
try:
gm = pow(g, -m, p) # gm = g^{-m}
except:
return None
ygqm = y # ygqm = y * g^{-qm}
for q in range(m):
if ygqm in table:
return q * m + table[ygqm]
ygqm = (ygqm * gm) % p
return None
# Pohlig–Hellman法
def pohlig_hellman_DLP(g, y, p):
crt_moduli = []
crt_remain = []
for q, _ in factor(p-1):
x = babystep_giantstep(pow(g,(p-1)//q,p), pow(y,(p-1)//q,p), p, q)
if (x is None) or (x <= 1):
continue
crt_moduli.append(q)
crt_remain.append(x)
x = crt(crt_remain, crt_moduli)
return x
g = 3
y = 5385116324746699759660077007129548063211490907227715474654765255668507958312745677683558789874078477569613259930365612562164095274660123330458355653249805062678976259429733060364358954180439218947514191603330532117142653558803034110759332447742304749985874760435453594107494324797235909651178472904825071375135846093354526936559640383917210702874692725723836865724807664892994298377375580807917514349966834376413176898806591411038129330967050554114677719107335006266
p = 1068910928091265978478887270179608140018534288604159452828300604294675735481804963679672853224192480667904101881092533866322948043654533322038484907159945421
x = pohlig_hellman_DLP(g, y, p)
print(long_to_bytes(x))
# print(pow(g, x, p) == y)Quick_Robert
题目描述：
nc 59.110.20.54:3042 https://en.wikipedia.org/wiki/Quadratic_residue
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Hi Crypto-ers! AL3XEI Here. In number theory, if there exists an integer q satisfying x^2=q(mod n), q is so called a quadratic residue.
We write this calculation as L(a,p), which its value shows a is or is not quadratic residue modulo p.
Below, you need to give me the answer of the sum of L(a*l**2+b*l+1,p), where a,b are integers, p is a prime, and l rise from 0 to p-1.
For example, given a = 2, b = 3, c = 1, p = 5, the answer will be
L(1, 5) + L(6, 5) + L(15, 5) + L(28, 5) + L(45, 5) = 1.
Hope you success!
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||做题流程：
更新前：
经过测试发现给的a，b，p满足a是二次剩余
$$a=t^2$$
所以满足完全平方式：
$$ax^2+bx+1=(tx+1)^2\ (mod\ p)$$
所以按理来说，题目答案应该都为0
题目有些小问题，传入答案和算出来不相符，这题全部传p-1即出
更新后：
$$ \begin{equation} L(a,p)=\left\{ \begin{aligned} 0 \quad a是模p下的某个因子\\ 1 \quad a是模p下的二次剩余\\ -1 \quad a是模p下二次非剩余\\ \end{aligned} \right . \end{equation} $$
会发现，L函数的求和结果仅与a是否是模p下的二次剩余有关。如果a是模p下的二次剩余，求和结果为-1；否则为1。以及更新前的那一种情况。
card_game
题目描述：
AL3XEI送给了你这个游戏的关键数据，你能预测接下来要出的牌吗 nc 59.110.20.54 4953
from Crypto.Util.number import *
from cards import Heart, Spade, Club, Diamond
from secret import flag
def choose_card(num):
x = (num>>5)%4
if x == 0:
return (Heart[(num>>6)%13]), 'Heart'
if x%4 == 1:
return (Spade[(num>>6)%13]), 'Spade'
if x%4 == 2:
return (Diamond[(num>>6)%13]), 'Diamond'
else:
return (Club[(num>>6)%13]), 'Club'
def GAME():
banner = '''
#### ## ##### ##### #### ## # # ######
# # # # # # # # # # # # ## ## #
# # # # # # # # # # # ## # #####
# ###### ##### # # # ### ###### # # #
# # # # # # # # # # # # # # #
#### # # # # ##### #### # # # # ######
'''
print(banner)
meum = '''option:
1: start game
2: get hint
3: exit
'''
print(meum)
while True:
print('input your option: ', end='')
your_input = input()
if your_input == '1':
n = getPrime(36)
m = getPrime(16)
c = getPrime(16)
seed = getPrime(36)
out = seed
round = 0
score = 0
res = []
while True:
round += 1
res = []
print(f'round:{round}')
print(f'score:{score}')
for i in range (3):
out = (out*m+c)%n
res.append(out)
if round == 1:
for i in res:
card, suit = choose_card(i)
print(card)
elif round==2 or round==3: #gift
for i in res:
card, suit = choose_card(i)
print(card)
print(f'gift: {res}')
else:
cards = []
suits = []
for i in range(len(res)):
card, suit = choose_card(res[i])
cards.append(card)
suits.append(suit)
print("Give me your guess: (example: Heart_1 Club_2 Diamond_3)")
try:
g_1, g_2, g_3 = input().split()
g_1, g_2, g_3 = g_1.split('_'), g_2.split('_'), g_3.split('_')
except ValueError:
print("Please enter in the correct format.")
return
if (g_1[0] == suits[0] and g_1[1] == cards[0][15]) and (g_2[0] == suits[1] and g_2[1] == cards[1][15]) and (g_3[0] == suits[2] and g_3[1] == cards[2][15]):
for i in cards:
print(i)
print("Congratulations! You matched the cards!")
score += 1
else:
for i in cards:
print(i)
print("Try again!")
if score == 50:
print('The flag is your reward!')
print(flag)
return
else:
continue
if your_input == '2':
print("Have you ever heard of LCG?")
if your_input == '3':
break
if __name__ == '__main__':
GAME()做题流程：
简单的lcg（靶机似乎检查不出10，所以就跑了100组找flag）
exp:
from pwn import *
from Crypto.Util.number import *
from gmpy2 import *
io = remote("59.110.20.54", 4953)
io.recv()
io.sendline(str(1).encode())
io.recvuntil(b'gift: ')
t = io.recvuntil(b']').decode().strip()
t = t[1:len(t) - 1]
x_list = t.split(', ')
# print(x_list)
x = []
for i in x_list:
xx = int(i)
x.append(xx)
io.recvuntil(b'gift: ')
t = io.recvuntil(b']').decode().strip()
t = t[1:len(t) - 1]
x_list = t.split(', ')
for i in range(len(x_list)):
xx = int(x_list[i])
x.append(xx)
x6 = int(x_list[2])
print(x)
t = []
for i in range(1, len(x)):
t.append(x[i] - x[i-1])
m = 0
for i in range(1, len(t)-1):
m = GCD(t[i+1]*t[i-1] - t[i]*t[i], m)
print(m)
assert isPrime(m)
a = (x[2] - x[1]) * inverse(x[1] - x[0], m)
b = (x[1] - a*x[0]) % m
# x.append(x6)
def choose_card(num):
x = (num>>5)%4
if x == 0:
return ((num>>6)%13 + 1), 'Heart'
if x%4 == 1:
return ((num>>6)%13 + 1), 'Spade'
if x%4 == 2:
return ((num>>6)%13 + 1), 'Diamond'
else:
return ((num>>6)%13 + 1), 'Club'
out = x6
print(out)
for i in range(100):
res = []
answer = []
for j in range(3):
out = (out * a + b) % m
res.append(out)
for j in res:
card, suit = choose_card(j)
if card >= 2 and card <= 10:
ans = suit + '_' + str(card)
if card == 1:
ans = suit + '_A'
if card == 11:
ans = suit + '_J'
if card == 12:
ans = suit + '_Q'
if card == 13:
ans = suit + '_K'
answer.append(ans)
ans = (' '.join(answer)).encode()
print(ans)
x = io.recv()
if b'flag' in x:
print(x)
sleep(0.1)
io.sendline(ans)
io.interactive()WEEK4
EzComplex
题目描述：
And u, my friend: Complex factors! (In a double sense)
#sage9.3
from Crypto.Util.number import *
flag = b'FAKE{Do_You_know_Complex_numbers}'
p = random_prime(1 << 384)
q = random_prime(1 << 384)
n = p * q
e = 0x10001
N = pow(p, 2) + pow(q, 2)
m = bytes_to_long(flag)
c = pow(m,e,n)
print(c)
print(N)
'''
122977267154486898127643454001467185956864368276013342450998567212966113302012584153291519651365278888605594000436279106907163024162771486315220072170917153855370362692990814276908399943293854077912175867886513964032241638851526276
973990451943921675425625260267293227445098713194663380695161260771362036776671793195525239267004528550439258233703798932349677698127549891815995206853756301593324349871567926792912475619794804691721625860861059975526781239293017498
'''做题流程：
题目给了$$p^2+q^2$$，发现这式子在复数域内可分解为$$(p+qi)(p-qi)$$于是我们可以将给出的数在复数域分解，得到p和q
exp：
from Crypto.Util.number import *
from gmpy2 import *
# N = 973990451943921675425625260267293227445098713194663380695161260771362036776671793195525239267004528550439258233703798932349677698127549891815995206853756301593324349871567926792912475619794804691721625860861059975526781239293017498
# f = ZZ[i](N)
# for i in divisors(f):
# if (i[0] ** 2 + i[1] ** 2 == N):
# p = abs(int(i[0]))
# q = abs(int(i[1]))
# if isPrime(p) and isPrime(q):
# n = i[0] * i[1]
# print(p)
# print(q)
# print(n)
p = 29962125885196559918101088622575501736433575381042696980660846307183241725227137854663856022170515177120773072848343
q = 8732781022306464325787401448517171026218291389436971731700810979177651389459896422549428444142746055523338740248707
n = p * q
e = 0x10001
c = 122977267154486898127643454001467185956864368276013342450998567212966113302012584153291519651365278888605594000436279106907163024162771486315220072170917153855370362692990814276908399943293854077912175867886513964032241638851526276
phi = (p - 1) * (q - 1)
d = invert(e, phi)
m = powmod(c, d, n)
print(long_to_bytes(m))ext^7gcd
题目描述：
题目链接：nc 59.110.20.54:1789 （下sagemath! 不下的统统发配到安东星当嘿奴！）
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Hi Crypto-ers! AL3XEI here. Solving extended gcd over 2 primes can be easy, but what about 7 primes?
primes : [938770989594038574883307091377, 731124780451059048515699872973, 705906522337130351303390881793, 1259253321424214851154594220511, 638192849150199238389371476021, 1160157641563492827848830377527, 1225294646722407790694425867847] ( 100 bits )
Give me a0,...a5,a6:做题流程：
题目大概意思是让$$\sum_{i=1}^7 a[i]p[i]$$的和为1，我们直接用两数做exgcd，让后面的和为0即可
exp：
p = [5902710342749394849998943371028129845573814056445154853443, 4636015201465011031253453796366492861048284694454948943011, 4002400072383962140402233513848277026571627310391097106009, 5300996721183835725509763065691627002815254108296157953417, 6076354674723684660152317912448324904347788150826788336229, 4066402285311826559568946174406730844378217729090270993737, 4206730190819808557122468467946725462023809374891116910767]
a = [0] * 7
u, d, v = xgcd(p[0], p[1])
a[0] = d
a[1] = v
for i in range(2,len(p) - 1):
a[i + 1] += p[i]
a[i] -= p[i + 1]
t = 0
for i in range(len(p)):
t += a[i] * p[i]
print(t)
ans = ''
for i in a:
ans = ans + str(i) +','
print(ans)Algebra （复现）
题目描述：
Recently jrl888 has learned something about groebner_basis.But could U plz help him to sovle his linear algebra homework?
#utf-8
#sage
import os
from Crypto.Util.number import *
from Crypto.Util.Padding import pad
from secret import flag,e
from functools import reduce
assert reduce(lambda x,y:x&y,[i^3 - 10*i^2 + 31*i - 30==0 for i in e])
LEN = 32
flag = pad(flag,36)
def LongArray(t:list):
return [bytes_to_long(t[i]) for i in range(len(t))]
def BytesArray(t:list):
return [long_to_bytes(t[i]) for i in range(len(t))]
def xor(a, b):
return bytes([a[i%len(a)] ^^ b[i%len(b)] for i in range(max(len(a), len(b)))])
def ArrayXor(a:list,b:bytes):
return [xor(a[i],b) for i in range(len(a))]
def scissors(flag:bytes):
return [flag[i:i+len(flag)//3] for i in range(0, len(flag), len(flag)//3)]
def challenge(m: bytes, bits: int, level: int):
p = getPrime(bits)
M = random_matrix(Zmod(p), LEN).matrix_from_rows_and_columns(range(LEN), range(LEN-level))
c = vector(GF(p), m) * M
return {"p": p, "M": M.list(), "c": c.list()}
def groebner_challenge(m,e):
p = getPrime(1024)
s = sum(m)
c = [pow(m[i],e[i],p) for i in range(3)]
c.insert(0,s)
c.insert(0,p)
return c
key = os.urandom(LEN)
Get_key = challenge(key,256,0x10)
S_bytes = scissors(flag)
C_bytes = ArrayXor(S_bytes,key)
C_long = LongArray(C_bytes)
groebner_challenge = groebner_challenge(C_long,e)
with open('keyTask.chall', 'w') as f:
f.write(f"{Get_key}")
with open('groebnerTask.chall','w') as f:
f.write(f"{groebner_challenge}")做题流程：
题目可以分为两部分，第一部分为解challenge函数获得key，第二部分则为解gorebner_challenge函数得到c_long，然后将两者xor即可
第一部分：
key对应的m向量是按字节拆分的，所以都是小量，可以通过构造格来规约出key
$m=(k_1,k_2,...,k_{32})$
$$ M=\left(\begin{matrix} M_{1,1}&M_{1,2}&...&M_{1,16}\\ M_{2,1}&M_{2,2}&...&M_{2,16}\\ &&...\\ M_{31,1}&M_{31,2}&...&M_{31,16}\\ M_{32,1}&M_{32,2}&...&M_{32,16} \end{matrix}\right) $$
$m*M=c\ (mod\ p)$
$M$和$c$都是已知量，我们要得到$m$，我们想要构造出格，首先得需要将这条等式抽取出线性方程出来
我们可以得到（总共16条）：
$M_{1,i}*k_1+M_{2,i}*k_2+...+M_{31,i}*k_{31}+M_{32,i}*k_{32}=c_i\ (mod\ p)$
我们可以构造出这么一个格（在其他师傅的帮助下）
$$ L=\left(\begin{matrix} M_{1,1}&M_{1,2}&...&M_{1,16}&1&0&...&0&0\\ M_{2,1}&M_{2,2}&...&M_{2,16}&0&1&...&0&0\\ &&...\\ M_{31,1}&M_{31,2}&...&M_{31,16}&0&0&...&1&0\\ M_{32,1}&M_{32,2}&...&M_{32,16}&0&0&...&0&1\\ p&0&...&0&0&0&...&0&0\\ 0&p&...&0&0&0&...&0&0\\ &&...\\ 0&0&...&p&0&0&...&0&0\\ c_1&c_2&...&c_{32}&0&0&...&0&0 \end{matrix}\right) $$
满足：
$(k_1,k_2,...,k_{32},k_{1mod},k_{2mod},...k_{16mod},-1)L=(0,0,...,0,k_1,k_2,...,k_{32})$
所以我们就可以得到key
第二部分：
首先需要求得e，e的约束条件为：${e_i}^3-10*{e_i}^2+31*{e_i}-30=0$
我们可以用roots函数直接解就可以解出e的值
$e=[2,3,5]$
groebner_challenge即为：
$$ {m_0}^{e_0}\equiv c_0\ (mod\ p)\\ {m_1}^{e_1}\equiv c_1\ (mod\ p)\\ {m_2}^{e_2}\equiv c_2\ (mod\ p)\\ s=m_1+m_2+m_3 $$
所以我们可以根据groebner将$m_0,m_1,m_2$求出
然后将得到的m与key异或即可得到flag
exp：
from Crypto.Util.number import *
def BytesArray(t:list):
return [long_to_bytes(t[i]) for i in range(len(t))]
def xor(a, b):
return bytes([a[i%len(a)] ^^ b[i%len(b)] for i in range(max(len(a), len(b)))])
def ArrayXor(a:list,b:bytes):
return [xor(a[i],b) for i in range(len(a))]
p = 76231309481023608274751321361920497941621991893430257210800219032855778863403
m = [16697564195803960524955618666471317999653475911677692593955332155554421639339, 24805565422829448264880670396335760401288936419812226622903667065319545007990, 30402002570955975554182190550978255206265920770702396357369433463733972557272, 18233447181850080393551606050467637029754113002670714480589747787334593064733, 592902654848011644470609316176765466448791324270572419003746985532591397159, 38141098394328701291718984482265005575605052524114181112646883764482370463339, 19538035520885458475321686600845898258764219979337957736187681124215270558985, 20238271906530455379759697476409410947082642723781332031138364999846953950236, 68589425835163943859976893853743850381901810189392551426919445548155584771402, 69125498641336015332539393144100425718253100049458707350849969745083544909112, 13083949682120928694566559154939525096970647194043481405708057328879273858093, 23203059113121714797053512829874540997525934591781746540284169378085299649376, 22946531388117317614240915936458387347604741596963582908127101794515625023753, 55979468873975052067342467012297454154725653733173077039679834697623008679331, 30639339327762413454972420838209328855396759486202041356245020097084204753692, 72148374844384373140537647811727349763363643424440303708852930034097897492230, 70510577909447876165042155961990008987054640378802283966455273008397938569580, 7816397571019557637378232515822996961951657038149768517938709736489000871357, 71385034180207364002198196251789729137138388141957414602914243475029669555970, 23879618498527644070533133010929524881849183976915843192427726963620597127184, 17735043770749200859447594711305199064407694651519169622831117483831984480389, 23976962869545273044554865578229826802425540170337686767966000016386989130328, 4813526999083764015441613591159575786598306005687621653546973702651642297987, 35706013043056210868734160987149285571667410945166974218110532901324694790051, 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25506065854504640436633838443529482237490038072404045113454162320518595298079, 24598282043408933159434555506241937793897636834036366695267201954251938064858, 40359136257256317951754486181700633715943232386029795075349229741392377893448, 41753903921049595397751509756734177717249754689414242359419638438895614782681, 64879894430542426137516569367284410206800804149311771326329785080288758261071, 31682887186457559477375016497207344351697184042518871050776477362607703713335, 29968228072586790097820746477232816665998277976293252190030364133538849649097, 332255312561919030611963580501150855624827653577824313728984209608512608771, 33823033061488824234179656069812811550521458222627846709618871103804433549208, 40256197078476374288168370733269644672544776862251441956395184831531034573120, 63854791069720406920587264743813005867085205938858782942089091387745143688524, 9599189722183226358779095857498561886058642596617187395926371060462688656609, 15029540387621509138061041056904048961380890903724088755367710335622982174182, 4834678835879134834601247929812861614226805889003245637987605009945117449222, 49032287443959922585421022539339859727864184118407327061056787486660050994804, 51367113126213677371544088617641070281761594598856355289598680348862100934405, 48099687480283705985883062779219537419919474724954533559850612088090057306918, 55520602086715679118869322729503627581286641464273224324645023518549139088388, 50455510074969331802134040882996226109444134111548070407754215749016079079591, 47469806992474607142964806583892893209350327489840529459975202523406918697529, 44993893961585674228825543823064277790256859558754760867449903789983284056192, 44122596973664102569554815809415734634633243724572865236160697307096168452789, 51722296980185400816766674111348260571814278086142919892660507537043249830719, 2033567717312718757627805714157011922823676173550156447506958538133031286918, 40903326746018205875236484413558515226676475499740080681613680228360211918942, 45655754955370338497959237080418596437202658977517625068449957735452901887933, 13099233879696255324623677988804870917874154288631096861534955732046228968134, 44471530296771048523910819473361036714610802054279177471367823293743719275909, 25446261500563608722277325170677124816913924327250182158338980791838121166348, 20849472122256100875237011040249343324234928290319054354358242725759352931027, 7037043514495750961085179755568922433574397862705004833537643401449768094927, 24602719773333598554726432771595598259193579434836329001621386950000691219145, 18291650246498286332477867018368277382676465438496649012143967117655345637528, 45539989423554662584586894487111357151994014405213908150771179299468367899190, 48070107064454632531764035109162049005752680792201710661207400175358438021031, 7593113852866099746235678251926660680184416554718335029164595384991677535670, 61267284459965876196585417165926198770265833151343328469624242730879803451439, 3113616736283221407577816039505851478576505404761990976205583322559028256017, 29330053766980680089057055489775792668017015563299551837945432855633479513403, 38650331327684731179494096039889807053556745918527992295694445248090022667695, 11185985969572649911287822641562854469066291745462641774733857682450748347757, 6571676849591061846860086681136363771968700745359806059302040914080951597505, 47756994940258770519162165424758057472757403664170491681038228297319879170179, 32594475773547428735290676052531964976552484974356093150173758902449423156454, 31898634435507821969130133343503506337057311382300091683049093677942058183477, 8353498532203907327130477695937160917023156103120835230016413595452591896676, 72216190258743114705738161722736218780580609507689664769226245468683927077534, 70887162563386966001868090323354098874355491350818633411742235015483133077695, 53428119825008762677728594318441425057537661648075595012957502970943136262892, 32863943200860906581953022085708385110199346863351756782360531422328330178353, 69608025594463019257125425333532340909708104310858865262120126307135308366029, 33452066316790958427311031033544525015058584636612574435078141485268045480510, 67467748971757982782108778816344194052265871654600993221694391564870705065723, 4109223118757802968784775933084268418756424413308874230869847907255969302298, 874689888905623826173288368495929100158181002920189916388429819486644481023, 72378176399887630170201236756088580064855288788646391253391062547296108569964]
c = [53988415223839046381660672886792550892557190087087742629543368068682997090947, 21920921577840820689544269317401273370645213368453408007695580910149937697350, 29475771140129436159914858194223947593631108556842828359576509962355002130884, 31590148131791243731394919647376320328981021184223344832519185603844396786591, 40158574856962337545114912732379830254905090560850444592715018068912713975950, 50202503631530908716292345385552528345477433154392551391113477385703155787943, 25774597836388201526898377602793037428257024917440689218589384298072305574879, 63699495213620446235153554941891496976361246452059711453175708378318694602997, 20163212118036162236820095294493608896188807674678722559179017053183514140545, 19274318563716163915370869155502529679348083562418954598176006625003116718683, 61195117146757818795182876923087120232550209256816533077870026077903026793552, 64135143979846412750088422623420891325395709280682206900910074454563319174684, 21787908653560434902963868824798375507100016805476198412260169885990367978999, 8441422610194193525495290892888645173453076691768846248230542826479457290786, 24175440953264371229111128918926940451898832762196824660170198350642339016663, 59119734184764887826210301129920567765450070009167528626807613085641307427339]
M = matrix(ZZ, 32, 16, m)
E = diagonal_matrix([1] * 32)
P = diagonal_matrix([p] * 16)
C = matrix(ZZ, c)
L = block_matrix(ZZ, [[M,E], [P,0], [C,0]])
key = list(L.LLL()[1][16:])
for i in range(len(key)):
key[i] = abs(key[i])
key = bytes(key)
PR.<i> = PolynomialRing(ZZ)
f = i ^ 3 - 10 * i ^ 2 + 31 * i - 30
e = [i[0] for i in f.roots()]
grob = [175336555462486363373099551411803174933803940918372428249159666803182759268063415863987676455854054651631174131625763475189413468427467197699058719725221879406119373683175842618465694427132003565774900609456204965408254598477034791500576573579131820364396996254469692964946065509325801687720344376041097328929, 192597139210277682598060185912821582569043452465684540030278464832244948354365, 5415723658972576382153559473862560277755192970021711034483296770242757614573901416501357332661976379693731699836578087114136761491831672836130172409491889, 210713951733721296094981135225517096332793112439184310028590576805069783972692891743044656754643189870169698041576462365740899368554671164493356650858567594970345928936103914826926922045852943068526737627918609421198466329605091625, 93558120697660628972553751937347865465963385519812302371069578286123647411810258547153399045605149278436900736665388355004346922404097196048139360206875149390218160164739477798859206611473675859708579299466581718543909912951088772842957187413726251892347470983848602814387339449340072310561011153714207338630]
p, s, c = grob[0], grob[1], grob[2:]
PR.<x1, x2, x3> = PolynomialRing(Zmod(p))
f1 = x1 ^ e[2] - c[0]
f2 = x2 ^ e[1] - c[1]
f3 = x3 ^ e[0] - c[2]
f4 = x1 + x2 + x3 - s
f = [f1, f2, f3, f4]
res = Ideal(f).groebner_basis()
point = {x1: 1, x2: 2, x3: 3}
c_long= [poly.subs(point) for poly in res]
for i in range(3):
c_long[i] = int(p - c_long[i])
c_bytes = BytesArray(c_long)
S_bytes = ArrayXor(c_bytes, key)
flag = [i[:12].decode() for i in S_bytes]
print(''.join(flag))