RzVJVFlaSkZGUk1HV1daWkdOQ0RFNEpJSE5RWEdOS05ISlNHSTNCT0daWVVXS1pDRzQzV01UQ0NISkVTNElKQkdKUkZFUEpYRjVIVk0zMlpIQVpXNjQyTkdaSlRBNFMzR1pKVENPMllIVjJWWVRMQ0daTERDTVpYR0JURk1TMlpHQlRWR0xDWkdaS1ZRWUo1R0ZURVFRSlNHQlRGNFQyTUc1SVRHUURFSFU3REVZSkVHNVdFS1FEUEdKUEVJS1NYRzQ0RkNRU0lITkNIQ1NaUEdWWlc0UlJZR1pZSEdRVFBHSVVXSVMzQkc0M0RHMkJIRzQ0R1lLU0VHQlFBPT09PQ==

flag{cl@ss1cal_c1pher_@re_really_1nterest1ng}

from Crypto.Util.number import *
from gmpy2 import *
import random

get_context().precision = 2048

L = 5
S = getPrime(144)
a = getPrime(32)
b = random.randint(0, S - 1)

def split_and_pad_single_char_rule(msg, L):
    segments = []
    assert L >= 1
    pad_len = L - 1
    for char_idx, char_byte in enumerate(msg):
        char_ascii = char_byte
        pad_bytes = bytes([(char_ascii + i + 1) % 256 for i in range(pad_len)])
        seg_bytes = bytes([char_byte]) + pad_bytes
        segments.append(bytes_to_long(seg_bytes))
    return segments

def encrypt_segment(m_i, a, b, M):
    return (a * m_i + b) % M

flag = "flag{___________________}"
msg_bytes = flag.encode()
m_segments = split_and_pad_single_char_rule(msg_bytes, L)
c_segments = [encrypt_segment(mi, a, b, S) for mi in m_segments]

print(f"a = {a}")
print(f"S = {S}")
print(f"L = {L}")
print(f"C = {c_segments}")
print(f'M = {m_segments}')

'''
a = 3517115977
S = 13338196046628817705384101887069807236659077
L = 5
C = [6399813929853868574459915097120849511644924, 6399813929853868574460006087942330564102834, 6399813929853868574459839271436281967929999, 6399813929853868574459930262257763020387909, 6399813929853868574460233564996033195247609, 6399813929853868574460112243900725125303729, 6399813929853868574459111344864433548266719, 6399813929853868574459930262257763020387909, 6399813929853868574460036418216157581588804, 6399813929853868574459808941162454950444029, 6399813929853868574459111344864433548266719, 6399813929853868574460036418216157581588804, 6399813929853868574459808941162454950444029, 6399813929853868574460127409037638634046714, 6399813929853868574459096179727520039523734, 6399813929853868574459930262257763020387909, 6399813929853868574459899931983936002901939, 6399813929853868574460127409037638634046714, 6399813929853868574459945427394676529130894, 6399813929853868574459172005412087583238659, 6399813929853868574460097078763811616560744, 6399813929853868574459808941162454950444029, 6399813929853868574460188069585292669018654, 6399813929853868574459960592531590037873879, 6399813929853868574460188069585292669018654, 6399813929853868574459960592531590037873879, 6399813929853868574460263895269860212733579]
'''

#python
from Crypto.Util.number import *

a = 3517115977
S = 13338196046628817705384101887069807236659077
L = 5
C = [6399813929853868574459915097120849511644924, 6399813929853868574460006087942330564102834, 6399813929853868574459839271436281967929999, 6399813929853868574459930262257763020387909, 6399813929853868574460233564996033195247609, 6399813929853868574460112243900725125303729, 6399813929853868574459111344864433548266719, 6399813929853868574459930262257763020387909, 6399813929853868574460036418216157581588804, 6399813929853868574459808941162454950444029, 6399813929853868574459111344864433548266719, 6399813929853868574460036418216157581588804, 6399813929853868574459808941162454950444029, 6399813929853868574460127409037638634046714, 6399813929853868574459096179727520039523734, 6399813929853868574459930262257763020387909, 6399813929853868574459899931983936002901939, 6399813929853868574460127409037638634046714, 6399813929853868574459945427394676529130894, 6399813929853868574459172005412087583238659, 6399813929853868574460097078763811616560744, 6399813929853868574459808941162454950444029, 6399813929853868574460188069585292669018654, 6399813929853868574459960592531590037873879, 6399813929853868574460188069585292669018654, 6399813929853868574459960592531590037873879, 6399813929853868574460263895269860212733579]

def construct_m_from_char(char, L):
    char_ascii = ord(char)
    pad_len = L - 1
    pad_bytes = bytes([(char_ascii + i + 1) % 256 for i in range(pad_len)])
    seg_bytes = bytes([ord(char)]) + pad_bytes
    return bytes_to_long(seg_bytes)


known_chars = ['f', 'l', 'a', 'g']
derived_b = []
for idx, char in enumerate(known_chars):
    m_i = construct_m_from_char(char, L)
    b = (C[idx] - a * m_i) % S
    derived_b.append(b)


b = derived_b[0]
print(f"推导出的私钥b = {b}")

a_inv = inverse(a, S)

flag = ""
M = []
for c in C:
    m_i = ((c - b) % S) * a_inv % S
    M.append(m_i)
    seg_bytes = long_to_bytes(m_i)
    original_char = chr(seg_bytes[0])
    flag += original_char

print(flag)
#flag{s1gn_1n_t0geth5r_xixi}

from Crypto.Util.number import *
import random

flag = "flag{_______________________________}"
m = bin(bytes_to_long(flag.encode()))[2:]
p = getPrime(300)
q = getPrime(300)
n = p * q

R.<x> = PolynomialRing(Zmod(n))

def gen(m):
    C = []
    for bit in m:
        if bit == '0':
            C.append(random.randint(1, n-1))
        else:
            x = random.randint(1, 2^80)
            y = random.randint(1, p-1)
            val = 65537 + x*(1-x) +(q - x)*y + (y + x)*(q + x)
            C.append(R(val))
    return C

c = gen(m)
print(f"n = {n}")
print(f"c = {c}")

0: c_i为mod(n)的随机数
1: c_i为65537 + x*(1-x) +(q - x)*y + (y + x)*(q + x) -->  65537 + qx + 2qy + x

#sage
from Crypto.Util.number import *
n = 
c = 
flag = ""

PR.<x> = PolynomialRing(Zmod(n))
for i in range(len(c)):
    f = x - c[i]
    res = f.small_roots(X=2^80,beta=0.49)
    if(res != []):
        flag += "1"
    else:
        flag += "0"


print(long_to_bytes(int(flag,2)))
#flag{where_1s_th5_flag_where}

from Crypto.Util.number import *
from gmpy2 import *


def gen():
    while(1):
        p1 = getPrime(128)
        p2 = getPrime(512)
        q2 = getPrime(512)
        s = q2 & ((1 << 56) - 1)
        q1 = 2 * p1 + s
        r1 = 2 * q1 + s
        if is_prime(q1) and is_prime(r1):
            n1 = p1 * q1 * r1
            n2 = p2 * q2
            break
    return n1,n2,p1,p2


n1,n2, p1, p2 = gen()
e = 65537

flag = "flag{---------------------------------------}".encode()
m1 = bytes_to_long(flag[: (len(flag)+1) // 2])
m2 = bytes_to_long(flag[(len(flag)+1) // 2 :])

c1 = powmod(m1, e, n1)
c2 = powmod(m2, e, n2)

gift = p2 >> 262

print(f"e = {e}")
print(f"n1 = {n1}")
print(f"n2 = {n2}")
print(f"c1 = {c1}")
print(f"c2 = {c2}")
print(f"p1 = {p1}")
print(f"gift = {gift}")

'''
e = 65537
n1 = 153535945724301761635048132162798014938917969845079448489545851494873442295873133893384411532854581537976576911336083
n2 = 84803188245030813883191077133506154725049469687779805365997839479650548017159380111143407950887981137367898417071670318175553216747909857623397932606557900805065642334402683077054566841962022705300815246585360967197421835628665369002004215185956537117678561509558467837953178340079218753108643544534307300779
c1 = 91344805342373294041484814707589753503672726499268929615405258196853851463816933913580106446612439099622637694719344
c2 = 65030067863230521561732635665855986696538207379818716373900645903663706519394086998921178373079966943522635174648820466855368885032783946013202871621053763074374114131710373913193434831822631037825109588592562599802388631816046111419285162200967000421088941791542557891726383026274591733889350668008350880276
p1 = 267735952598198080786845163083151774667
gift = 1068605981024067598428983610552162240530726981658336444437430658822896756780
'''

#sage
from Crypto.Util.number import *
from gmpy2 import *

e = 65537
n1 = 153535945724301761635048132162798014938917969845079448489545851494873442295873133893384411532854581537976576911336083
n2 = 84803188245030813883191077133506154725049469687779805365997839479650548017159380111143407950887981137367898417071670318175553216747909857623397932606557900805065642334402683077054566841962022705300815246585360967197421835628665369002004215185956537117678561509558467837953178340079218753108643544534307300779
c1 = 91344805342373294041484814707589753503672726499268929615405258196853851463816933913580106446612439099622637694719344
c2 = 65030067863230521561732635665855986696538207379818716373900645903663706519394086998921178373079966943522635174648820466855368885032783946013202871621053763074374114131710373913193434831822631037825109588592562599802388631816046111419285162200967000421088941791542557891726383026274591733889350668008350880276
p1 = 267735952598198080786845163083151774667
gift = 1068605981024067598428983610552162240530726981658336444437430658822896756780

PR.<x> = PolynomialRing(Zmod(n1//p1))
f = (2*p1 + x)*(4*p1 + 3*x)
res1 = f.monic().small_roots(X=2^56,beta=0.4)
print(res1)
s = int(res1[0])
q1 = 2 * p1 + s
r1 = 2 * q1 + s
d1 = inverse(e , (p1 - 1)*(q1 - 1) * (r1 - 1))
m1 = powmod(c1, d1, n1)


p2l = n2 * inverse(s, 2 ** 56) % 2 ** 56
PR.<x> = PolynomialRing(Zmod(n2))
g = gift * (2 ** 262) + x * 2 ** 56 + p2l
res2 = g.monic().small_roots(X=2^206,beta=0.4)
print(res2)
p2 = gift * (2 ** 262) + int(res2[0]) * 2 ** 56 + p2l
q2 = n2 // p2
d2 = inverse(e, (p2-1)*(q2-1))
m2 = powmod(c2, d2, n2)

print(long_to_bytes(m1) + long_to_bytes(m2))
#flag{Im_a_fw_that_only_crafts_RSA_challenges}

from Crypto.Util.number import *

def tran(n):
s_bin = bin(n)[2:]
bit_map = {'0': '10', '1': '01'}
p_bin = '11' + ''.join([bit_map[bit] for bit in s_bin[1:]])
return int(p_bin, 2)

def keygen(nbit):
while True:
s = getPrime(nbit)
p = tran(s)
if not isPrime(p):
continue
s_bin = bin(s)[2:].zfill(nbit)
q_bin = (s_bin[:nbit // 2]
 + '1' * (nbit // 2)
 + s_bin[nbit // 2:]
 + '1' * (nbit // 2))
q = int(q_bin, 2)
if isPrime(q):
return p,q

flag = "flag{____________________________}"
nbit = 256
p, q = keygen(nbit)
m = bytes_to_long(flag.encode())
e= 65537
n = p * q
c = pow(m, e, n)

print(f'n = {n}')
print(f'c = {c}')

"""
n = 97500437901440388417198788454954892885829765317271438600836638419723842224011100091990654907349042873594131382232421640267091732569264390052236076620148372084122607139079558728860385251369576795723604753566616558793072715394596559965112752835650808765911364805382628147988309718393764596614456741590220757591
c = 7738615614182124736230909980262535479827406389377664909203540758689122759528168600427345931034997504030657746278863273550729288326235414854206217548620396163736109673531409510422631464901846302450760457216706035370273167926580473904029057693564485585891556568420324605915383565319685765532478198539656924536
"""

#python

from Crypto.Util.number import *

nbit = 256
e = 65537
n = 97500437901440388417198788454954892885829765317271438600836638419723842224011100091990654907349042873594131382232421640267091732569264390052236076620148372084122607139079558728860385251369576795723604753566616558793072715394596559965112752835650808765911364805382628147988309718393764596614456741590220757591
c = 7738615614182124736230909980262535479827406389377664909203540758689122759528168600427345931034997504030657746278863273550729288326235414854206217548620396163736109673531409510422631464901846302450760457216706035370273167926580473904029057693564485585891556568420324605915383565319685765532478198539656924536


def dfs(h, s_prefix, p_prefix):
    p_remain = 2 * nbit - len(p_prefix)
    p_max = int(p_prefix + "1" * p_remain, 2)
    p_min = int(p_prefix + "0" * p_remain, 2)

    s_half = nbit // 2
    s_len = len(s_prefix)
    s_remain = nbit - s_len

    if s_len <= s_half:
        q_pre0 = (s_prefix + "0" * (s_half - s_len)
                  + "1" * s_half
                  + "0" * s_half
                  + "1" * s_half)
        q_pre1 = (s_prefix + "1" * (s_half - s_len)
                  + "1" * s_half
                  + "1" * s_half
                  + "1" * s_half)
    else:
        s_pre128 = s_prefix[:s_half]
        s_suf_cur = s_prefix[s_half:]
        q_pre0 = (s_pre128 + "1" * s_half
                  + s_suf_cur + "0" * (s_half - (s_len - s_half))
                  + "1" * s_half)
        q_pre1 = (s_pre128 + "1" * s_half
                  + s_suf_cur + "1" * (s_half - (s_len - s_half))
                  + "1" * s_half)

    q_max = int(q_pre1, 2)
    q_min = int(q_pre0, 2)

    if q_max * p_max < n or q_min * p_min > n:
        return

    if h == nbit:
        p = p_max
        q = int(s_prefix[:s_half] + "1" * s_half + s_prefix[s_half:] + "1" * s_half, 2)

        if p * q != n:
            return
        if isPrime(p) and isPrime(q):
            phi = (p - 1) * (q - 1)
            d = inverse(e, phi)
            flag = long_to_bytes(pow(c, d, n))
            print(f"flag: {flag.decode()}")
            print(f"p = {p}")
            print(f"q = {q}")
            exit()
        return

    dfs(h + 1, s_prefix + "0", p_prefix + "10")
    dfs(h + 1, s_prefix + "1", p_prefix + "01")


dfs(1, s_prefix="1", p_prefix="11")
#flag{n1ce_th1s_RSA_I_can_do_it}

from Crypto.Util.number import *

def ECC(bit):
    g = getPrime(bit)
    a = getPrime(bit)
    b = getPrime(bit)

    E = EllipticCurve(GF(g),[a,b])
    J = E.random_point()
    K = E.random_point()
    L = E.random_point()

    r = getPrime(bit // 2)
    k = getPrime(16)

    s  = r * J
    s1 = r * J + k * L
    s2 = r * k * J

    return L.xy(), s.xy(), s1.xy(), s2.xy(), K.xy()

def RSA(m, s, bit):
    p = getPrime(bit)
    q = getPrime(bit)
    rr = getPrime(bit)
    n = p * q

    gift = pow(rr, rr * (p-1), n)
    enc = pow(m, int(s), n)

    return gift, n, enc

flag = "flag{--------------------------------}"
m = bytes_to_long(flag.encode())

L, s, s1, s2, K = ECC(256)
gift, n, enc = RSA(m, abs(int(s[0] - s[1])), 512) 

print("L =", L)
print("s1 =", s1)
print("s2 =", s2)
print("K =", K)
print("enc =", enc)
print("gift =", gift)
print("n =", n)

'''
L = (5612832632021037413595021905856059690922175615680426850888866965067320107819, 44286844991960812568914524464365492264373223903614475371204877844888511445056)
s1 = (3105425529931638108939225244969805843864193431777172585017902596003213488900, 21204057924591170352686471525538286905154747896755584173932333298433282086561)
s2 = (17163600514231693116809112204202083823354850361231568034507586407851022654385, 54523130652066750636213932541583111123904814992668862332727980305098543395332)
K = (84626796737477467367556465702814556148204747766624017939626441693356336891461, 20412858373065309258609569831347478221615957387864164638932871773748933195219)
enc = 77779248799562415787538731320739960822457760506615718084036279480880899171418681853821326436404494983875803921684003465855970542931724878457768817162166413967384579329072032251210520838992258491716245608876204830909672245330785235016998427930933850050898878548191256398496024681498083646200326639489612460844
gift = 27203859362379532209762716293585970661584968016465564915669656593570376250661463300469214869975225133883120425672896040102408082124157996563344160198308488970094544684114508100388704667496464400261830996514109943777210955076236899363247079300339008914936852187908757699066223721473477803084358704291887973927
n = 99350851709648177478181442570691890135193362203180628334780894515389735176666242281991349782055218048443285160186921692026870729324336754641181928398906259668775047724023372863155472201773397077316170491389813660679924150036914095032544796724427607899057109320556570067643629947815982002736525967748207154359
'''

#sage
from Crypto.Util.number import *


L = (5612832632021037413595021905856059690922175615680426850888866965067320107819, 44286844991960812568914524464365492264373223903614475371204877844888511445056)
s1 = (3105425529931638108939225244969805843864193431777172585017902596003213488900, 21204057924591170352686471525538286905154747896755584173932333298433282086561)
s2 = (17163600514231693116809112204202083823354850361231568034507586407851022654385, 54523130652066750636213932541583111123904814992668862332727980305098543395332)
K = (84626796737477467367556465702814556148204747766624017939626441693356336891461, 20412858373065309258609569831347478221615957387864164638932871773748933195219)
enc = 77779248799562415787538731320739960822457760506615718084036279480880899171418681853821326436404494983875803921684003465855970542931724878457768817162166413967384579329072032251210520838992258491716245608876204830909672245330785235016998427930933850050898878548191256398496024681498083646200326639489612460844
gift = 27203859362379532209762716293585970661584968016465564915669656593570376250661463300469214869975225133883120425672896040102408082124157996563344160198308488970094544684114508100388704667496464400261830996514109943777210955076236899363247079300339008914936852187908757699066223721473477803084358704291887973927
n = 99350851709648177478181442570691890135193362203180628334780894515389735176666242281991349782055218048443285160186921692026870729324336754641181928398906259668775047724023372863155472201773397077316170491389813660679924150036914095032544796724427607899057109320556570067643629947815982002736525967748207154359

temp1 = (s2[1] ** 2 - s1[1] ** 2 - s2[0] ** 3 + s1[0] ** 3)
temp2 = (L[1] ** 2 - s2[1] ** 2 - L[0] ** 3 + s2[0] ** 3)
temp3 = (K[1] ** 2 - L[1] ** 2 - K[0] ** 3 + L[0] ** 3)
k1g = temp1 * (L[0] - s2[0]) - temp2 * (s2[0] - s1[0])
k2g = temp2 * (K[0] - L[0]) - temp3 * (L[0] - s2[0])
k3g = temp1 * (K[0] - L[0]) - temp3 * (s2[0] - s1[0])
g = GCD(k1g, k2g)
g = GCD(g, k3g)

for i in range(2,1000):
        while(g % i == 0):
            g //= i
a = inverse(s2[0]-s1[0],g)*temp1 % g
b = (s1[1] ** 2 - s1[0]**3-a*s1[0]) % g

E = EllipticCurve(GF(g),[a,b])
L = E(L)
s1 = E(s1)
s2 = E(s2)

base = L
k = 0
for j in range(2, 1000000):
    base += L
    if (s1 - base) * j == s2:
           k = j
           break
assert (s1 - k * L) * j == s2

s = s1 - k * L

e = abs(int(s[0] - s[1]))
p = GCD((gift - 1), n)
q = n // p
d = inverse(e, (p-1)*(q-1))
m = pow(enc, d, n)
print(long_to_bytes(int(m)))
#flag{this_1s_a_so_EZ_Ecc_and_RSA_}

from Crypto.Util.number import *


def gen_rev_sum(m,p):
    sum = 0
    round = 0
    while m > 0:
        digit = m % p
        if round % 2 == 0:
            sum -= digit
        else:
            sum += digit
        m = m // p
        round += 1
    return sum // 2025


e = 65537
p = getPrime(256)
q = getPrime(256)
n = p*q

m1 = getRandomNBitInteger(2048)
m2 = getRandomNBitInteger(2048)
sum1 = gen_rev_sum(m1, p)
sum2 = gen_rev_sum(m2, p)

flag = "flag{--------------------------}"
m = bytes_to_long(flag.encode())

print("m1 =",m1)
print("m2 =",m2)
print("sum1 =",sum1)
print("sum2 =",sum2)
print("n =",n)
print("c =",pow(m,e,n))

'''
m1 = 17322548249387769406385507000191215801044910756841784387283679508067232037647009879640247663005640315645559929483973978388785385751219073137080976227046261663059832428571101292873255962114141666488474602734594597852331665601154571683480014721045567844719377268571343706508041194359642732322649799872642255094259428635455750138217286588825326703937255171250131117864604764478573786940615096044575610751081788573681131616312486987096717266320380202191909867687322859634487150465591581523036586129341984826904474237818210411872793917742756628712320922128969576851582027757934655202892557206052328142121974846460835879379
m2 = 29770749505949559271464509877642735633388289947852331255230201935471628731047838190019590503471311260422939188831886032391799282413808339483805109656799786202448656409753608524222447399741340441803183979217817801933166848028113568228217090419247166878248450792302177597130681740006379413412297487888656975884867850858832779733076818160854085244264177562471933684902341628858046181331683501978826962693104997686104748486850900546849316714934730338449894336151567737740558472664876717516650156395237362632196760323299658988296623556674223583771795447537227301625104687705109034611911834940501083977979641467845119043780
sum1 = -108877560874638575191632670246326227208412819991287356983577291185528002487
sum2 = -47122048431044787786292644180145597499319125719652288525187634667738055282
n = 9020951256034058214321622067945640395058903219618790136239198219605516437223449048642101160150934286238922049363203171871230111420670637737169565825694393
c = 3323425622556846027480153848276857423081641901016156494250966280342935316300495906916254739461788219592704051961044937129981786472345610933524261214506540
e = 65537
'''

#python
from Crypto.Util.number import *
from tqdm import *

m1 = 17322548249387769406385507000191215801044910756841784387283679508067232037647009879640247663005640315645559929483973978388785385751219073137080976227046261663059832428571101292873255962114141666488474602734594597852331665601154571683480014721045567844719377268571343706508041194359642732322649799872642255094259428635455750138217286588825326703937255171250131117864604764478573786940615096044575610751081788573681131616312486987096717266320380202191909867687322859634487150465591581523036586129341984826904474237818210411872793917742756628712320922128969576851582027757934655202892557206052328142121974846460835879379
m2 = 29770749505949559271464509877642735633388289947852331255230201935471628731047838190019590503471311260422939188831886032391799282413808339483805109656799786202448656409753608524222447399741340441803183979217817801933166848028113568228217090419247166878248450792302177597130681740006379413412297487888656975884867850858832779733076818160854085244264177562471933684902341628858046181331683501978826962693104997686104748486850900546849316714934730338449894336151567737740558472664876717516650156395237362632196760323299658988296623556674223583771795447537227301625104687705109034611911834940501083977979641467845119043780
sum1 = -108877560874638575191632670246326227208412819991287356983577291185528002487
sum2 = -47122048431044787786292644180145597499319125719652288525187634667738055282
n = 9020951256034058214321622067945640395058903219618790136239198219605516437223449048642101160150934286238922049363203171871230111420670637737169565825694393
c = 3323425622556846027480153848276857423081641901016156494250966280342935316300495906916254739461788219592704051961044937129981786472345610933524261214506540
e = 65537

for i in trange(2025):
        for j in range(2025):
            sum1_ = sum1*2025+i
            sum2_ = sum2*2025+j
            kp = GCD(m1 + sum1_, m2 + sum2_)
            if kp > 2 ** 255:
                for k in range(1, 10000):
                    if (kp % k == 0):
                        p = kp // k - 1
                        if (isPrime(p) and len(bin(p)[2:]) == 256):
                            q = n // p
                            d = inverse(e, (p - 1) * (q - 1))
                            print(long_to_bytes(pow(c, d, n)))
                            break
#flag{Reverse_Sum_Mod_p+i_GCD_2025!}

from Crypto.Util.number import *
from gmpy2 import *
import random

def RSA(m,nbit):
    while True:
        p, q, e = getPrime(nbit), getPrime(nbit), getPrime(nbit)
        n = p * q
        phi_n = (p - 1) * (q - 1)
        d = int(inverse(e, phi_n))
        if len(bin(d)[2:]) == 1024:
            break

    keep_bits = nbit * 2 - 100
    mask = int((1 << keep_bits) - 1)
    d_ = d & mask
    c = powmod(m, e, n)
    return c,n,e,d_

def gen(nbit):

    c, n, e, d_ = RSA(m, nbit)
    N = getPrime(nbit * 2)
    t = random.randint(1, nbit * 2 - 1)
    C = [random.randint(0, N - 1) for _ in range(t - 1)] + [powmod(d_,1,N)]
    R.<x> = GF(N)[]
    f = R(0)
    for i in range(t):
        f += x ** (t - i - 1) * C[i]
    enc = [(a, f(a)) for a in [random.randint(1, N - 1) for _ in range(t)]]

    with open("output.txt", "w", encoding="utf-8") as f_out:
        f_out.write(f"c = {c}\n")
        f_out.write(f"n = {n}\n")
        f_out.write(f"e = {e}\n")
        f_out.write(f"N = {N}\n")
        f_out.write(f"enc = {enc}\n")

flag = "flag{-------------------------------}"
m = bytes_to_long(flag.encode())

if __name__ == "__main__":
    gen(512)

('c=', '0x7a7e031f14f6b6c3292d11a41161d2491ce8bcdc67ef1baa9eL')
('e=', '0x872a335')
#q + q*p^3 =1285367317452089980789441829580397855321901891350429414413655782431779727560841427444135440068248152908241981758331600586
#qp + q *p^2 = 1109691832903289208389283296592510864729403914873734836011311325874120780079555500202475594

# happy
# python
A = 1285367317452089980789441829580397855321901891350429414413655782431779727560841427444135440068248152908241981758331600586
B = 1109691832903289208389283296592510864729403914873734836011311325874120780079555500202475594
e_hex = "0x872a335"
c_hex = "0x7a7e031f14f6b6c3292d11a41161d2491ce8bcdc67ef1baa9e"
e = int(e_hex, 16)
c = int(c_hex, 16)

quotient = A // B
remainder = A % B

p = B // remainder
q = B // (p*(1+p))
n = p*q
d = inverse(e, n - p - q + 1)
print("happy:",long_to_bytes(powmod(c, d, n)))
#flag{happy_rsa_1}

from gmpy2 import *
from Crypto.Util.number import *



flag  = '****************************'
p = getPrime(2048)
q = getPrime(2048)
m1 = bytes_to_long(bytes(flag.encode()))

e1e2 = 3087
n = p*q
print()

flag1 = pow(m1,e1,n)
flag2 = pow(m1,e2,n)
print('flag1= '+str(flag1))
print('flag2= '+str(flag2))
print('n= '+str(n))


#flag1= 463634070971821449698012827631572665302589213868521491855038966879005784397309389922926838028598122795187584361359142761652619958273094398420314927073008031088375892957173280915904309949716842152249806486027920136603248454946737961650252641668562626310035983343018705370077783879047584582817271215517599531278507300104564011142229942160380563527291388260832749808727470291331902902518196932928128107067117198707209620169906575791373793854773799564060536121390593687449884988936522369331738199522700261116496965863870682295858957952661531894477603953742494526632841396338388879198270913523572980574440793543571757278020533565628285714358815083303489096524318164071888139412436112963845619981511061231001617406815056986634680975142352197476024575809514978857034477688443230263761729039797859697947454810551009108031457294164840611157524719173343259485881089252938664456637673337362424443150013961181619441267926981848009107466576314685961478748352388452114042115892243272514245081604607798243817586737546663059737344687130881861357423084448027959893402445303299089606081931041217035955143939567456782107203447898345284731038150377722447329202078375870541529539840051415759436083384408203659613313535094343772238691393447475364806171594
#flag2= 130959534275704453216282334815034647265875632781798750901627773826812657339274362406246297925411291822193191483409847323315110393729020700526946712786793380991675008128561863631081095222226285788412970362518398757423705216112313533155390315204875516645459370629706277876211656753247984282379731850770447978537855070379324935282789327428625259945250066774049650951465043700088958965762054418615838049340724639373351248933494355591934236360506778496741051064156771092798005112534162050165095430065000827916096893408569751085550379620558282942254606978819033885539221416335848319082054806148859427713144286777516251724474319613960327799643723278205969253636514684757409059003348229151341200451785288395596484563480261212963114071064979559812327582474674812225260616757099890896900340007990585501470484762752362734968297532533654846190900571017635959385883945858334995884341767905619567505341752047589731815868489295690574109758825021386698440670611361127170896689015108432408490763723594673299472336065575301681055583084547847733168801030191262122130369687497236959760366874106043801542493392227424890925595734150487586757484304609945827925762382889592743709682485229267604771944535469557860120878491329984792448597107256325783346904408
#n= 609305637099654478882754880905638123124918364116173050874864700996165096776233155524277418132679727857702738043786588380577485490575591029930152718828075976000078971987922107645530323356525126496562423491563365836491753476840795804040219013880969539154444387313029522565456897962200817021423704204077133003361140660038327458057898764857872645377236870759691588009666047187685654297678987435769051762120388537868493789773766688347724903911796741124237476823452505450704989455260077833828660552130714794889208291939055406292476845194489525212129635173284301782141617878483740788532998492403101324795726865866661786740345862631916793208037250277376942046905892342213663197755010315060990871143919384283302925469309777769989798197913048813940747488087191697903624669415774198027063997058701217124640082074789591591494106726857376728759663074734040755438623372683762856958888826373151815914621262862750497078245369680378038995425628467728412953392359090775734440671874387905724083226246587924716226512631671786591611586774947156657178654343092123117255372954798131265566301316033414311712092913492774989048057650627801991277862963173961355088082419091848569675686058581383542877982979697235829206442087786927939745804017455244315305118437

e1e2 = 3087
flag1= 463634070971821449698012827631572665302589213868521491855038966879005784397309389922926838028598122795187584361359142761652619958273094398420314927073008031088375892957173280915904309949716842152249806486027920136603248454946737961650252641668562626310035983343018705370077783879047584582817271215517599531278507300104564011142229942160380563527291388260832749808727470291331902902518196932928128107067117198707209620169906575791373793854773799564060536121390593687449884988936522369331738199522700261116496965863870682295858957952661531894477603953742494526632841396338388879198270913523572980574440793543571757278020533565628285714358815083303489096524318164071888139412436112963845619981511061231001617406815056986634680975142352197476024575809514978857034477688443230263761729039797859697947454810551009108031457294164840611157524719173343259485881089252938664456637673337362424443150013961181619441267926981848009107466576314685961478748352388452114042115892243272514245081604607798243817586737546663059737344687130881861357423084448027959893402445303299089606081931041217035955143939567456782107203447898345284731038150377722447329202078375870541529539840051415759436083384408203659613313535094343772238691393447475364806171594
flag2= 130959534275704453216282334815034647265875632781798750901627773826812657339274362406246297925411291822193191483409847323315110393729020700526946712786793380991675008128561863631081095222226285788412970362518398757423705216112313533155390315204875516645459370629706277876211656753247984282379731850770447978537855070379324935282789327428625259945250066774049650951465043700088958965762054418615838049340724639373351248933494355591934236360506778496741051064156771092798005112534162050165095430065000827916096893408569751085550379620558282942254606978819033885539221416335848319082054806148859427713144286777516251724474319613960327799643723278205969253636514684757409059003348229151341200451785288395596484563480261212963114071064979559812327582474674812225260616757099890896900340007990585501470484762752362734968297532533654846190900571017635959385883945858334995884341767905619567505341752047589731815868489295690574109758825021386698440670611361127170896689015108432408490763723594673299472336065575301681055583084547847733168801030191262122130369687497236959760366874106043801542493392227424890925595734150487586757484304609945827925762382889592743709682485229267604771944535469557860120878491329984792448597107256325783346904408
n= 609305637099654478882754880905638123124918364116173050874864700996165096776233155524277418132679727857702738043786588380577485490575591029930152718828075976000078971987922107645530323356525126496562423491563365836491753476840795804040219013880969539154444387313029522565456897962200817021423704204077133003361140660038327458057898764857872645377236870759691588009666047187685654297678987435769051762120388537868493789773766688347724903911796741124237476823452505450704989455260077833828660552130714794889208291939055406292476845194489525212129635173284301782141617878483740788532998492403101324795726865866661786740345862631916793208037250277376942046905892342213663197755010315060990871143919384283302925469309777769989798197913048813940747488087191697903624669415774198027063997058701217124640082074789591591494106726857376728759663074734040755438623372683762856958888826373151815914621262862750497078245369680378038995425628467728412953392359090775734440671874387905724083226246587924716226512631671786591611586774947156657178654343092123117255372954798131265566301316033414311712092913492774989048057650627801991277862963173961355088082419091848569675686058581383542877982979697235829206442087786927939745804017455244315305118437
for e1 in range(2, e1e2):
    if e1e2 % e1 == 0:
        e2 = e1e2 // e1
        t, s1, s2 = gcdext(e1, e2)
        m = iroot((powmod(flag1,s1,n)*powmod(flag2,s2,n)) % n, t)
        if m[1]:
            if long_to_bytes(m[0]).startswith(b'NSSCTF{'): # 知道flag头，过滤非flag，不知道就输出全部找flag
                print(long_to_bytes(m[0]))
#NSSCTF{d64dba66-b608-4255-b888-0b0f25c2f90e}

from gmpy2 import *
from Crypto.Util.number import *



flag  = '***************'

p = getPrime(512)
q = getPrime(512)
m1 = bytes_to_long(bytes(flag.encode()))


n = p*q
e1 = getPrime(32)
e2 = getPrime(32)
print()

flag1 = pow(m1,e1,n)
flag2 = pow(m1,e2,n)
print('flag1= '+str(flag1))
print('flag2= '+str(flag2))
print('e1= ' +str(e1))
print('e2= '+str(e2))
print('n= '+str(n))


#flag1= 100156221476910922393504870369139942732039899485715044553913743347065883159136513788649486841774544271396690778274591792200052614669235485675534653358596366535073802301361391007325520975043321423979924560272762579823233787671688669418622502663507796640233829689484044539829008058686075845762979657345727814280
#flag2= 86203582128388484129915298832227259690596162850520078142152482846864345432564143608324463705492416009896246993950991615005717737886323630334871790740288140033046061512799892371429864110237909925611745163785768204802056985016447086450491884472899152778839120484475953828199840871689380584162839244393022471075
#e1= 3247473589
#e2= 3698409173
#n= 103606706829811720151309965777670519601112877713318435398103278099344725459597221064867089950867125892545997503531556048610968847926307322033117328614701432100084574953706259773711412853364463950703468142791390129671097834871371125741564434710151190962389213898270025272913761067078391308880995594218009110313

flag1= 100156221476910922393504870369139942732039899485715044553913743347065883159136513788649486841774544271396690778274591792200052614669235485675534653358596366535073802301361391007325520975043321423979924560272762579823233787671688669418622502663507796640233829689484044539829008058686075845762979657345727814280
flag2= 86203582128388484129915298832227259690596162850520078142152482846864345432564143608324463705492416009896246993950991615005717737886323630334871790740288140033046061512799892371429864110237909925611745163785768204802056985016447086450491884472899152778839120484475953828199840871689380584162839244393022471075
e1= 3247473589
e2= 3698409173
n= 103606706829811720151309965777670519601112877713318435398103278099344725459597221064867089950867125892545997503531556048610968847926307322033117328614701432100084574953706259773711412853364463950703468142791390129671097834871371125741564434710151190962389213898270025272913761067078391308880995594218009110313
_, s1, s2 = gcdext(e1, e2)
m = (powmod(flag1, s1, n)*(powmod(flag2, s2, n))) % n
print(long_to_bytes(m))
#NSSCTF{xxxxx******xxxxx}

from gmpy2 import *
from Crypto.Util.number import *

flag  = '**********'

p = getPrime(512)
q = next_prime(p)
m1 = bytes_to_long(bytes(flag.encode()))


e = 0x10001
n = p*q


flag1 = pow(m1,e,n)
print('flag= '+str(flag1))
print('n= '+str(n))


flag= 10227915341268619536932290456122384969242151167487654201363877568935534996454863939953106193665663567559506242151019201314446286458150141991211233219320700112533775367958964780047682920839507351492644735811096995884754664899221842470772096509258104067131614630939533042322095150722344048082688772981180270243
n= 52147017298260357180329101776864095134806848020663558064141648200366079331962132411967917697877875277103045755972006084078559453777291403087575061382674872573336431876500128247133861957730154418461680506403680189755399752882558438393107151815794295272358955300914752523377417192504702798450787430403387076153

flag= 10227915341268619536932290456122384969242151167487654201363877568935534996454863939953106193665663567559506242151019201314446286458150141991211233219320700112533775367958964780047682920839507351492644735811096995884754664899221842470772096509258104067131614630939533042322095150722344048082688772981180270243
n= 52147017298260357180329101776864095134806848020663558064141648200366079331962132411967917697877875277103045755972006084078559453777291403087575061382674872573336431876500128247133861957730154418461680506403680189755399752882558438393107151815794295272358955300914752523377417192504702798450787430403387076153

temp = iroot(n, 2)[0]
q = next_prime(temp)
p = n // q
d = inverse(65537, n - p - q + 1)
print(long_to_bytes(powmod(flag, d, n)))
#NSSCTF{no_why}

var="************************************"
flag='NSSCTF{' + base64.b16encode(base64.b32encode(base64.b64encode(var.encode()))) + '}'
print(flag)

小明不小心泄露了源码，输出结果为：4A5A4C564B36434E4B5241544B5432454E4E32465552324E47424758534D44594C4657564336534D4B5241584F574C4B4B463245365643424F35485649534C584A5A56454B4D4B5049354E47593D3D3D，你能还原出var的正确结果吗？

c = "4A5A4C564B36434E4B5241544B5432454E4E32465552324E47424758534D44594C4657564336534D4B5241584F574C4B4B463245365643424F35485649534C584A5A56454B4D4B5049354E47593D3D3D"
base32_bytes = bytes.fromhex(c)
base64_bytes = base64.b32decode(base32_bytes)
var = base64.b64decode(base64_bytes).decode("utf-8")
print("还原的var：", var)
#5e110989-dc43-1bd3-00b4-9009206158fe

#69f7906323b4f7d1e4e972acf4abfbfc,得到的结果用NSSCTF{}包裹。
md5在线解密即可
#md5yyds

#ZmxhZ3tHYXFZN0t0RXRyVklYMVE1b1A1aUVCUkNZWEVBeThyVH0=
base64
#flag{GaqY7KtEtrVIX1Q5oP5iEBRCYXEAy8rT}

#dict:{0: 'J', 1: 'K', 2: 'L', 3: 'M', 4: 'N', 5: 'O', 6: 'x', 7: 'y', 8: 'U', 9: 'V', 10: 'z', 11: 'A', 12: 'B', 13: 'C', 14: 'D', 15: 'E', 16: 'F', 17: 'G', 18: 'H', 19: '7', 20: '8', 21: '9', 22: 'P', 23: 'Q', 24: 'I', 25: 'a', 26: 'b', 27: 'c', 28: 'd', 29: 'e', 30: 'f', 31: 'g', 32: 'h', 33: 'i', 34: 'j', 35: 'k', 36: 'l', 37: 'm', 38: 'W', 39: 'X', 40: 'Y', 41: 'Z', 42: '0', 43: '1', 44: '2', 45: '3', 46: '4', 47: '5', 48: '6', 49: 'R', 50: 'S', 51: 'T', 52: 'n', 53: 'o', 54: 'p', 55: 'q', 56: 'r', 57: 's', 58: 't', 59: 'u', 60: 'v', 61: 'w', 62: '+', 63: '/', 64: '='}

#chipertext:FlZNfnF6Qol6e9w17WwQQoGYBQCgIkGTa9w3IQKw

encode_dict = {
    0: 'J', 1: 'K', 2: 'L', 3: 'M', 4: 'N', 5: 'O', 6: 'x', 7: 'y', 8: 'U', 9: 'V',
    10: 'z', 11: 'A', 12: 'B', 13: 'C', 14: 'D', 15: 'E', 16: 'F', 17: 'G', 18: 'H',
    19: '7', 20: '8', 21: '9', 22: 'P', 23: 'Q', 24: 'I', 25: 'a', 26: 'b', 27: 'c',
    28: 'd', 29: 'e', 30: 'f', 31: 'g', 32: 'h', 33: 'i', 34: 'j', 35: 'k', 36: 'l',
    37: 'm', 38: 'W', 39: 'X', 40: 'Y', 41: 'Z', 42: '0', 43: '1', 44: '2', 45: '3',
    46: '4', 47: '5', 48: '6', 49: 'R', 50: 'S', 51: 'T', 52: 'n', 53: 'o', 54: 'p',
    55: 'q', 56: 'r', 57: 's', 58: 't', 59: 'u', 60: 'v', 61: 'w', 62: '+', 63: '/', 64: '='
}

decode_dict = {v: k for k, v in encode_dict.items()}
ciphertext = "FlZNfnF6Qol6e9w17WwQQoGYBQCgIkGTa9w3IQKw"


def custom_base64_decode(s):
    values = [decode_dict[c] for c in s]

    padding = 0
    if values and values[-1] == 64:
        padding = 1
        if len(values) > 1 and values[-2] == 64:
            padding = 2

    # 移除填充字符
    values = [v for v in values if v != 64]

    # 将数值转换为6位二进制字符串，不足6位的在前面补0
    bits = []
    for v in values:
        bits.append(format(v, '06b'))

    # 合并所有二进制位
    all_bits = ''.join(bits)

    # 按8位分割成字节
    bytes_list = []
    for i in range(0, len(all_bits) - (len(all_bits) % 8), 8):
        byte_bits = all_bits[i:i + 8]
        if len(byte_bits) == 8:  # 确保是完整的8位
            bytes_list.append(int(byte_bits, 2))

    # 根据填充数量移除相应的字节
    if padding > 0:
        bytes_list = bytes_list[:-padding]

    # 转换为字符串并返回
    return bytes(bytes_list).decode('utf-8', errors='replace')

plaintext = custom_base64_decode(ciphertext)
print("解密结果:", plaintext)
#BJD{D0_Y0u_kNoW_Th1s_b4se_map}

from Crypto.Util.number import *
from secret import flag

m = bytes_to_long(flag)
p = getPrime(512)
q = getPrime(512)
e = 65537
n = p*q
c = pow(m,e,n)
print(f'p = {p}')
print(f'q = {q}')
print(f'c = {c}')
'''
p = 12567387145159119014524309071236701639759988903138784984758783651292440613056150667165602473478042486784826835732833001151645545259394365039352263846276073
q = 12716692565364681652614824033831497167911028027478195947187437474380470205859949692107216740030921664273595734808349540612759651241456765149114895216695451
c = 108691165922055382844520116328228845767222921196922506468663428855093343772017986225285637996980678749662049989519029385165514816621011058462841314243727826941569954125384522233795629521155389745713798246071907492365062512521474965012924607857440577856404307124237116387085337087671914959900909379028727767057
'''

p = 12567387145159119014524309071236701639759988903138784984758783651292440613056150667165602473478042486784826835732833001151645545259394365039352263846276073
q = 12716692565364681652614824033831497167911028027478195947187437474380470205859949692107216740030921664273595734808349540612759651241456765149114895216695451
c = 108691165922055382844520116328228845767222921196922506468663428855093343772017986225285637996980678749662049989519029385165514816621011058462841314243727826941569954125384522233795629521155389745713798246071907492365062512521474965012924607857440577856404307124237116387085337087671914959900909379028727767057
n = p*q
d = inverse(65537, n - p - q + 1)
print(long_to_bytes(powmod(c, d, n)))
#LitCTF{it_is_easy_to_solve_question_when_you_know_p_and_q}

from Crypto.Util.number import *
from flag import *

n1 = 103835296409081751860770535514746586815395898427260334325680313648369132661057840680823295512236948953370895568419721331170834557812541468309298819497267746892814583806423027167382825479157951365823085639078738847647634406841331307035593810712914545347201619004253602692127370265833092082543067153606828049061
n2 = 115383198584677147487556014336448310721853841168758012445634182814180314480501828927160071015197089456042472185850893847370481817325868824076245290735749717384769661698895000176441497242371873981353689607711146852891551491168528799814311992471449640014501858763495472267168224015665906627382490565507927272073
e = 65537
m = bytes_to_long(flag)
c = pow(m, e, n1)
c = pow(c, e, n2)

print("c = %d" % c)

# output
# c = 60406168302768860804211220055708551816238816061772464557956985699400782163597251861675967909246187833328847989530950308053492202064477410641014045601986036822451416365957817685047102703301347664879870026582087365822433436251615243854347490600004857861059245403674349457345319269266645006969222744554974358264

n1 = 103835296409081751860770535514746586815395898427260334325680313648369132661057840680823295512236948953370895568419721331170834557812541468309298819497267746892814583806423027167382825479157951365823085639078738847647634406841331307035593810712914545347201619004253602692127370265833092082543067153606828049061
n2 = 115383198584677147487556014336448310721853841168758012445634182814180314480501828927160071015197089456042472185850893847370481817325868824076245290735749717384769661698895000176441497242371873981353689607711146852891551491168528799814311992471449640014501858763495472267168224015665906627382490565507927272073
e = 65537
c = 60406168302768860804211220055708551816238816061772464557956985699400782163597251861675967909246187833328847989530950308053492202064477410641014045601986036822451416365957817685047102703301347664879870026582087365822433436251615243854347490600004857861059245403674349457345319269266645006969222744554974358264
p1 = 10169921435575123642561867469669552661717864247752251361375671837367086221354750692635829007786009042729357644276462913457660789233674358081650339142863821
q1 = 10210039189276167395636779557271057346691950991057423589319031237857569595284598319093522326723650646963251941930167018746859556383067696079622198265424441
p2 = 10210039189276167395636779557271057346691950991057423589319031237857569595284598319093522326723650646963251941930167018746859556383067696079622198265424441
q2 = 11300955505231233842374743324817494386700809291852528704864397779486924493760947925710590633254027339824598181322986060728301639209174112581120081509548753

d2 = inverse(e, n2 - p2 - q2 + 1)
d1 = inverse(e, n1 - p1 - q1 + 1)
print(long_to_bytes(powmod(powmod(c,d2, n2), d1, n1)))
#SangFor{qSccmm1WrgvIg2Uq_cZhmqNfEGTz2GV8}

from Crypto.Util.number import *
from hashlib import md5
from secret import flag

#flag全是由小写字母及数字组成
m=md5(flag).hexdigest()
print(flag[:13]+flag[15:18]+flag[19:34]+flag[35:38])
print(m)
# b'LitCTF{md5can3derypt213thoughcrsh}'
# 496603d6953a15846cd7cc476f146771

known_part = "LitCTF{md5can3derypt213thoughcrsh}"
md5_hash = "496603d6953a15846cd7cc476f146771"
# 我们需要找到 flag[13:15], flag[18:19], flag[34:35]
chars = 'abcdefghijklmnopqrstuvwxyz0123456789'

def find_flag():
    for part1 in itertools.product(chars, repeat=2):
        p1 = ''.join(part1)
        for c2 in chars:
            for c3 in chars:
                flag = f"{known_part[:13]}{p1}{known_part[13:16]}{c2}{known_part[16:31]}{c3}{known_part[31:]}"
                hashed = hashlib.md5(flag.encode()).hexdigest()
                if hashed == md5_hash:
                    print(flag)
                    return flag
    print("未找到匹配的flag")
    return None

if __name__ == "__main__":
    find_flag()
#LitCTF{md5can123dexrypt213thoughcrpsh}

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luig vy cxwpf{Jnxwobuqg_O_Cogiqi!}

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Aut zure Jk kmea ccfnent ow itgkplcknf zx wue Htanesu hamtuxgf. Qa hnbn eaetgv ndez lawm goow nk tvsn wf nzvwgltf hh bhrot dycifrjbuek vg yttrtm in htyslnaazjjlr pwjcodvicqoa uxwl qs. Jk qivr xgecjdrj cpez uh lba cvxlcmfzcfwas bl xcr rskylwtvuw inq yglnhezkwb hrxg. Oy daik jxprgnwx po gnnqr agvapa jhycqcr gpv gwgagwqmvza, shz wr njde pupboneq zqmm oe vzy piry xn ohx eggioa qrvdekf li zifgeww gngky qshxyitvupk, qdipn fwuyj kfyriggkty vtvwlnucz xcr pupfyytvuwa aaj eglnefvxvdrtew. Ndel zxw hnbg tyan qkjn tb zjw pkipk xn jhyvawa aaj xn cbtushcuvtrby. Jk ommp, tukamfbxg, swmuvkbke vt vzy jepkbaige, yzcyh qkwwuaigk iqr Fkyirnzkgh, wnq nxtd gnge, uo wr nxtd gng jyot bl vinxopv, Yjezona ia Ccj, cj Prglm Feogfxo.

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#include <stdio.h>
#include <string.h>
#include <stdlib.h>

int main()
{
freopen("flag.txt","r",stdin);
freopen("flag_encode.txt","w",stdout);
char key[] = /*SADLY SAYING! Key is eaten by Monster!*/;
int len = strlen(key);
char ch;
int index = 0;
while((ch = getchar()) != EOF){
if(ch>='a'&&ch<='z'){
putchar((ch-'a'+key[index%len]-'a')%26+'a');
++index;
}else if(ch>='A'&&ch<='Z'){
putchar((ch-'A'+key[index%len]-'a')%26+'A');
++index;
}else{
putchar(ch);
}
}
return 0;
}

SWZxWl=F=DQef0hlEiSUIVh9ESCcMFS9NF2NXFzM
今年是本世纪的第23年呢

key是23

W型栅栏
BASE64
凯撒密码
#NSSCTF{LeT_Us_H4V3_fU0!!!!!}

from random import choice
from Crypto.Util.number import isPrime, sieve_base as primes
from flag import flag


def getPrime(bits):
    while True:
        n = 2
        while n.bit_length() < bits:
            n *= choice(primes)
        if isPrime(n + 1):
            return n + 1

e = 0x10001
m = int.from_bytes(flag.encode(), 'big')
p, q = [getPrime(2048) for _ in range(2)]
n = p * q
c = pow(m, e, n)

# n = 32849718197337581823002243717057659218502519004386996660885100592872201948834155543125924395614928962750579667346279456710633774501407292473006312537723894221717638059058796679686953564471994009285384798450493756900459225040360430847240975678450171551048783818642467506711424027848778367427338647282428667393241157151675410661015044633282064056800913282016363415202171926089293431012379261585078566301060173689328363696699811123592090204578098276704877408688525618732848817623879899628629300385790344366046641825507767709276622692835393219811283244303899850483748651722336996164724553364097066493953127153066970594638491950199605713033004684970381605908909693802373826516622872100822213645899846325022476318425889580091613323747640467299866189070780620292627043349618839126919699862580579994887507733838561768581933029077488033326056066378869170169389819542928899483936705521710423905128732013121538495096959944889076705471928490092476616709838980562233255542325528398956185421193665359897664110835645928646616337700617883946369110702443135980068553511927115723157704586595844927607636003501038871748639417378062348085980873502535098755568810971926925447913858894180171498580131088992227637341857123607600275137768132347158657063692388249513
# c = 26308018356739853895382240109968894175166731283702927002165268998773708335216338997058314157717147131083296551313334042509806229853341488461087009955203854253313827608275460592785607739091992591431080342664081962030557042784864074533380701014585315663218783130162376176094773010478159362434331787279303302718098735574605469803801873109982473258207444342330633191849040553550708886593340770753064322410889048135425025715982196600650740987076486540674090923181664281515197679745907830107684777248532278645343716263686014941081417914622724906314960249945105011301731247324601620886782967217339340393853616450077105125391982689986178342417223392217085276465471102737594719932347242482670320801063191869471318313514407997326350065187904154229557706351355052446027159972546737213451422978211055778164578782156428466626894026103053360431281644645515155471301826844754338802352846095293421718249819728205538534652212984831283642472071669494851823123552827380737798609829706225744376667082534026874483482483127491533474306552210039386256062116345785870668331513725792053302188276682550672663353937781055621860101624242216671635824311412793495965628876036344731733142759495348248970313655381407241457118743532311394697763283681852908564387282605279108

def pollard(N):
    a = 2
    n = 2
    while True:
        a = powmod(a, n, N)
        p = gcd(a-1, N)
        if p != 1 and p != N:
            return p
        n += 1

n = 32849718197337581823002243717057659218502519004386996660885100592872201948834155543125924395614928962750579667346279456710633774501407292473006312537723894221717638059058796679686953564471994009285384798450493756900459225040360430847240975678450171551048783818642467506711424027848778367427338647282428667393241157151675410661015044633282064056800913282016363415202171926089293431012379261585078566301060173689328363696699811123592090204578098276704877408688525618732848817623879899628629300385790344366046641825507767709276622692835393219811283244303899850483748651722336996164724553364097066493953127153066970594638491950199605713033004684970381605908909693802373826516622872100822213645899846325022476318425889580091613323747640467299866189070780620292627043349618839126919699862580579994887507733838561768581933029077488033326056066378869170169389819542928899483936705521710423905128732013121538495096959944889076705471928490092476616709838980562233255542325528398956185421193665359897664110835645928646616337700617883946369110702443135980068553511927115723157704586595844927607636003501038871748639417378062348085980873502535098755568810971926925447913858894180171498580131088992227637341857123607600275137768132347158657063692388249513
c = 26308018356739853895382240109968894175166731283702927002165268998773708335216338997058314157717147131083296551313334042509806229853341488461087009955203854253313827608275460592785607739091992591431080342664081962030557042784864074533380701014585315663218783130162376176094773010478159362434331787279303302718098735574605469803801873109982473258207444342330633191849040553550708886593340770753064322410889048135425025715982196600650740987076486540674090923181664281515197679745907830107684777248532278645343716263686014941081417914622724906314960249945105011301731247324601620886782967217339340393853616450077105125391982689986178342417223392217085276465471102737594719932347242482670320801063191869471318313514407997326350065187904154229557706351355052446027159972546737213451422978211055778164578782156428466626894026103053360431281644645515155471301826844754338802352846095293421718249819728205538534652212984831283642472071669494851823123552827380737798609829706225744376667082534026874483482483127491533474306552210039386256062116345785870668331513725792053302188276682550672663353937781055621860101624242216671635824311412793495965628876036344731733142759495348248970313655381407241457118743532311394697763283681852908564387282605279108
e = 0x10001

p = pollard(n)
q = n // p
d = invert(e, (p-1)*(q-1))
print(long_to_bytes(powmod(c, d, n)))
#NCTF{Th3r3_ar3_1ns3cure_RSA_m0duli_7hat_at_f1rst_gl4nce_appe4r_t0_be_s3cur3}

from Crypto.Util.number import *
from Crypto.Util.Padding import *

FLAG = bytes_to_long(pad(b"flag{??????}",64))
def init_key():
    p, q = getPrime(512), getPrime(512)
    n = p*q
    e = 9
    while(GCD((p-1)*(q-1),e)!=1):
        p, q = getPrime(512), getPrime(512)
        n = p*q
    d = inverse(e,(p-1)*(q-1))
    return n,e,d

n_list=list()
c_list=list()
for i in range(9):
    N,e,d=init_key()
    n_list.append(N)
    c=pow(FLAG,e,N)
    c_list.append(pow(FLAG,e,N))
    assert(pow(c,d,N)==FLAG)
print("n_list:",n_list)
print("c_list:",c_list)

n_list: [71189786319102608575263218254922479901008514616376166401353025325668690465852130559783959409002115897148828732231478529655075366072137059589917001875303598680931962384468363842379833044123189276199264340224973914079447846845897807085694711541719515881377391200011269924562049643835131619086349617062034608799, 92503831027754984321994282254005318198418454777812045042619263533423066848097985191386666241913483806726751133691867010696758828674382946375162423033994046273252417389169779506788545647848951018539441971140081528915876529645525880324658212147388232683347292192795975558548712504744297104487514691170935149949, 100993952830138414466948640139083231443558390127247779484027818354177479632421980458019929149817002579508423291678953554090956334137167905685261724759487245658147039684536216616744746196651390112540237050493468689520465897258378216693418610879245129435268327315158194612110422630337395790254881602124839071919, 59138293747457431012165762343997972673625934330232909935732464725128776212729547237438509546925172847581735769773563840639187946741161318153031173864953372796950422229629824699580131369991913883136821374596762214064774480548532035315344368010507644630655604478651898097886873485265848973185431559958627423847, 66827868958054485359731420968595906328820823695638132426084478524423658597714990545142120448668257273436546456116147999073797943388584861050133103137697812149742551913704341990467090049650721713913812069904136198912314243175309387952328961054617877059134151915723594900209641163321839502908705301293546584147, 120940513339890268554625391482989102665030083707530690312336379356969219966820079510946652021721814016286307318930536030308296265425674637215009052078834615196224917417698019787514831973471113022781129000531459800329018133248426080717653298100515701379374786486337920294380753805825328119757649844054966712377, 72186594495190221129349814154999705524005203343018940547856004977368023856950836974465616291478257156860734574686154136925776069045232149725101769594505766718123155028300703627531567850035682448632166309129911061492630709698934310123778699316856399909549674138453085885820110724923723830686564968967391721281, 69105037583161467265649176715175579387938714721653281201847973223975467813529036844308693237404592381480367515044829190066606146105800243199497182114398931410844901178842049915914390117503986044951461783780327749665912369177733246873697481544777183820939967036346862056795919812693669387731294595126647751951, 76194219445824867986050004226602973283400885106636660263597964027139613163638212828932901192009131346530898961165310615466747046710743013409318156266326090650584190382130795884514074647833949281109675170830565650006906028402714868781834693473191228256626654011772428115359653448111208831188721505467497494581]
c_list: [62580922178008480377006528793506649089253164524883696044759651305970802215270721223149734532870729533611357047595181907404222690394917605617029675103788705320032707977225447998111744887898039756375876685711148857676502670812333076878964148863713993853526715855758799502735753454247721711366497722251078739585, 46186240819076690248235492196228128599822002268014359444368898414937734806009161030424589993541799877081745454934484263188270879142125136786221625234555265815513136730416539407710862948861531339065039071959576035606192732936477944770308784472646015244527805057990939765708793705044236665364664490419874206900, 85756449024868529058704599481168414715291172247059370174556127800630896693021701121075838517372920466708826412897794900729896389468152213884232173410022054605870785910461728567377769960823103334874807744107855490558726013068890632637193410610478514663078901021307258078678427928255699031215654693270240640198, 14388767329946097216670270960679686032536707277732968784379505904021622612991917314721678940833050736745004078559116326396233622519356703639737886289595860359630019239654690312132039876082685046329079266785042428947147658321799501605837784127004536996628492065409017175037161261039765340032473048737319069656, 1143736792108232890306863524988028098730927600066491485326214420279375304665896453544100447027809433141790331191324806205845009336228331138326163746853197990596700523328423791764843694671580875538251166864957646807184041817863314204516355683663859246677105132100377322669627893863885482167305919925159944839, 2978800921927631161807562509445310353414810029862911925227583943849942080514132963605492727604495513988707849133045851539412276254555228149742924149242124724864770049898278052042163392380895275970574317984638058768854065506927848951716677514095183559625442889028813635385408810698294574175092159389388091981, 16200944263352278316040095503540249310705602580329203494665614035841657418101517016718103326928336623132935178377208651067093136976383774189554806135146237406248538919915426183225265103769259990252162411307338473817114996409705345401251435268136647166395894099897737607312110866874944619080871831772376466376, 31551601425575677138046998360378916515711528548963089502535903329268089950335615563205720969393649713416910860593823506545030969355111753902391336139384464585775439245735448030993755229554555004154084649002801255396359097917380427525820249562148313977941413268787799534165652742114031759562268691233834820996, 25288164985739570635307839193110091356864302148147148153228604718807817833935053919412276187989509493755136905193728864674684139319708358686431424793278248263545370628718355096523088238513079652226028236137381367215156975121794485995030822902933639803569133458328681148758392333073624280222354763268512333515]

n_list = [
   71189786319102608575263218254922479901008514616376166401353025325668690465852130559783959409002115897148828732231478529655075366072137059589917001875303598680931962384468363842379833044123189276199264340224973914079447846845897807085694711541719515881377391200011269924562049643835131619086349617062034608799,
   92503831027754984321994282254005318198418454777812045042619263533423066848097985191386666241913483806726751133691867010696758828674382946375162423033994046273252417389169779506788545647848951018539441971140081528915876529645525880324658212147388232683347292192795975558548712504744297104487514691170935149949,
   100993952830138414466948640139083231443558390127247779484027818354177479632421980458019929149817002579508423291678953554090956334137167905685261724759487245658147039684536216616744746196651390112540237050493468689520465897258378216693418610879245129435268327315158194612110422630337395790254881602124839071919,
   59138293747457431012165762343997972673625934330232909935732464725128776212729547237438509546925172847581735769773563840639187946741161318153031173864953372796950422229629824699580131369991913883136821374596762214064774480548532035315344368010507644630655604478651898097886873485265848973185431559958627423847,
   66827868958054485359731420968595906328820823695638132426084478524423658597714990545142120448668257273436546456116147999073797943388584861050133103137697812149742551913704341990467090049650721713913812069904136198912314243175309387952328961054617877059134151915723594900209641163321839502908705301293546584147,
   120940513339890268554625391482989102665030083707530690312336379356969219966820079510946652021721814016286307318930536030308296265425674637215009052078834615196224917417698019787514831973471113022781129000531459800329018133248426080717653298100515701379374786486337920294380753805825328119757649844054966712377,
   72186594495190221129349814154999705524005203343018940547856004977368023856950836974465616291478257156860734574686154136925776069045232149725101769594505766718123155028300703627531567850035682448632166309129911061492630709698934310123778699316856399909549674138453085885820110724923723830686564968967391721281,
   69105037583161467265649176715175579387938714721653281201847973223975467813529036844308693237404592381480367515044829190066606146105800243199497182114398931410844901178842049915914390117503986044951461783780327749665912369177733246873697481544777183820939967036346862056795919812693669387731294595126647751951,
   76194219445824867986050004226602973283400885106636660263597964027139613163638212828932901192009131346530898961165310615466747046710743013409318156266326090650584190382130795884514074647833949281109675170830565650006906028402714868781834693473191228256626654011772428115359653448111208831188721505467497494581]
c_list = [
   62580922178008480377006528793506649089253164524883696044759651305970802215270721223149734532870729533611357047595181907404222690394917605617029675103788705320032707977225447998111744887898039756375876685711148857676502670812333076878964148863713993853526715855758799502735753454247721711366497722251078739585,
   46186240819076690248235492196228128599822002268014359444368898414937734806009161030424589993541799877081745454934484263188270879142125136786221625234555265815513136730416539407710862948861531339065039071959576035606192732936477944770308784472646015244527805057990939765708793705044236665364664490419874206900,
   85756449024868529058704599481168414715291172247059370174556127800630896693021701121075838517372920466708826412897794900729896389468152213884232173410022054605870785910461728567377769960823103334874807744107855490558726013068890632637193410610478514663078901021307258078678427928255699031215654693270240640198,
   14388767329946097216670270960679686032536707277732968784379505904021622612991917314721678940833050736745004078559116326396233622519356703639737886289595860359630019239654690312132039876082685046329079266785042428947147658321799501605837784127004536996628492065409017175037161261039765340032473048737319069656,
   1143736792108232890306863524988028098730927600066491485326214420279375304665896453544100447027809433141790331191324806205845009336228331138326163746853197990596700523328423791764843694671580875538251166864957646807184041817863314204516355683663859246677105132100377322669627893863885482167305919925159944839,
   2978800921927631161807562509445310353414810029862911925227583943849942080514132963605492727604495513988707849133045851539412276254555228149742924149242124724864770049898278052042163392380895275970574317984638058768854065506927848951716677514095183559625442889028813635385408810698294574175092159389388091981,
   16200944263352278316040095503540249310705602580329203494665614035841657418101517016718103326928336623132935178377208651067093136976383774189554806135146237406248538919915426183225265103769259990252162411307338473817114996409705345401251435268136647166395894099897737607312110866874944619080871831772376466376,
   31551601425575677138046998360378916515711528548963089502535903329268089950335615563205720969393649713416910860593823506545030969355111753902391336139384464585775439245735448030993755229554555004154084649002801255396359097917380427525820249562148313977941413268787799534165652742114031759562268691233834820996,
   25288164985739570635307839193110091356864302148147148153228604718807817833935053919412276187989509493755136905193728864674684139319708358686431424793278248263545370628718355096523088238513079652226028236137381367215156975121794485995030822902933639803569133458328681148758392333073624280222354763268512333515]
n = 1
for i in n_list:
   n = n * i

n_ = []
for i in n_list:
   n_.append(n // i)

t = []
for i in range(9):
   t.append(inverse(n_[i], n_list[i]))

x = 0
for i in range(len(n_list)):
   x = c_list[i] * n_[i] * t[i] + x
x = x % n
print(x)
x = iroot(x, 9)[0]
print(long_to_bytes(x))
flag{H0w_Fun_13_HAstads_broadca5t_AtTack!}

e = 65537
n = 87924348264132406875276140514499937145050893665602592992418171647042491658461
c = 87677652386897749300638591365341016390128692783949277305987828177045932576708

from Crypto.Util.number import *
from secret import flag

m = bytes_to_long(flag)
n  = 1
for i in range(15):
    n *=getPrime(32)
e = 65537
c = pow(m,e,n)
print(f'n = {n}')
print(f'c = {c}')
'''
n = 15241208217768849887180010139590210767831431018204645415681695749294131435566140166245881287131522331092026252879324931622292179726764214435307
c = 12608550100856399369399391849907846147170257754920996952259023159548789970041433744454761458030776176806265496305629236559551086998780836655717
'''

#factordb
e = 65537
n = 87924348264132406875276140514499937145050893665602592992418171647042491658461
c = 87677652386897749300638591365341016390128692783949277305987828177045932576708
p = 275127860351348928173285174381581152299
q = 319576316814478949870590164193048041239
d = inverse(e, n - p - q + 1)
print(long_to_bytes(powmod(c,d,n)))
#LitCTF{factordb!!!}

#yafu

primes = [
    2201440207,
    2719600579,
    4044505687,
    2758708999,
    2923522073,
    3989697563,
    3355651511,
    2151018733,
    4021078331,
    2315495107,
    2906576131,
    2767137487,
    2585574697,
    3354884521,
    4171911923
]

c = 12608550100856399369399391849907846147170257754920996952259023159548789970041433744454761458030776176806265496305629236559551086998780836655717
e = 65537
n = 15241208217768849887180010139590210767831431018204645415681695749294131435566140166245881287131522331092026252879324931622292179726764214435307

phi_factors = [p - 1 for p in primes]
phi = 1
for factor in phi_factors:
    phi *= factor
d = inverse(e, phi)
print(long_to_bytes(powmod(c, d, n)))
#LitCTF{Mu1tiple_3m4ll_prim5_fac7ors_@re_uns4f5}

from Crypto.Util.number import *
m=bytes_to_long(b'xxxxxx')
p=getPrime(256)
q=getPrime(256)
e=74
n=p*q
c=pow(m,e,n)
print("p=",p)
print("q=",q)
print("c=",c)
#p= 86053582917386343422567174764040471033234388106968488834872953625339458483149
#q= 72031998384560188060716696553519973198388628004850270102102972862328770104493
#c= 3939634105073614197573473825268995321781553470182462454724181094897309933627076266632153551522332244941496491385911139566998817961371516587764621395810123

p= 86053582917386343422567174764040471033234388106968488834872953625339458483149
q= 72031998384560188060716696553519973198388628004850270102102972862328770104493
c= 3939634105073614197573473825268995321781553470182462454724181094897309933627076266632153551522332244941496491385911139566998817961371516587764621395810123
e = 74
n = p*q
phi = (p-1)*(q-1)
t = gcd(e, phi)
d = inverse(e // t, phi)
print(long_to_bytes(iroot(powmod(c, d, n), t)[0]))
#LitCTF{e_1s_n0t_@_Prime}

#python
from Crypto.Util.number import *
from gmpy2 import *

n = 125997816345753096048865891139073286898143461169514858050232837657906289840897974068391106608902082960171083817785532702158298589600947834699494234633846206712414663927142998976208173208829799860130354978308649020815886262453865196867390105038666506017720712272359417586671917060323891124382072599746305448903
e = 65537
c = 16076213508704830809521504161524867240789661063230251272973700316524961511842110066547743812160813341691286895800830395413052502516451815705610447484880112548934311914559776633140762863945819054432492392315491109745915225117227073045171062365772401296382778452901831550773993089344837645958797206220200272941
s = 35935569267272146368441512592153486419244649035623643902985220815940198358146024590300394059909370115858091217597774010493938674472746828352595432824315405933241792789402041405932624651226442192749572918686958461029988244396875361295785103356745756304497466567342796329331150560777052588294638069488836419744297241409127729615544668547101580333420563318486256358906310909703237944327684178950282413703357020770127158209107658407007489563388980582632159120621869165333921661377997970334407786581024278698231418756106787058054355713472306409772260619117725561889350862414726861327985706773512963177174611689685575805282

p_q = iroot(iroot((s + 2 * n ** 2), 2)[0] + 2 * n, 2)[0]
phi = n - p_q + 1
d = inverse(e, phi)
print(long_to_bytes(powmod(c, d, n)))

#python
from Crypto.Util.number import *
from tqdm import *

c = 1426774899479339414711783875769670405758108494041927642533743607154735397076811133205075799614352194241060726689487117802867974494099614371033282640015883625484033889861

for i in trange(65536):
    byte_pair = i.to_bytes(2, 'big')
    repeated_bytes = byte_pair * 35
    m2 = bytes_to_long(repeated_bytes)
    m = abs(c - m2)
    if b'palu' in long_to_bytes(m):
        print(long_to_bytes(m))

# sage

from gmpy2 import *
from Crypto.Util.number import *
import hashlib

N = [23796646026878116589547283793150995927866567938335548416869023482791889761195291718895745055959853934513618760888513821480917766191633897946306199721200583177442944168533218236080466338723721813833112934172813408785753690869328477108925253250272864647989241887047368829689684698870160049332949549671046125158024445929082758264311584669347802324514633164611600348485747482925940752960745308927584754759033237553398957651216385369140164712159020014009858771182426893515016507774993840721603911101735647966838456333878426803669855790758035721418868768618171692143354466457771363078719423863861881209003100274869680348729, 19552522218179875003847447592795537408210008360038264050591506858077823059915495579150792312404199675077331435544143983146080988327453540449160493126531689234464110427289951139790715136775261122038034076109559997394039408007831367922647325571759843192843854522333120187643778356206039403073606561618190519937691323868253954852564110558105862497499849080112804340364976236598384571278659796189204447521325485338769935361453819608921520780103184296098278610439625935404967972315908808657494638735904210709873823527111315139018387713381604550946445856087746716671838144925662314348628830687634437271225081272705532826343, 20588310030910623387356293638800302031856407530120841616298227518984893505166480372963166394317326422544430837759332223527939420321960057410073228508230111170414845403161052128790464277007579491219950440477721075788978767309211469555824310913593208232853272958011299985202799390532181335087622499894389777412111445377637396650710486263652440053717323053536700098339137819966260269752816515681602936416736576044630343136577023173210517247609888936337876211461528203642347119434700140264859102502126842250671976238033270367185358966766106988830596616311824691409766437473419074865115209866730272194297815209976737570183, 18468380817178794606027384089796802449939260582378979728469492439450780893746976934315768186829245395964644992296264093276556001477514083927556578752836255491334765496791841945178275793885002188397918857222419803612711637177559554489679414049308077300718317502586411333302434329130562745942681716547306138457088216901181646333860559988117376012816579422902808478175975263110581667936249474308868051767856694498210084853797453949193117835061402537058150493808371384063278793041752943930928932275052745657700368980150842377283198946138726219378646040515809994704174471793592322237777371900834531014326150160506449286179]
E = [229904181453273080302209653709086531153804577507365859149808244958841045687064628362978517491609413507875726243121473678430010600891588643092042173698830147997497783886459583186019270582236955524620567373560535686287255124958954671737097645556109314142383275516997850786599322033792080045303427363366927030304214333894247469120513426641296678531965795930756543043851154646310114366477311633838078242963665452936523438928643273392454483600446242320078010627755587492056369779661382734170244060951095344418599686788550312205964136120979823565225768814898285224838691541122088693411388097496320157113230752327025862802020421665288007529320920942060329299409362236414929126050037144149017275031336018100081931062647888329912802477032857776085190828105602067426203163344931483638271679183910241511044338001446584634203146294743522375846913845041274967653508735863706778364499099286484552570083394223973734909997825522191349543295855925973354640349809770822075226834555111927586299176453943116511915434890643239957459427390624136283086434711471863737451011157026905191204496081860277138227247744470804087252965368757930797560277881668806206419629425126031049566579233056222579590529869798537893505779097868221221068867624660759084762471141, 374749619911728044650812367560174497001343067563440477135516664935394734686391543012901514676044211541958613458868769659861216149364768233000844624035620893309356372294598009760824255187442531508754966566917198975934706398309982525100772311586501118200858124845012643495006029930202324305874402291277845166060497038915773767003006049720519011634861166208163030159519901867416488082395270295488885724507937683469910251316231210838654273986152493722244271430422693265608430755620420680629979226285393465423870727975987787149515374769359243334743541460110042872587610309611770320600248289328406805995688596910226273861759369388105641549933915686192055533242723330981192183310876306968103333706140401422550917946410378174896274789619184565321544130428008804628699594759946577979319393247067750024729672029363433673084437510430506410293512293930056667971242862448029841846596288648691077795207341975907335202945548990662460491169957175452745622341245617265849042542964819126377775749222973138584978725470886059043251544634105653274564085280013340679259157119014619894553239015777411757887293044706448625760604242512494466386343040583010961386979963779928616733980046763291988848903515836247301007113187121999960487508948748354549628160741, 111738429639840672983162926852338651562094139707285850255632987705635459657893186493838711733560515475806567653354737245246745810892238414756414117557971683747269900627524702653772058841085258035513296218047505149691384287812041721130367506731427022265277885965948486359682023555050085264531256406043361391744086539522028829421284667293339869140564699750714145488199268791908205712660933607330454849730499840287271163350865799682565216636393526339218836244889719975150503253630419647851422620890082315396457329065508602521784001607236788620811397449483104884860551374031790663030220424841642241965983726516537123807061999084476076850833658360594525986997125319941689903869138176347916707622148840226672408554102717625456819726220575710494929111642866840516339713870850732638906870325693572445316904688582043485093120585767903009745325497085286577015692005747499504730575062998090846463157669448943725039951120963375521054164657547731579771203443617489609201617736584055562887243883898406182052632245189418568410854530995044542628531851356363297989653392057214167031332353949367816700838296651167799441279086074308299608106786918676697564002641234952760724731325383088682051108589283162705846714876543662335188222683115878319143239781, 185935167438248768027713217055147583431480103445262049361952417166499278728434926508937684304985810617277398880507451351333771783039360671467147075085417403764439214700549777320094501151755362122677245586884124615115132430034242191429064710012407308619977881929109092467325180864745257810774684549914888829203014922855369708286801194645263982661023515570231007900615244109762444081806466412714045462184361892356485713147687194230341085490571821445962465385514845915484336766973332384198790601633964078447446832581798146300515184339036127604597014458389481920870330726947546808739829589808006774479656385317205167932706748974482578749055876192429032258189528408353619365693624106394913101463023497175917598944803733849984703912670992613579847331081015979121834040110652608301633876167262248103403520536210279949844194696898862249482809107840303473964914083996538912970715834110371196970613332286296427286356036576876121010776933023901744994067564045429384172315640135483480089769992730928266885675143187679290648773060781987273082229827156531141515679114580622348238382074084270808291251400949744720804368426414308355267344210055608246286737478682527960260877955900464059404976906697164610891962198768354924180929300959036213841843941]

M = 2^1000  
L = Matrix(ZZ, [
    [M, E[0], E[1], E[2], E[3]],
    [0, -N[0]^2, 0, 0, 0],
    [0, 0, -N[1]^2, 0, 0],
    [0, 0, 0, -N[2]^2, 0],
    [0, 0, 0, 0, -N[3]^2],
])

L = L.LLL()
for row in L:
    if row[0] % M == 0:
        d = abs(row[0] // M)
        if 1 < d < 2^800: 
            print("Found d:", d)
            flag = "palu{" + hashlib.md5(str(d).encode()).hexdigest() + "}"
            print(flag)
            break

#python

import sys

def decrypt(c: bytes, prefix: bytes) -> bytes:
    N = len(c)
    p = bytearray(N)
    L = len(prefix)
    p[:L] = prefix
    for i in range(N - 1):
        if i + 1 >= L:
            p[i + 1] = c[i] ^ p[i]
    return bytes(p)


with open('flag.enc', 'rb') as f:
    ciphertext = f.read()
    known_prefix = b"palu{"
    plaintext = decrypt(ciphertext, known_prefix)
    flag = plaintext.decode('utf-8')

print(flag)

这是使用flask框架编写的RSA广播的空间站系统，你有办法登录并解密密文吗

function downloadAppFile(filename) {
          const iframe = document.createElement('iframe');
          iframe.style.display = 'none';
          document.body.appendChild(iframe);
          const downloadUrl = `/file/download?path=${encodeURIComponent(filename)}`;
          iframe.src = downloadUrl;
          
          setTimeout(() => {
          document.body.removeChild(iframe);
          }, 2000);
          }

downloadAppFile("app.py");

import sqlite3
import os
import hashlib
from flask import Flask, render_template, request, redirect, url_for, session, flash, g,send_file, abort
from Crypto.PublicKey import RSA
from Crypto.Util.number import bytes_to_long, getPrime
import string
from secret import flag    

app = Flask(__name__)
app.secret_key = os.urandom(24) # 用于 session 管理

# 修改数据库路径
# Ensure this line points to the data directory
DATABASE = 'data/users.db'
E = getPrime(7)
NUM_USERS = 128


# assert NUM_USERS >= E 
print(f"E: {E}")
FLAG = flag.encode('utf-8')

def get_db():
    db = getattr(g, '_database', None)
    if db is None:
        # Ensure the directory exists when connecting
        db_dir = os.path.dirname(DATABASE)
        if not os.path.exists(db_dir):
             os.makedirs(db_dir, exist_ok=True)
        db = g._database = sqlite3.connect(DATABASE)
        db.row_factory = sqlite3.Row # 让查询结果可以通过列名访问
    return db

@app.teardown_appcontext
def close_connection(exception):
    db = getattr(g, '_database', None)
    if db is not None:
        db.close()

import random
from gmssl import sm3, func 

def sm3_hash(data):
    """计算数据的 SM3 哈希值"""
    if isinstance(data, str):
        data = data.encode('utf-8')
    hash_bytes = sm3.sm3_hash(func.bytes_to_list(data))
    print(f"计算 {data} 的 SM3 哈希值为: {hash_bytes}")
    return hash_bytes

def generate_rsa_pair(message, e):
    """生成 RSA 公钥 N 和对应的密文 C"""
    key = RSA.generate(1024)
    n = key.n
    m_long = bytes_to_long(message)
    c = pow(m_long, e, n)
    return n, c

def init_db():
    """初始化数据库，创建表并填充用户数据"""
    db_path = os.path.join('/app', DATABASE) # 在容器内的绝对路径
    db_dir = os.path.dirname(db_path)
    os.makedirs(db_dir, exist_ok=True) # 确保容器内的目录存在

    # 检查数据库文件是否存在于容器内的预期路径
    if os.path.exists(db_path):
         print(f"数据库文件 {db_path} 已存在，跳过初始化。")
         # 即使文件存在，也要确保表结构是最新的
         # 可以考虑在这里添加检查表是否存在的逻辑，如果不存在则创建
         # return # 如果确定存在就跳过，否则继续执行建表逻辑

    print(f"初始化数据库 {db_path}...")
    with app.app_context():
        db = get_db()
        cursor = db.cursor()
        # 检查 users 表是否存在
        cursor.execute("SELECT name FROM sqlite_master WHERE type='table' AND name='users';")
        table_exists = cursor.fetchone()

        if not table_exists:
            print("创建 users 表...")
            cursor.execute('''
                CREATE TABLE users (
                    id INTEGER PRIMARY KEY AUTOINCREMENT,
                    username TEXT UNIQUE NOT NULL,
                    password_hash TEXT NOT NULL,
                    n TEXT NOT NULL -- 存储大整数 N
                )
            ''')
            db.commit() # 提交建表操作
        else:
            print("users 表已存在。")
            # 检查是否需要填充数据
            cursor.execute("SELECT COUNT(*) FROM users")
            user_count = cursor.fetchone()[0]
            if user_count >= NUM_USERS:
                print(f"数据库中已有 {user_count} 个用户，跳过填充。")
                return # 如果用户数量足够，则跳过填充

        # --- 填充用户数据的逻辑 ---
        print("开始填充用户数据...")
        generated_n_set = set()
        # 获取当前数据库中的用户数量
        cursor.execute("SELECT COUNT(*) FROM users")
        current_user_count = cursor.fetchone()[0]
        users_added_this_run = 0

        # 从 current_user_count + 1 开始生成用户，直到达到 NUM_USERS
        for i in range(current_user_count, NUM_USERS):
            username = str(i + 1)
            random.seed(username)

            characters = string.ascii_letters + string.digits
            password = "".join(random.choices(characters, k=6))
            password_hash = sm3_hash(password)

            n, c = None, None
            attempts = 0
            max_attempts = NUM_USERS * 5
            while attempts < max_attempts:
                n_candidate, c_candidate = generate_rsa_pair(FLAG, E)
                if n_candidate not in generated_n_set:
                    # 还需要检查数据库中是否已存在此 N
                    cursor.execute("SELECT 1 FROM users WHERE n = ?", (str(n_candidate),))
                    n_exists_in_db = cursor.fetchone()
                    if not n_exists_in_db:
                        n = n_candidate
                        c = c_candidate
                        generated_n_set.add(n)
                        break
                attempts += 1

            if n is None:
                print(f"警告：无法为用户 {username} 生成唯一的 N，已尝试 {max_attempts} 次。")
                continue

            try:
                cursor.execute("INSERT INTO users (username, password_hash, n) VALUES (?, ?, ?)",
                               (username, password_hash, str(n)))
                users_added_this_run += 1
                print(f"添加用户 {username} 到数据库。")
            except sqlite3.IntegrityError:
                print(f"用户名 {username} 已存在或 N 值冲突，跳过。")
            except Exception as e:
                print(f"添加用户 {username} 时出错: {e}")

        db.commit()
        print(f"数据库初始化/填充完成，本次运行添加了 {users_added_this_run} 个用户。")

@app.route('/')
def index():
    if 'username' in session:
        return redirect(url_for('dashboard'))
    return render_template('index.html') 

@app.route('/login', methods=['GET', 'POST'])
def login():
    if request.method == 'POST':
        username = request.form['username']
        password_hash_attempt = sm3_hash(request.form['password_hash'])
        db = get_db()
        cursor = db.cursor()
        cursor.execute("SELECT password_hash FROM users WHERE username = ?", (username,))
        user = cursor.fetchone()

        if  user and user['password_hash'] == password_hash_attempt:
            session['username'] = username
            flash('登录成功！', 'success')
            return redirect(url_for('dashboard'))
        else:
            flash('无效的用户名或密码。', 'error')
            return redirect(url_for('login')) 
    

    if 'username' in session:
        return redirect(url_for('dashboard')) 
    return render_template('index.html')

@app.route('/dashboard')
def dashboard():
    if 'username' not in session:
        flash('请先登录。', 'error')
        return redirect(url_for('login'))

    username = session['username']
    db = get_db()
    cursor = db.cursor()
    cursor.execute("SELECT n  FROM users WHERE username = ?", (username,))
    user_data = cursor.fetchone()

    if not user_data:
        # 用户在 session 中但数据库中找不到？异常情况
        session.pop('username', None)
        flash('发生错误，请重新登录。', 'error')
        return redirect(url_for('login'))

    n = user_data['n']
#     c = user_data['c']
    m = bytes_to_long(FLAG)
    c = str(pow(m, E, int(n)))
    return render_template('dashboard.html', username=username, n=n, c=c, e=E)

@app.route('/logout')
def logout():
    session.pop('username', None)
    flash('您已成功登出。', 'success')
    return redirect(url_for('login'))



@app.route('/file/download', methods=['GET'])
def download_file():
    path = request.args.get('path', '')
    
    if not path:
        return "Error: No path parameter provided", 400
    
    try:

        if not os.path.isabs(path):
            path = os.path.join(os.path.dirname(__file__), path)
        
        if not os.path.exists(path) or not os.path.isfile(path):
            return f"Error: File not found: {path}", 404

        return send_file(
            path,
            as_attachment=True,
            download_name=os.path.basename(path),
            mimetype='application/octet-stream'
        )
    
    except Exception as e:
        return f"Error: {str(e)}", 500


if __name__ == '__main__':
    init_db() # 启动时检查并初始化数据库
    app.run(host='0.0.0.0', port=8000, debug=True)

DATABASE = 'data/users.db'

username = str(i + 1)
            random.seed(username)

            characters = string.ascii_letters + string.digits
            password = "".join(random.choices(characters, k=6))

downloadAppFile("data/users.db"); 

import random
import string
import requests
import re
import sqlite3
from typing import Dict, List, Tuple
from gmpy2 import iroot, invert
from Crypto.Util.number import long_to_bytes


def generate_password(username: str) -> str:
    """根据用户名生成密码"""
    random.seed(username)
    characters = string.ascii_letters + string.digits
    return ''.join(random.choices(characters, k=6))


def get_all_n_from_db(db_path: str) -> Dict[str, int]:
    """从本地数据库获取所有用户的n值"""
    try:
        with sqlite3.connect(db_path) as conn:
            cursor = conn.cursor()
            cursor.execute("SELECT username, n FROM users")
            return {row[0]: int(row[1]) for row in cursor.fetchall()}
    except sqlite3.Error as e:
        print(f"数据库错误: {e}")
        return {}


def collect_c_values(users: Dict[str, int], base_url: str) -> Dict[int, int]:
    """通过HTTP请求收集c值"""
    c_data = {}

    for username, n in users.items():
        password = generate_password(username)
        session = requests.Session()

        # 登录获取session
        try:
            login_resp = session.post(
                f"{base_url}/login",
                data={"username": username, "password_hash": password},
                allow_redirects=False,
                timeout=5
            )

            if login_resp.status_code != 302 or 'dashboard' not in login_resp.headers.get('Location', ''):
                print(f"[!] 用户 {username} 登录失败")
                continue
        except Exception as e:
            print(f"[!] 用户 {username} 登录请求异常: {str(e)}")
            continue

        # 获取dashboard页面
        try:
            dashboard_resp = session.get(f"{base_url}/dashboard", timeout=5)
            if dashboard_resp.status_code != 200:
                print(f"[!] 用户 {username} 访问dashboard失败")
                continue

            # 精确匹配c值
            c_match = re.search(r'<span class="data-value">(\d+)</span>', dashboard_resp.text)
            if c_match:
                c_data[n] = int(c_match.group(1))
                print(f"[+] 成功获取用户 {username} 的 c={c_data[n]}")
            else:
                print(f"[!] 用户 {username} 的c值解析失败")
        except Exception as e:
            print(f"[!] 用户 {username} 请求异常: {str(e)}")

    return c_data


def chinese_remainder_theorem(moduli: List[int], residues: List[int]) -> int:
    """实现中国剩余定理"""
    total = 0
    product = 1

    for m in moduli:
        product *= m

    for m, r in zip(moduli, residues):
        p = product // m
        total += r * invert(p, m) * p

    return total % product


if __name__ == '__main__':
    # 从本地数据库获取所有n值
    print("[+] 正在从本地数据库读取n值...")
    all_users = get_all_n_from_db('users.db')
    print(f"[+] 成功读取 {len(all_users)} 个用户的n值")

    # 收集c值
    e = 71
    URL = 'http://challenge.qsnctf.com:32237'  # 修复了URL中的空格
    print(f"[+] 开始收集 {e} 个用户的c值...")

    c_data = collect_c_values(all_users, URL)

    if len(c_data) < e:
        print(f"[!] 警告：只收集到 {len(c_data)} 个c值，需要至少 {e} 个")

    n_list = list(c_data.keys())[:e]
    c_list = [c_data[n] for n in n_list]

    print("[+] 开始解密流程...")
    M = chinese_remainder_theorem(n_list, c_list)
    m = iroot(M, e)[0]
    flag = long_to_bytes(m)
    print(flag)

在佛经残卷中发现神秘密文，据传加密者用"六道轮回"之法将真言藏于时空循环中。

import base64


def samsara_encrypt(text, key_word):
    cycle_step = len(key_word) % 6 + 1

    phase1 = bytes([(c >> cycle_step) | ((c << (8 - cycle_step)) & 0xFF) for c in text])

    phase2 = base64.b85encode(phase1)

    phase3 = bytes([(c >> cycle_step) | ((c << (8 - cycle_step)) & 0xFF) for c in phase2])

    return bytes([phase3[i] ^ key_word[i % len(key_word)] for i in range(len(phase3))])


if __name__ == "__main__":
    flag = b"palu{********}"  # 可替换flag
    key = b""
    cipher = samsara_encrypt(flag, key)

    # 修复点：使用latin-1编码处理二进制数据
    print("轮回密文:", cipher.decode('latin-1'))  # 输出示例：¨×èÄÅÉØÛÚ

轮回密文: y¦_›6>X¬y–!,!n¡mSaÜñüë—9¼6™

import base64


def samsara_decrypt(cipher_text, key_word):
    # 步骤1: 与关键词异或
    step1 = bytes([cipher_text[i] ^ key_word[i % len(key_word)] for i in range(len(cipher_text))])

    # 计算循环位移量
    cycle_step = len(key_word) % 6 + 1

    # 步骤2: 逆向循环右移（即循环左移cycle_step位）
    step2 = bytes([((c << cycle_step) | (c >> (8 - cycle_step))) & 0xFF for c in step1])

    # 步骤3: Base85解码
    step3 = base64.b85decode(step2)

    # 步骤4: 再次逆向循环右移（即循环左移cycle_step位）
    return bytes([((c << cycle_step) | (c >> (8 - cycle_step))) & 0xFF for c in step3])


if __name__ == "__main__":
    # 密文和密钥
    cipher_text = "y¦_›6>X¬y–!,!n¡mSaÜñüë—9¼6™".encode('latin-1')
    key_word = b"Bore"  # 需要填入正确的密钥

    # 解密
    plain_text = samsara_decrypt(cipher_text, key_word)
    print("解密结果:", plain_text.decode('utf-8', errors='replace'))

# palu{reincarnation_cipher}

from flask import Flask, render_template, request, redirect, url_for, session, flash, send_from_directory, make_response
import os
from gmssl import sm4


def xor(byte1, byte2):
    result = bytes(x ^ y for x, y in zip(byte1, byte2))
    return result


key = os.urandom(16)
iv = os.urandom(16)
sm4_encryption = sm4.CryptSM4()

app = Flask(__name__, template_folder='templates', static_folder='static')
app.secret_key = b'palupalupalupalupalupalupalupalupalu' 
# 保留原始的用户数据访问对象 (DAO)
class UserDAO(object):
    def __init__(self):
        self.users: dict[str, str] = {}

    def getPassword(self, uid: str) -> str:
        if uid not in self.users:
            raise Exception('用户不存在')
        return self.users[uid]

    def create(self, uid: str, password: str):
        if uid in self.users:
            raise Exception('用户已注册')
        self.users[uid] = password
        return

DAO = UserDAO()
DAO.create('demoUser', '123456')

# --- Flask 路由 --- 

@app.route('/')
def index():
    if 'uid' in session:
        return redirect(url_for('profile'))
    return redirect(url_for('login'))

@app.route('/register', methods=['GET', 'POST'])
def register():
    if request.method == 'POST':
        uid = request.form.get('uid')
        if 'admin' in uid:
            flash('不可以是admin哦', 'error')
            return redirect(url_for('register'))
        password = request.form.get('password')
        confirm_password = request.form.get('confirm_password')

        if not uid or not password:
            flash('用户ID和密码不可为空', 'error')
            return redirect(url_for('register'))

        if password != confirm_password:
            flash('两次输入的密码不一致', 'error')
            return redirect(url_for('register'))

        try:
            DAO.create(uid, password)
            flash('注册成功，请登录', 'success')
            return redirect(url_for('login'))
        except Exception as e:
            flash(str(e.args[0]), 'error')
            return redirect(url_for('register'))

    return render_template('register.html')

@app.route('/login', methods=['GET', 'POST'])
def login():
    if request.method == 'POST':
        uid = request.form.get('uid')
        password = request.form.get('password')

        if not uid or not password:
            flash('用户ID和密码不可为空', 'error')
            return redirect(url_for('login'))

        try:
            stored_password = DAO.getPassword(uid)
            if stored_password != password:
                raise Exception('用户ID或密码错误')

            user_level = 'admin' if uid == 'admin' else 'guest'
            
            sm4_encryption.set_key(key, sm4.SM4_ENCRYPT)
            token_payload = f"{uid}:{user_level}".encode('utf-8')
            token = sm4_encryption.crypt_cbc(iv, token_payload).hex()

            session['uid'] = uid
            flash(f'登录成功，您的 token 是: {token}', 'success')
            # 创建响应对象并设置 cookie
            response = make_response(redirect(url_for('profile')))
            response.set_cookie('auth_token', token, httponly=True, samesite='Lax') # 设置 cookie
            return response

        except Exception as e:
            flash(str(e.args[0]), 'error') # 显示更具体的错误信息
            return redirect(url_for('login'))

    return render_template('login.html')

@app.route('/profile')
def profile():
    if 'uid' not in session:
        return redirect(url_for('login'))
    
    # 可以在这里添加解密 token 显示信息的逻辑，但暂时只显示用户名
    username = session.get('uid')
    return render_template('profile.html', username=username)

@app.route('/logout')
def logout():
    session.pop('uid', None)
    flash('您已成功登出', 'info')
    return redirect(url_for('login'))

@app.route('/file', methods=['GET', 'POST'])
def read_file_page():
    if 'uid' not in session :
        flash('请先登录', 'warning')
        return redirect(url_for('login'))
    print(session)
    
    file_content = None
    error_message = None
    file_path_requested = ''

    if request.method == 'POST':
        token = request.cookies.get('auth_token') # 从 cookie 获取 token
        file_path = request.form.get('path')
        file_path_requested = file_path # 保留用户输入的路径以便回显
        if not file_path:
            error_message = '路径不可为空'
        else:
            try:
                # 保留原始的 SM4 CBC 令牌验证逻辑
                sm4_encryption.set_key(key, sm4.SM4_DECRYPT)
                token_decrypted = sm4_encryption.crypt_cbc(iv, bytes.fromhex(token))
                decrypted_str = token_decrypted.decode('utf-8', errors='ignore') 
                parts = decrypted_str.split(':')[-2:]

                uid_from_token, lv = parts

                if 'admin' in lv:
                    print(f"管理员 {uid_from_token} 尝试读取: {file_path}")
                    try:

                        with open(file_path, 'r', encoding='utf-8') as f:
                            file_content = f.read()
                    except FileNotFoundError:
                        error_message = '文件未找到'
                    except Exception as e:
                        print(f"读取文件错误: {e}")
                        error_message = '读取文件失败'
                else:
                    error_message = '非管理员，无权限读取服务器文件'
            except ValueError as e:
                 error_message = f'token非法: {e}'
            except Exception as e:
                print(f"Token 解密/验证错误: {e}")
                error_message = 'token无效或已过期'

    if error_message:
        flash(error_message, 'error')
        
    return render_template('file_viewer.html', file_content=file_content, file_path_requested=file_path_requested)

# 移除 Flask-RESTX 的 404 处理，使用 Flask 默认或自定义模板
@app.errorhandler(404)
def page_not_found(e):
    # 可以创建一个 templates/404.html 页面
    return render_template('404.html'), 404 

if __name__ == '__main__':
    # 确保 static 文件夹存在
    if not os.path.exists('static'):
        os.makedirs('static')
    # 确保 templates 文件夹存在
    if not os.path.exists('templates'):
        os.makedirs('templates')
    # 404 页面
    if not os.path.exists('templates/404.html'):
        with open('templates/404.html', 'w', encoding='utf-8') as f:
            f.write('<!doctype html><title>404 Not Found</title><h1>页面未找到</h1><p>您访问的页面不存在。</p><a href="/">返回首页</a>')

    if not os.path.exists('static/style.css'):
         with open('static/style.css', 'w', encoding='utf-8') as f:
            f.write('''
body { font-family: sans-serif; margin: 20px; background-color: #f4f4f4; }
.container { max-width: 600px; margin: auto; background: #fff; padding: 20px; border-radius: 8px; box-shadow: 0 0 10px rgba(0,0,0,0.1); }
h1 { color: #333; }
.form-group { margin-bottom: 15px; }
label { display: block; margin-bottom: 5px; }
input[type="text"], input[type="password"] { width: calc(100% - 22px); padding: 10px; border: 1px solid #ddd; border-radius: 4px; }
button { background-color: #5cb85c; color: white; padding: 10px 15px; border: none; border-radius: 4px; cursor: pointer; }
button:hover { background-color: #4cae4c; }
a { color: #0275d8; text-decoration: none; }
a:hover { text-decoration: underline; }
.flash-messages { margin-bottom: 15px; }
.alert { padding: 10px; border-radius: 4px; margin-bottom: 10px; }
.alert-error { background-color: #f8d7da; color: #721c24; border: 1px solid #f5c6cb; }
.alert-success { background-color: #d4edda; color: #155724; border: 1px solid #c3e6cb; }
.alert-info { background-color: #d1ecf1; color: #0c5460; border: 1px solid #bee5eb; }
.alert-warning { background-color: #fff3cd; color: #856404; border: 1px solid #ffeeba; }
.file-content { margin-top: 20px; padding: 15px; background-color: #eee; border: 1px solid #ddd; border-radius: 4px; white-space: pre-wrap; word-wrap: break-word; }
nav { margin-bottom: 20px; text-align: right; }
nav span { margin-right: 15px; }
            ''')

    app.run(debug=True, host='0.0.0.0', port=10002)