Magic RSA Writeup

Solved by: Legend

• We are given a python code containing how the flag.txt is getting encrypted with RSA and an output.txt containing the cipher.

from secrets import randbits
from sympy import nextprime

e = 3

def encrypt(inp):
        p = nextprime(randbits(2048))
        q = nextprime(randbits(2048))
        n = p * q
        enc = [pow(ord(c), e, n) for c in inp]
        return [n, enc]

plaintext = open('flag.txt').read()

with open('output.txt', 'w') as f:
    data = encrypt(plaintext)
    f.write(f'Semiprime:\nN: {data[0]}\nCiphertext:\n')
    f.write(''.join(f'{b} ' for b in data[1]))
    f.write('\n\n')

• I used ChatGPT to make a script to solve it.

import gmpy2

N = 292661735803169078279687796534368733968232055929694715453717384181208539846645017378459508481927733219065809706996972833902743250671173212610674572380079245835772007065919936022084401497853611610920914306013040436502207047619016113234947051878549793269852855316328078769491183468515501156324665790842023112309668506350354977653838139155232422868462129041940364012648613391176971689126513558396465218392059219609662829793402841289708970576750698757213264731256720405308346659459733504680423032430634001779369250142543104703669906030549585514247663929431837546466696121103600101025434247152431200408744676625328330247569014313252820778269086840631297075563756934662979588351413726196027845505808290890109883253252054958997436359016852222176230489468164288277709046892991459049248340800616885136366469783271661343653314539194467688757972713531491290238432270971346559967725437118531023032768463200227986539449334624183071042562539584305305367245588508498775214112729500313280502474837332653452065755426475638743763861804587979560695676963674789819860296303566053542883415223272958687917330474367563315425617320128680682444959701586681495270336801802382200546403246134181793704030611664095075430115127507174884551339452808218398863888817

ciphertext = [
    1061208, 1259712, 912673, 1092727, 1860867, 175616, 166375, 941192, 185193, 1030301,
    941192, 185193, 912673, 140608, 175616, 185193, 140608, 941192, 970299, 1061208,
    175616, 912673, 117649, 912673, 185193, 148877, 912673, 125000, 110592, 1030301,
    132651, 132651, 1061208, 117649, 117649, 1061208, 166375, 1953125
]

def integer_cube_root(n):
    return int(gmpy2.iroot(n, 3)[0])

plaintext_ascii = []
for c in ciphertext:
    ascii_value = integer_cube_root(c)
    plaintext_ascii.append(ascii_value)

flag = ''
for ascii_value in plaintext_ascii:
    flag += chr(ascii_value)

print(f'Flag: {flag}')

Flag: flag{87b9eb9a4894bcf8a1a95a20e33f11f7}