SRA
400 points
AUTHOR: F0XTR0T
Description
I just recently learnt about the SRA public key cryptosystem… or wait, was it supposed to be RSA? Hmmm, I should probably check…
Connect to the program on our server: your port
Requirements
sudo apt install sagemath
sage-python -m pip install pwn
sage-python -m pip install pycryptodome
the script below will do it smoothly and it is important to remember to enter port number for your instance
from sage.all import *
from pwn import *
from gmpy2 import is_prime
from string import ascii_letters, digits
from Crypto.Util.number import bytes_to_long, long_to_bytes, inverse
r = remote('saturn.picoctf.net', your port)
def is_printable(text):
alphabet = ascii_letters + digits
for i in text:
if i not in alphabet:
return False
return True
e = 65537
r.recvuntil(b'anger = ')
c = int(r.recvline().strip().decode())
r.recvuntil(b'envy = ')
d = int(r.recvline().strip().decode())
r.recvline()
print(c)
print(d)
K = divisors(d*e - 1)
print("Done")
list_prime = []
for k in K:
pp = ((d*e - 1)//k) + 1
if is_prime(pp) and int(pp).bit_length() == 128:
list_prime.append(pp)
list_text = []
for p in list_prime:
for q in list_prime:
try:
if inverse(e, (p - 1) * (q - 1)) == d:
n = p*q
list_text.append(long_to_bytes(int(pow(c, d, n))))
except:
pass
list_text = set(list_text)
for text in list_text:
try:
text = text.decode()
if is_printable(text):
print(text)
r.recvuntil(b'> ')
r.sendline(text.encode())
print(r.recvline())
print(r.recvline())
print(r.recvline())
break
except:
continue
r.close()
