[CISCN 2022 东北赛区]math

题目展现

import gmpy2
from Crypto.Util.number import *
from flag import flag
assert flag.startswith(b"flag{")
assert flag.endswith(b"}")
message=bytes_to_long(flag)
def keygen(nbit, dbit):
    if 2*dbit < nbit:
        while True:
            a1 = getRandomNBitInteger(dbit)
            b1 = getRandomNBitInteger(nbit//2-dbit)

            n1 = a1*b1+1

            if isPrime(n1):
                break
        while True:
            a2 = getRandomNBitInteger(dbit)
            b2 = getRandomNBitInteger(nbit//2-dbit)

            n2=a2*b2+1

            n3=a1*b2+1
            if isPrime(n2) and isPrime(n3):
                break
        while True:
            a3=getRandomNBitInteger(dbit)
            if gmpy2.gcd(a3,a1*b1*a2*b2)==1:
                v1=(n1-1)*(n2-1) # phi1
                k=(a3*inverse(a3,v1)-1)//v1  # k * phi1=k * v1 = ed-1
                v2=k*b1+1
                if isPrime(v2):
                    return a3,n1*n2,n3*v2
def encrypt(msg, pubkey):
    return pow(msg, pubkey[0], pubkey[1])

nbit = 1024
dbit = 256
e, n1, n2=keygen(nbit, dbit)
print('e =', e)
print('n1 =', n1)
print('n2 =', n2)
c1 = encrypt(message, [e, n1])
c2 = encrypt(message, [e, n2])
print('enc1 =', c1)
print('enc2 =', c2)
# e = 86905291018330218127760596324522274547253465551209634052618098249596388694529
# n1 = 11218