Crypto

[2024 网鼎杯]？？？

不知道哪一题，朋友发我的

题目

# coding: utf-8
#!/usr/bin/env python2

import gmpy2
import random
import binascii
from hashlib import sha256
from sympy import nextprime
from Crypto.Cipher import AES
from Crypto.Util.Padding import pad
from Crypto.Util.number import long_to_bytes
# from FLAG import flag
flag = 'wdflag{123}'

def victory_encrypt(plaintext, key):
    key = key.upper()
    key_length = len(key)
    plaintext = plaintext.upper()
    ciphertext = ''

    for i, char in enumerate(plaintext):
        if char.isalpha():
            shift = ord(key[i % key_length]) - ord('A')
            encrypted_char = chr((ord(char) - ord('A') + shift) % 26 + ord('A'))
            ciphertext += encrypted_char
        else:
            ciphertext += char

    return ciphertext

victory_key = "WANGDINGCUP"
victory_encrypted_flag = victory_encrypt(flag, victory_key)

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
a = 0
b = 7
xG = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
yG = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
G = (xG, yG)
n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
h = 1
zero = (0,0)

dA = nextprime(random.randint(0, n))

if dA > n:
    print("warning!!")

def addition(t1, t2):
    if t1 == zero:
        return t2
    if t2 == zero:
        return t2
    (m1, n1) = t1
    (m2, n2) = t2
    if m1 == m2:
        if n1 == 0 or n1 != n2:
            return zero
        else:
            k = (3 * m1 * m1 + a) % p * gmpy2.invert(2 * n1 , p) % p
    else:
        k = (n2 - n1 + p) % p * gmpy2.invert((m2 - m1 + p) % p, p) % p
    m3 = (k * k % p - m1 - m2 + p * 2) % p
    n3 = (k * (m1 - m3) % p - n1 + p) % p
    return (int(m3),int(n3))

def multiplication(x, k):
    ans = zero
    t = 1
    while(t <= k):
        if (k &t )>0:
            ans = addition(ans, x)
        x = addition(x, x)
        t <<= 1
    return ans

def getrs(z, k):
    (xp, yp) = P
    r = xp
    s = (z + r * dA % n) % n * gmpy2.invert(k, n) % n
    return r,s

z1 = random.randint(0, p)
z2 = random.randint(0, p)
k = random.randint(0, n)
P = multiplication(G, k)
hA = multiplication(G, dA)
r1, s1 = getrs(z1, k)
r2, s2 = getrs(z2, k)

print("r1 = {}".format(r1))
print("r2 = {}".format(r2))
print("s1 = {}".format(s1))
print("s2 = {}".format(s2))
print("z1 = {}".format(z1))
print("z2 = {}".format(z2))

key = sha256(long_to_bytes(dA)).digest()
cipher = AES.new(key, AES.MODE_CBC)
iv = cipher.iv
encrypted_flag = cipher.encrypt(pad(victory_encrypted_flag.encode(), AES.block_size))
encrypted_flag_hex = binascii.hexlify(iv + encrypted_flag).decode('utf-8')
print(victory_encrypted_flag)
print(encrypted_flag)
print("Encrypted flag (AES in CBC mode, hex):", encrypted_flag_hex)

# output
# r1 = 111817653331957669294460466848850458804857945556928458406600106150268654577388
# r2 = 111817653331957669294460466848850458804857945556928458406600106150268654577388
# s1 = 86614391420642776223990568523561232627667766343605236785504627521619587526774
# s2 = 99777373725561160499828739472284705447694429465579067222876023876942075279416
# z1 = 96525870193778873849147733081234547336150390817999790407096946391065286856874
# z2 = 80138688082399628724400273131729065525373481983222188646486307533062536927379
# ('Encrypted flag (AES in CBC mode, hex):', u'6c201c3c4e8b0a2cdd0eca11e7101d45d7b33147d27ad1b9d57e3d1e20c7b3c2e36b8da3142dfd5abe335a604ce7018878b9f157099211a7bbda56ef5285ec0b')

解题

• SCDSA k复用，可以求出来k
• 求出rA

exp

from hashlib import *
from Crypto.Cipher import AES
from Crypto.Util.number import *


r1 = 111817653331957669294460466848850458804857945556928458406600106150268654577388
r2 = 111817653331957669294460466848850458804857945556928458406600106150268654577388
s1 = 86614391420642776223990568523561232627667766343605236785504627521619587526774
s2 = 99777373725561160499828739472284705447694429465579067222876023876942075279416
z1 = 96525870193778873849147733081234547336150390817999790407096946391065286856874
z2 = 80138688082399628724400273131729065525373481983222188646486307533062536927379
n  = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141

delta_z = (z1 - z2) % n
delta_s = (s1 - s2) % n
k = (delta_z * inverse(delta_s, n)) % n
print(k)
dA = (s1*k-z1)*inverse(r1,n)%n
print(dA == (s2*k-z2)*inverse(r2,n)%n)
key = sha256(long_to_bytes(dA)).digest()
cipher = AES.new(key, AES.MODE_CBC)
cipher.iv = bytes.fromhex("6c201c3c4e8b0a2cdd0eca11e7101d45")
enc = bytes.fromhex("6c201c3c4e8b0a2cdd0eca11e7101d45d7b33147d27ad1b9d57e3d1e20c7b3c2e36b8da3142dfd5abe335a604ce7018878b9f157099211a7bbda56ef5285ec0b")
dec = cipher.decrypt(enc)
print(dec)

def victory_decrypt(ciphertext, key):
    key = key.upper()
    key_length = len(key)
    ciphertext = ciphertext.upper()
    plaintext = ''
    
    for i, char in enumerate(ciphertext):
        if char.isalpha():
            shift = ord(key[i % key_length]) - ord('A')
            decrypted_char = chr((ord(char) - ord('A') - shift + 26) % 26 + ord('A'))
            plaintext += decrypted_char
        else:
            plaintext += char

    return plaintext

victory_key = "WANGDINGCUP"
# 下面手动
flag = victory_decrypt("SDSRDO{58UT00432L8228R9E3G927HDWS8D67G2}", victory_key)
print(flag)

[2024 SICTF]Math Cocktail

题目

from secret import key
x = key
M = 94665789456132156456789461321289656332321
n = 123456789123456789
k = x + pow(x,-1,M)
result = pow(x,n,M) + pow(x,-n,M)
print("k = " + str(k))
flag = "SICTF{"+str(result)+"}"
#k = 15396893775857205606087136852231851457937

解题

• 和校科协的一道免试题一模一样
• 递推就行

exp

M = 94665789456132156456789461321289656332321
k = 15396893775857205606087136852231851457937
n = 123456789123456789
dic = {1:k}
def cal(n):
    if n in dic:
        None
    else:
        if n%2 == 0:
            ans = (cal(n//2)**2-2)%M
            dic[n] = ans
        else:
            ans = (cal(n//2+1)*cal(n//2)-dic[1])%M
            dic[n] = ans
    return dic[n]
print("[+]可能的结果")
print("SICTF{"+str(cal(n))+"}")
print("SICTF{"+str(cal(n)+M)+"}")

[2024 隼目]Math

题目

from Crypto.Util.number import *
from gmpy2 import next_prime
from secrets import flag
l=2331
key=0
for k in range(2**(l-1),2**l):
    s=bin(k)[2:]
    if(k%2==1 and '1111' not in s and '0000' not in s):
        key+=1
p=next_prime(key)
q=getPrime(2048)
n=p*q
e=65537
m=bytes_to_long(flag)
c=pow(m,e,n)
print(f'n=',n)
print(f'c=',c)

'''
n=739243847275389709472067387827484120222494013590074140985399787562594529286597003777105115865446795908819036678700460141950875653695331369163361757157565377531721748744087900881582744902312177979298217791686598853486325684322963787498115587802274229739619528838187967527241366076438154697056550549800691528794136318856475884632511630403822825738299776018390079577728412776535367041632122565639036104271672497418509514781304810585503673226324238396489752427801699815592314894581630994590796084123504542794857800330419850716997654738103615725794629029775421170515512063019994761051891597378859698320651083189969905297963140966329378723373071590797203169830069428503544761584694131795243115146000564792100471259594488081571644541077283644666700962953460073953965250264401973080467760912924607461783312953419038084626809675807995463244073984979942740289741147504741715039830341488696960977502423702097709564068478477284161645957293908613935974036643029971491102157321238525596348807395784120585247899369773609341654908807803007460425271832839341595078200327677265778582728994058920387721181708105894076110057858324994417035004076234418186156340413169154344814582980205732305163274822509982340820301144418789572738830713925750250925049059
c=229043746793674889024653533006701296308351926745769842802636384094759379740300534278302123222014817911580006421847607123049816103885365851535481716236688330600113899345346872012870482410945158758991441294885546642304012025685141746649427132063040233448959783730507539964445711789203948478927754968414484217451929590364252823034436736148936707526491427134910817676292865910899256335978084133885301776638189969716684447886272526371596438362601308765248327164568010211340540749408337495125393161427493827866434814073414211359223724290251545324578501542643767456072748245099538268121741616645942503700796441269556575769250208333551820150640236503765376932896479238435739865805059908532831741588166990610406781319538995712584992928490839557809170189205452152534029118700150959965267557712569942462430810977059565077290952031751528357957124339169562549386600024298334407498257172578971559253328179357443841427429904013090062097483222125930742322794450873759719977981171221926439985786944884991660612824458339473263174969955453188212116242701330480313264281033623774772556593174438510101491596667187356827935296256470338269472769781778576964130967761897357847487612475534606977433259616857569013270917400687539344772924214733633652812119743
'''