标签：int expr CryptoSystem recvuntil print import Paillier pow

Paillier CryptoSystem

Introduce

一种较新的非对称加密模式，一种支持加法同态的公钥密码系统。

Key Generation

常见加密方式有两种，下面给出参数选取方式

Encryption

Decryption

Proof

Homomorphic properties

Problem

DASCTF Apr not RSA

from Crypto.Util.number import getPrime as bytes_to_long
from secret import flag,p,q
from sympy import isprime,nextprime
import random
m=bytes_to_long(flag)
n=p*q
g=n+1
r=random.randint(1,n)
c=(pow(g,m,n*n)*pow(r,n,n*n))%(n*n)
print "c=%d"%(c)
print "n=%d"%(n)

第二类加密方式
exp：

from Crypto.Util.number import long_to_bytes,inverse
from sympy import nextprime
from gmpy2 import iroot
def L(x,n):
    return (x-1)/n
c=
n=
#factor(n)
a = iroot(n,2)[0]
p = nextprime(a)
q = n//p
assert p*q == n
Lambda = (p-1)*(q-1)
miu = inverse(Lambda,n)
m = (L(pow(c,Lambda,n**2),n)*miu)%n
print long_to_bytes(m)

2022BytesCTF compare

from Crypto.Util.number import getPrime, getRandomNBitInteger, inverse
from fractions import Fraction
from gmpy2 import lcm
import re

N = 512
safe_expr = re.compile(r'^([-+*/0-9.~%^&()=|<>]|and|or|not|MSG)+$')

def encode(m, n, g):
    r = getRandomNBitInteger(N)
    c = pow(g, m, n*n) * pow(r, n, n*n) % (n*n)
    return c

def decode(c, n, l, u):
    return int(Fraction(pow(c, l, n * n) - 1, n) * u % n)

def round(expr):
    p = getPrime(N)
    q = getPrime(N)

    n = p * q
    g = getRandomNBitInteger(N)
    print('n =', n)
    print('g =', g)

    a = getRandomNBitInteger(N)
    b = getRandomNBitInteger(N)

    print('a =', encode(a, n, g))
    print('b =', encode(b, n, g))

    msg = int(input("msg = "))

    l = int(lcm(p - 1, q - 1))
    u = inverse(Fraction(pow(g, l, n * n) - 1, n), n)

    return (a > b) is bool(eval(expr, None, {'MSG': decode(msg, n, l, u)}))

def main():
    expr = input('Hello, Give me your expr: ')
    expr = re.sub(r'\s', '', expr)

    if safe_expr.match(expr) is None:
        raise Exception('Hacker?')

    for i in range(100):
        print('Round:', i)
        try:
            assert round(expr)
        except:
            print('You lost.')
            break
    else:
        print('Congratulations!')
        print(open('/flag').read())

if __name__ == '__main__':
    main()

from pwn import *
from Crypto.Util.number import *
import gmpy2
p=remote('ip')
p.recvuntil(b'Hello, Give me your expr: ')
p.sendline(b'MSG < 2**512')
for i in range(100):
    p.recvuntil(b'n = ')
    n=int(p.recvuntil(b'\n')[:-1].decode())
    mod=n*n
    p.recvuntil(b'a =')
    a=int(p.recvuntil(b'\n')[:-1].decode())
    p.recvuntil(b'b =')
    b=int(p.recvuntil(b'\n')[:-1].decode())
    msg=a*gmpy2.invert(b,mod)%mod
    p.sendline(str(msg).encode())
    print(i)
p.interactive()

标签：int,expr,CryptoSystem,recvuntil,print,import,Paillier,pow
From： https://www.cnblogs.com/App1eTree/p/17064345.html