recover_ecdsa.ex

from ecdsa import SigningKey
from ecdsa import VerifyingKey
import ecdsa
from ecdsa.numbertheory import inverse_mod
import hashlib
import binascii
import base64

curve_order = ecdsa.curves.NIST192p.order

# PRIME192v1, secp224r1, prime256v1, SECP384r1, and secp521r1 , SECP256k1

def string_to_number(tstr):
    return int(binascii.hexlify(tstr), 16)

def sha1(content):
    sha1_hash = hashlib.sha1()
    sha1_hash.update(content)
    return sha1_hash.digest()

def recover_key(c1, sig1, c2, sig2):

    n = curve_order

    # cut up the strings before we convert to number!
    s1 = string_to_number(sig1[-24:])
    s2 = string_to_number(sig2[-24:])
    r = string_to_number(sig1[-48:-24])

    z1 = string_to_number(sha1(c1))
    z2 = string_to_number(sha1(c2))

    # solve
    sdelta_inv = inverse_mod(((s1-s2)%n),n)
    k = ( ((z1-z2)%n) * sdelta_inv) % n
    inverse_r = inverse_mod(r,n)
    da = (((((s1*k) %n) -z1) %n) * inverse_r) % n
    print "n: " + str(n)
    print "da: " + str(da)
    recovered_private_key = SigningKey.from_secret_exponent(da, ecdsa.curves.NIST192p)
    return recovered_private_key.to_pem()

if __name__ == "__main__":

    challenge1 = '''
    {"session_id": "6621a96c7db568374f2885d6d135f395010e75a94ec2233a433ff8e2", "user": "peter"}
    '''
    sig1 = '''
    znnlVaDhCokfqzU5figrY2cZ1nk87rH/zcCHDV2rLJ6nhdjE9vzblfpkzrhqzVjY
    '''.strip()

    challenge2 = '''
    {"session_id": "9027072a68c41cf9fcaa92672091f7184b13b577924408ed25d971a5", "user": "peter"}
    '''
    sig2 = '''
    znnlVaDhCokfqzU5figrY2cZ1nk87rH/h9DI/NbP5Mk+XGpYdJHWvJCXToXsMhP6
    '''.strip()

    key = recover_key(challenge1,base64.b64decode(sig1),challenge2,base64.b64decode(sig2))
    print key

    #create the signature
    sk = SigningKey.from_pem(key)
    challenge = '''
    {"session_id": "6621a96c7db568374f2885d6d135f395010e75a94ec2233a433ff8e2", "user": "admin"}
    '''
    vk = sk.get_verifying_key()
    signature = sk.sign(challenge)
    try:
        # because who trusts python
        vk.verify(signature, challenge)
        print "good signature"
    except BadSignatureError:
        print "BAD SIGNATURE"
    encoded_signature = base64.b64encode(signature)
    print(encoded_signature)