barak
P = (71451574057642615329217496196104648829170714086074852, 69505051165402823276701818777271117086632959198597714,1)
Q = (40867727924496334272422180051448163594354522440089644, 56052452825146620306694006054673427761687498088402245,1)
from Crypto.Util.number import *
import gmpy2
from tqdm import tqdm
p = 73997272456239171124655017039956026551127725934222347
d = 68212800478915688445169020404812347140341674954375635
c = 1
E = (c, d, p)
PR.<x,y,z> = Zmod(p)[]
cubic = x**3 - d*x*y*z + z^3 + y^3
E = EllipticCurve_from_cubic(cubic, P, morphism=True)
#
PP = E(P)
QQ = E(Q)
#
# m = discrete_log(QQ,PP,operation = "+")
# print(m)
m = 1780694557271320552511299360138314441283923223949197
print(long_to_bytes(m))
for i in tqdm(range(1000000)):
M = m + i*int(PP.order())
if all(30<j<125 for j in long_to_bytes(M)):
print(long_to_bytes(M))
# break
print("Finished")
blue_office
import binascii
from Crypto.Util.number import *
import gmpy2
from tqdm import tqdm
enc = b'b0cb631639f8a5ab20ff7385926383f89a71bbc4ed2d57142e05f39d434fce'
enc = int(enc,16)
def dereseed(s):
return (s-2531011)//214013
# print(long_to_bytes(enc)[0])
S = bytes_to_long(b'C') ^ long_to_bytes(enc)[0]
print(long_to_bytes(enc)[0])
print(0xb0)
def reseed(s):
return s * 214013 + 2531011
for i in tqdm(range(2**16)):
s = (S<<16) + i
k = []
k.append(s)
for x in range(30):
s = reseed(s)
k.append(s)
m = b'C'
# if (long_to_bytes(enc)[2] ^ ((k[1] >> 16) & 0xff)).to_bytes(1, 'big') == b'C':
# print(i)
for j in range(len(long_to_bytes(enc))):
m += (long_to_bytes(enc)[j] ^ ((k[j] >> 16) & 0xff)).to_bytes(1, 'big')
if b'CCTF' in m:
print(m)
Derik
from Crypto.Util.number import *
import gmpy2
from z3 import *
C = [5960650533801939766973431801711817334521794480800845853788489396583576739362531091881299990317357532712965991685855356736023156123272639095501827949743772, 6521307334196962312588683933194431457121496634106944587943458360009084052009954473233805656430247044180398241991916007097053259167347016989949709567530079, 1974144590530162761749719653512492399674271448426179161347522113979158665904709425021321314572814344781742306475435350045259668002944094011342611452228289, 2613994669316609213059728351496129310385706729636898358367479603483933513667486946164472738443484347294444234222189837370548518512002145671578950835894451, 8127380985210701021743355783483366664759506587061015828343032669060653534242331741280215982865084745259496501567264419306697788067646135512747952351628613, 5610271406291656026350079703507496574797593266125358942992954619413518379131260031910808827754539354830563482514244310277292686031300804846114623378588204, 10543, 4]
c = 80607532565510116966388633842290576008441185412513199071132245517888982730482694498575603226192340250444218146275844981580541820190393565327655055810841864715587561905777565790204415381897361016717820490400344469662479972681922265843907711283466105388820804099348169127917445858990935539611525002789966360469324052731259957798534960845391898385316664884009395500706952606508518095360995300436595374193777531503846662413864377535617876584843281151030183895735511854
O = [1391526622949983, 2848691279889518, 89200900157319, 31337]
e = 3
d = (C[6]*e - O[3])//C[7]
print(d)
S = gmpy2.gcdext(C[1],C[2])
Solve = Solver()
p,q,r = Reals('p q r')
Solve.add(C[0]*p - C[1]*q == O[0])
Solve.add(C[2]*q - C[3]*r == O[1])
Solve.add(C[4]*r - C[5]*p == O[2])
Solve.check()
a = Solve.model()
print(a)
q = 8919642442779618620315315582249815126044061421894622037450496385178083791083142991676417756698881509754110765444929271564991855378540939292428839562446571
r = 6736304432663651651650099104581016800112378771266600017972326085742513966258250417227421932482058281545032658577816441378170466639375931780967727070265551
p = 9758621034843917661145412977193922808892309951663464821517963113005483457886774294910761723767526582514514505278091600074371768233672585649562672245905811
n = e*d*q*p*r
phi = (e-1)*(q-1)*(p-1)*(r-1)*(d-1)
D = gmpy2.invert(65537,phi)
print(long_to_bytes(gmpy2.powmod(c,D,n)))
DId it!
from pwn import *
from random import randint
import sys
# context.log_level = 'Debug'
while True:
c = remote('01.cr.yp.toc.tf',11337)
c.recvuntil(b'++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++')
c.recvuntil(b'+ .:: Hi all, she DID it, you should do it too! Are you ready? ::. +')
c.recvuntil(b'++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++')
n, l = 127, 20
cnt, STEP = 0, 2 * n // l - 1
m = []
for i in range(11):
k = ','.join(str((20*i + j)%n) for j in range(20)).encode()
k1 = eval(k)
# print(k)
c.sendline(k)
c.recvuntil(b'+ DID = ')
x = c.recvuntil(b'\n')[:-1]
x = eval(x)
# print(x)
for j in range(20):
if pow(int(k1[j]),2,n) not in x and pow(int(k1[j]),2,n)+1 not in x:
if k1[j] not in m:
m.append(int(k1[j]))
# print(m)
if len(m) == 20:
a = ','.join(str(l) for l in m)
c.sendline(a.encode())
c.interactive()
print(len(m),m)
c.close()
Insights
from Crypto.Util.number import *
import gmpy2
import sympy
import time
############################################
# Config
##########################################
"""
Setting debug to true will display more informations
about the lattice, the bounds, the vectors...
"""
debug = True
"""
Setting strict to true will stop the algorithm (and
return (-1, -1)) if we don't have a correct
upperbound on the determinant. Note that this
doesn't necesseraly mean that no solutions
will be found since the theoretical upperbound is
usualy far away from actual results. That is why
you should probably use `strict = False`
"""
strict = False
"""
This is experimental, but has provided remarkable results
so far. It tries to reduce the lattice as much as it can
while keeping its efficiency. I see no reason not to use
this option, but if things don't work, you should try
disabling it
"""
helpful_only = True
dimension_min = 7 # stop removing if lattice reaches that dimension
############################################
# Functions
##########################################
# display stats on helpful vectors
def helpful_vectors(BB, modulus):
nothelpful = 0
for ii in range(BB.dimensions()[0]):
if BB[ii, ii] >= modulus:
nothelpful += 1
print(nothelpful, "/", BB.dimensions()[0], " vectors are not helpful")
# display matrix picture with 0 and X
def matrix_overview(BB, bound):
for ii in range(BB.dimensions()[0]):
a = ('%02d ' % ii)
for jj in range(BB.dimensions()[1]):
a += '0' if BB[ii, jj] == 0 else 'X'
if BB.dimensions()[0] < 60:
a += ' '
if BB[ii, ii] >= bound:
a += '~'
print(a)
# tries to remove unhelpful vectors
# we start at current = n-1 (last vector)
def remove_unhelpful(BB, monomials, bound, current):
# end of our recursive function
if current == -1 or BB.dimensions()[0] <= dimension_min:
return BB
# we start by checking from the end
for ii in range(current, -1, -1):
# if it is unhelpful:
if BB[ii, ii] >= bound:
affected_vectors = 0
affected_vector_index = 0
# let's check if it affects other vectors
for jj in range(ii + 1, BB.dimensions()[0]):
# if another vector is affected:
# we increase the count
if BB[jj, ii] != 0:
affected_vectors += 1
affected_vector_index = jj
# level:0
# if no other vectors end up affected
# we remove it
if affected_vectors == 0:
print("* removing unhelpful vector", ii)
BB = BB.delete_columns([ii])
BB = BB.delete_rows([ii])
monomials.pop(ii)
BB = remove_unhelpful(BB, monomials, bound, ii - 1)
return BB
# level:1
# if just one was affected we check
# if it is affecting someone else
elif affected_vectors == 1:
affected_deeper = True
for kk in range(affected_vector_index + 1, BB.dimensions()[0]):
# if it is affecting even one vector
# we give up on this one
if BB[kk, affected_vector_index] != 0:
affected_deeper = False
# remove both it if no other vector was affected and
# this helpful vector is not helpful enough
# compared to our unhelpful one
if affected_deeper and abs(bound - BB[affected_vector_index, affected_vector_index]) < abs(
bound - BB[ii, ii]):
print("* removing unhelpful vectors", ii, "and", affected_vector_index)
BB = BB.delete_columns([affected_vector_index, ii])
BB = BB.delete_rows([affected_vector_index, ii])
monomials.pop(affected_vector_index)
monomials.pop(ii)
BB = remove_unhelpful(BB, monomials, bound, ii - 1)
return BB
# nothing happened
return BB
"""
Returns:
* 0,0 if it fails
* -1,-1 if `strict=true`, and determinant doesn't bound
* x0,y0 the solutions of `pol`
"""
def boneh_durfee(pol, modulus, mm, tt, XX, YY):
"""
Boneh and Durfee revisited by Herrmann and May
finds a solution if:
* d < N^delta
* |x| < e^delta
* |y| < e^0.5
whenever delta < 1 - sqrt(2)/2 ~ 0.292
"""
# substitution (Herrman and May)
PR.<u, x, y> = PolynomialRing(ZZ)
Q = PR.quotient(x * y + 1 - u) # u = xy + 1
polZ = Q(pol).lift()
UU = XX * YY + 1
# x-shifts
gg = []
for kk in range(mm + 1):
for ii in range(mm - kk + 1):
xshift = x ^ ii * modulus ^ (mm - kk) * polZ(u, x, y) ^ kk
gg.append(xshift)
gg.sort()
# x-shifts list of monomials
monomials = []
for polynomial in gg:
for monomial in polynomial.monomials():
if monomial not in monomials:
monomials.append(monomial)
monomials.sort()
# y-shifts (selected by Herrman and May)
for jj in range(1, tt + 1):
for kk in range(floor(mm / tt) * jj, mm + 1):
yshift = y ^ jj * polZ(u, x, y) ^ kk * modulus ^ (mm - kk)
yshift = Q(yshift).lift()
gg.append(yshift) # substitution
# y-shifts list of monomials
for jj in range(1, tt + 1):
for kk in range(floor(mm / tt) * jj, mm + 1):
monomials.append(u ^ kk * y ^ jj)
# construct lattice B
nn = len(monomials)
BB = Matrix(ZZ, nn)
for ii in range(nn):
BB[ii, 0] = gg[ii](0, 0, 0)
for jj in range(1, ii + 1):
if monomials[jj] in gg[ii].monomials():
BB[ii, jj] = gg[ii].monomial_coefficient(monomials[jj]) * monomials[jj](UU, XX, YY)
# Prototype to reduce the lattice
if helpful_only:
# automatically remove
BB = remove_unhelpful(BB, monomials, modulus ^ mm, nn - 1)
# reset dimension
nn = BB.dimensions()[0]
if nn == 0:
print("failure")
return 0, 0
# check if vectors are helpful
if debug:
helpful_vectors(BB, modulus ^ mm)
# check if determinant is correctly bounded
det = BB.det()
bound = modulus ^ (mm * nn)
if det >= bound:
print("We do not have det < bound. Solutions might not be found.")
print("Try with highers m and t.")
if debug:
diff = (log(det) - log(bound)) / log(2)
print("size det(L) - size e^(m*n) = ", floor(diff))
if strict:
return -1, -1
else:
print("det(L) < e^(m*n) (good! If a solution exists < N^delta, it will be found)")
# display the lattice basis
if debug:
matrix_overview(BB, modulus ^ mm)
# LLL
if debug:
print("optimizing basis of the lattice via LLL, this can take a long time")
BB = BB.LLL()
if debug:
print("LLL is done!")
# transform vector i & j -> polynomials 1 & 2
if debug:
print("looking for independent vectors in the lattice")
found_polynomials = False
for pol1_idx in range(nn - 1):
for pol2_idx in range(pol1_idx + 1, nn):
# for i and j, create the two polynomials
PR.<w, z> = PolynomialRing(ZZ)
pol1 = pol2 = 0
for jj in range(nn):
pol1 += monomials[jj](w * z + 1, w, z) * BB[pol1_idx, jj] / monomials[jj](UU, XX, YY)
pol2 += monomials[jj](w * z + 1, w, z) * BB[pol2_idx, jj] / monomials[jj](UU, XX, YY)
# resultant
PR.<q> = PolynomialRing(ZZ)
rr = pol1.resultant(pol2)
# are these good polynomials?
if rr.is_zero() or rr.monomials() == [1]:
continue
else:
print("found them, using vectors", pol1_idx, "and", pol2_idx)
found_polynomials = True
break
if found_polynomials:
break
if not found_polynomials:
print("no independant vectors could be found. This should very rarely happen...")
return 0, 0
rr = rr(q, q)
# solutions
soly = rr.roots()
if len(soly) == 0:
print("Your prediction (delta) is too small")
return 0, 0
soly = soly[0][0]
ss = pol1(q, soly)
solx = ss.roots()[0][0]
#
return solx, soly
def example():
############################################
# How To Use This Script
##########################################
#
# The problem to solve (edit the following values)
#
# the modulus
N = 12765231982257032754070342601068819788671760506321816381988340379929052646067454855779362773785313297204165444163623633335057895252608396010414744222572161530653104640020689896882490979790275711854268113058363186249545193245142912930804650114934761299016468156185416083682476142929968501395899099376750415294540156026131156551291971922076435528869024742993840057342092865203064721826362149723366381892539617642364692012936270150691803063945919154346756726869466855557344213050973081755499746750276623648407677639812809665472258655462846021403503851719008687214848550916999977775070011121527941755954255781343103086789
# the public exponent
e = 459650454686946706615371845737527916539205656667844780634386049268800615782964920944229084502752167395446158290854047696006034750210758341744841762479191173017773034647739346927390580848998121830029134542880713409306092967282675122699586503684943407535067216738556403169403622104762516293879994387324370835718056251706150557820106296417750402984941838652433642298378976899556042987560946508887315484380807248331504458640857234708123277403252632993828101306072382329879857946191508782246793011691530554606521701055094223574951862129713872918021549814674387049788995785872980320871421550616327471735316980754238323013
# the hypothesis on the private exponent (the theoretical maximum is 0.292)
delta = .291 # this means that d < N^delta
#
# Lattice (tweak those values)
#
# you should tweak this (after a first run), (e.g. increment it until a solution is found)
m = 6 # size of the lattice (bigger the better/slower)
# you need to be a lattice master to tweak these
t = int((1-2*delta) * m) # optimization from Herrmann and May
X = 2*floor(N^delta) # this _might_ be too much
Y = 1<<(1024 - 71) # correct if p, q are ~ same size
#
# Don't touch anything below
#
# Problem put in equation
P.<x,y> = PolynomialRing(ZZ)
pbar = int('10100000111001001100001011000110111010001101001011000110110000101101100',2)<<(1024-71)
A = int((N+1-2*pbar)/2)
pol = 1 + x * (A + y)
#
# Find the solutions!
#
# Checking bounds
if debug:
print("=== checking values ===")
print("* delta:", delta)
print("* delta < 0.292", delta < 0.292)
print("* size of e:", int(log(e)/log(2)))
print("* size of N:", int(log(N)/log(2)))
print("* m:", m, ", t:", t)
# boneh_durfee
if debug:
print("=== running algorithm ===")
start_time = time.time()
solx, soly = boneh_durfee(pol, e, m, t, X, Y)
# found a solution?
if solx > 0:
print("=== solution found ===")
if False:
print("x:", solx)
print("y:", soly)
d = int(pol(solx, soly) / e)
print("private key found:", d)
c = 10992248752412909788626396175372747713079469256270100576886987393986576680666320383209810005318254336440105142571546847427454822405793626080251363454531982746373841267986148332456716023293306870382809568309620264499225135226626560298741596462262513921032733814032790312163314776421380481083058518893602887082464123177575742160690315666730642727773288362853901330620841098230284739614618790097180848133698381487679399364400048499041582830157094876815030301231505774900176910650887780842536610942820066913075027528705150102760422836458745949063992228680293226303245265232017738712226154128654682937687199768621565945171
m = pow(c,d,N)
print("message found:", long_to_bytes(int(m)))
else:
print("=== no solution was found ===")
if debug:
print("=== %s seconds ===" % (time.time() - start_time))
if __name__ == "__main__":
example()
Reduction
from Crypto.Util.number import *
import gmpy2
from tqdm import tqdm
PKEY = 14192646310719975031517528381795548241077678859071194396837281472399230674325587198691913743313024193030641258581477544395982020385534616950314446352119543012689979705497443206671093873748633162188213109347667494028713308821945628880987033909436936504594085029207071182583896573425433818693447573712242776054326253393149643818428222532313129014785625379928796322492111783102063504659053965652092334907431265629283336869752591405010801363428649651892548988084920295512198406822149854508798413366425646089176325412867633899847841343293434518769693835679828109184625256833518392375615524221729773443578746961887429674099018040291053535429314874943299587513900900515776980848746070077651676814430155460898107362207677739452859298842563030631706907437662807884529549746843462830493900480079096937402325307522965877069080418178692616875205678928420840955518031258855869218152431304423803589723140983606576549207164114711076498723237274262054605174412193097533550076687418481230734706280737017543741247718967059747548710091320650704988384742281590019869955579949961574733610565593105027342454880292474482792325237942870408329807427182014062811782475262070063065860763705715879581562335668163076088547827008755841277828137570366416095778
enc = 93313196155732054514477836642637636744872135106456047659057794344503071105783322399713135615723000054324693644981340568454628360027598469597864407205974007198804288563284521413279406211756674451582156555173212403946908121125010635246043311803494356106191509999360722019559999844621905376368824621365540442906142224342650371557766313381899279520110833822291649001754956653102495882094754863493058001964760438040783400782352466943990226083197340594364084294954324101604417550048379969516185353765224920719355485680872367930581872987972421836853197205534334204586713387469939986387582911728909524428102693874671302382
# print(str(bin(PKEY))[2:2042])
N_ = int(str(bin(PKEY))[2:2042],2)
E_ = int(str(bin(PKEY))[2042:],2)
print(N_)
# print(E_)
def rational_to_quotients(x, y):
a = x // y
quotients = [a]
while a * y != x:
x, y = y, x - a * y
a = x // y
quotients.append(a)
return quotients
def convergents_from_quotients(quotients):
convergents = [(quotients[0], 1)]
for i in range(2, len(quotients) + 1):
quotients_partion = quotients[0:i]
denom = quotients_partion[-1] # 分母
num = 1
for _ in range(-2, -len(quotients_partion), -1):
num, denom = denom, quotients_partion[_] * denom + num
num += denom * quotients_partion[0]
convergents.append((num, denom))
return convergents
def WienerAttack(e, n):
quotients = rational_to_quotients(e, n)
convergents = convergents_from_quotients(quotients)
for (k, d) in convergents:
if k and not (e * d - 1) % k:
phi = (e * d - 1) // k
# check if (x^2 - coef * x + n = 0) has integer roots
coef = n - phi + 1
delta = coef * coef - 4 * n
if delta > 0 and gmpy2.iroot(delta, 2)[1] == True:
print('d = ' + str(d))
return d
# num = []
# for i in range(256):
# for j in sieve_base:
# if ((N_<<8) + i) % j == 0:
# break
# else:
# num.append((N_<<8) + i)
# print(len(num))
#
# con,k = [],[]
# for j in tqdm(range(256)):
# for i in num:
# N = i
# E = (E_<<8) + j
# d = WienerAttack(E,N)
# # print(d)
# if d != None:
# k.append(N)
# k.append(E)
# k.append(d)
# con.append(k)
# # print(con)
# print(con)
N = 28781418259071163834545208786492597316357138268450456443121779857237190669654679502925616925907115061139426651454246296829614929839091896732956124186768298711851015827257060255218333952539548249210858753648965921585289379414151961197198777686222970660319202167442420274437451557166736926361972983650143650097981777542950972139757680517744639660898696901009088978971506526002932830312595664154921938706240176536981793499426543601513874115451315768319593051858239793153849410530285884330866972048864103208648273010126369559341912163849839663249252300813799486995834473605326584986843653735963725697383056972744506296271
E = 19152712448778858582528734875468196678366984818842265525346340114296810907435357813959451387293270496095878944786775775749129832803842508074794234774568097809721690831345120778762600713106116293626590641716601095020202233532544196547654794913903350183891867544539554967347396716482565232986995497267273877597593761608770699282404807896050347585632153075234094034163801474316224123620090879021107631960008144066862084573910442635526649884938724881478713853362879412453150893601267748827792136092224063120914443976032390554506925020506643629449426005820918745312311984391868895996772772355715765028825561022860823765675
d = 10254340117704573547
for i in range(256):
C = (enc<<8) + i
m = pow(C,d,N)
if m.bit_length()<800:
print(long_to_bytes(m))
RISK
from Crypto.Util.number import *
import gmpy2
import requests
import time
import random
import math
pkey = (150953688, 373824666550208932851344358703053061405262438259996622188837935528607451817812480600479188884096072016823491996056842120586016323642383543231913508464973502962030059403443181467594283936168384790367731793997013711256520780338341018619858240958105689126133812557401122953030695509876185592917323138313818881164334490044163316692588337720342646339764174333821950301279825316497898035760524780198230860089280791887363472060435443944632303774987556026740232641561706904946900169858650106994947597642013168757868017723456208796677559254390940651802333382820063200360490892131573853635471525711894510477078934343423255983)
enc = 275574424285842306309073814038154403551700455145115884031072340378743712325975683329051874910297915882286569143815715537085387363420246497061870251520240399514896001311724695996978111559476733709139080970977190150345474341853495386364275702356438666152069791355990718058189043717952080875207858163490627801836274404446661613239167700736337269924479349700031535265765885064606399858172168036794462235707003475360358004643720927563261787867952228496769300443415094124132722170498229611285689671203272698693505808912907778910378274197503048226322090611405601517624884408718689404556983397217070272851442351897456769883
sh = requests.get(f'http://factordb.com/api?query={pkey[0]}')
r = sh.json()["factors"]
ab = gmpy2.iroot(pkey[1],4)[0]
print(ab)
h = pkey[1] - ab**4 - pkey[0]
xk = h**2 - 4 * (ab**4) * pkey[0]
xk1 = gmpy2.iroot(xk,2)[0]
a4s = (h + xk1) //2
b4r = (h - xk1) //2
s = [int(r[-1][0]) ** int(r[-1][1]),pkey[0]//(int(r[-1][0]) ** int(r[-1][1]))]
print(s)
for i in s:
print(GCD(a4s,i))
s = 14071
R = 10728
a = gmpy2.iroot(a4s//s,4)[0]
b = gmpy2.iroot(b4r//R,4)[0]
p = a**4 + R
q = b**4 + s
print(GCD(pkey[0],(p-1)*(q-1)))
print(p,q)
e = p[0]
print(GCD(e,p-1))
import random
import time
from tqdm import tqdm
from Crypto.Util.number import *
def AMM(o, r, q):
start = time.time()
print('\n----------------------------------------------------------------------------------')
print('Start to run Adleman-Manders-Miller Root Extraction Method')
print('Try to find one {:#x}th root of {} modulo {}'.format(r, o, q))
g = GF(q)
o = g(o)
p = g(random.randint(1, q))
while p ^ ((q - 1) // r) == 1:
p = g(random.randint(1, q))
print('[+] Find p:{}'.format(p))
t = 0
s = q - 1
while s % r == 0:
t += 1
s = s // r
print('[+] Find s:{}, t:{}'.format(s, t))
k = 1
while (k * s + 1) % r != 0:
k += 1
alp = (k * s + 1) // r
print('[+] Find alp:{}'.format(alp))
a = p ^ (r ** (t - 1) * s)
b = o ^ (r * alp - 1)
c = p ^ s
h = 1
for i in range(1, t):
d = b ^ (r ^ (t - 1 - i))
if d == 1:
j = 0
else:
print('[+] Calculating DLP...')
j = - discrete_log(d, a)
print('[+] Finish DLP...')
b = b * (c ^ r) ^ j
h = h * c ^ j
c = c ^ r
result = o ^ alp * h
end = time.time()
print("Finished in {} seconds.".format(end - start))
print('Find one solution: {}'.format(result))
return result
def onemod(p, r):
t = random.randint(2, p)
while pow(t, (p - 1) // r, p) == 1:
t = random.randint(2, p)
return pow(t, (p - 1) // r, p)
def solution(p, root, e):
while True:
g = onemod(p, e)
may = []
for i in tqdm(range(e)):
may.append(root * pow(g, i, p) % p)
if len(may) == len(set(may)):
return may
def solve_in_subset(ep, p):
cp = int(pow(c, inverse(int(e // ep), p - 1), p))
com_factors = []
while GCD(ep, p - 1) != 1:
com_factors.append(GCD(ep, p - 1))
ep //= GCD(ep, p - 1)
com_factors.sort()
cps = [cp]
for factor in com_factors:
mps = []
for cp in cps:
mp = AMM(cp, factor, p)
mps += solution(p, mp, factor)
cps = mps
for each in cps:
assert pow(each, e, p) == c % p
return cps
Suction
PKEY = 55208723145458976481271800608918815438075571763947979755496510859604544396672
ENC = 127194641882350916936065994389482700479720132804140137082316257506737630761
c = ENC
e = int(bin(PKEY)[-8:],2)
# print(e)
from Crypto.Util.number import *
# from flag import flag
import gmpy2
import requests
from tqdm import *
a = 0
# for i in tqdm(range(2**8)):
# a = (PKEY>>8)<<8
# A = a + i
# # print(A)
# sh = requests.get(f'http://factordb.com/api?query={A}')
# ciper = sh.json()['factors']
# if len(ciper) == 2:
# print(A,ciper)
n = 55208723145458976481271800608918815438075571763947979755496510859604544396613
p = 188473222069998143349386719941755726311
q = 292926085409388790329114797826820624883
for i in tqdm(range(2**8)):
for j in range(2**8):
C = (c<<8) + i
E = (e<<8) + j
try:
assert GCD(E,(p-1)*(q-1)) == 1
d = inverse(E,(p-1)*(q-1))
m = (gmpy2.powmod(C,d,n))
if m < 2**200:
print(long_to_bytes(m))
except:
pass
