def search_k(group, mink, maxk, sig, h):
precomp = dsa.prepare_recover_x(group, sig)
print 'search from', '%08x..%08x' % (mink, maxk), 'starting'
for k in xrange(mink, maxk):
# k value has entropy at top 32 bits, and assume key has 256-bit q
k = k << 224
x = dsa.recover_x_given_sig_k(group, k, sig, h, precomp)
# check if we got a working private key by checking if it yields
# our known public value
if pow(group.g, x, group.p) == pubkey:
print 'found key, x =', x
break
print 'search from', '%08x..%08x' % (mink, maxk), 'finished'
def search_k(group, mink, maxk, sig, h):
precomp = dsa.prepare_recover_x(group, sig)
print 'search from', '%08x..%08x' % (mink, maxk), 'starting'
for k in xrange(mink, maxk):
# k value has entropy at top 32 bits, and assume key has 256-bit q
k = k << 224
x = dsa.recover_x_given_sig_k(group, k, sig, h, precomp)
# check if we got a working private key by checking if it yields
# our known public value
if pow(group.g, x, group.p) == pubkey:
print 'found key, x =', x
break
print 'search from', '%08x..%08x' % (mink, maxk), 'finished'
m='d6340bfcda59b6b75b59ca634813d572de800e8f')
]
if __name__ == '__main__':
pub = (group, y)
# check signatures for sanity
for s in sigs:
sig = (s['r'], s['s'])
dsa.verify_sha1(pub, sig, s['msg'])
# look at all pairs for signatures and see if key falls out
for i1, d1 in enumerate(sigs):
for i2, d2 in enumerate(sigs):
if i1 == i2:
continue
m1 = dsa.hash(d1['msg'])
m2 = dsa.hash(d2['msg'])
s1 = d1['s']
s2 = d2['s']
sd = (s1 - s2) % group.q
invsd = rsa.invmod(sd, group.q)
k = (((m1 - m2) % group.q) * invsd) % group.q
x = dsa.recover_x_given_sig_k(group, k, (d1['r'], d1['s']),
d1['msg'])
if dsa.sha1('%x' % x).hexdigest() == hash_x:
print 'i1: %d, i2: %d, k: 0x%x, x: 0x%x' % (i1, i2, k, x)
exit(0)
import dsa
p = 0x800000000000000089e1855218a0e7dac38136ffafa72eda7859f2171e25e65eac698c1702578b07dc2a1076da241c76c62d374d8389ea5aeffd3226a0530cc565f3bf6b50929139ebeac04f48c3c84afb796d61e5a4f9a8fda812ab59494232c7d2b4deb50aa18ee9e132bfa85ac4374d7f9091abc3d015efc871a584471bb1
q = 0xf4f47f05794b256174bba6e9b396a7707e563c5b
g = 0x5958c9d3898b224b12672c0b98e06c60df923cb8bc999d119458fef538b8fa4046c8db53039db620c094c9fa077ef389b5322a559946a71903f990f1f7e0e025e2d7f7cf494aff1a0470f5b64c36b625a097f1651fe775323556fe00b3608c887892878480e99041be601a62166ca6894bdd41a7054ec89f756ba9fc95302291
y = 0x84ad4719d044495496a3201c8ff484feb45b962e7302e56a392aee4abab3e4bdebf2955b4736012f21a08084056b19bcd7fee56048e004e44984e2f411788efdc837a0d2e5abb7b555039fd243ac01f0fb2ed1dec568280ce678e931868d23eb095fde9d3779191b8c0299d6e07bbb283e6633451e535c45513b2d33c99ea17
hash_x = '0954edd5e0afe5542a4adf012611a91912a3ec16'
group = dsa.group(p, q, g)
if __name__ == '__main__':
# smoke test
pub, priv = dsa.gen_pair(group)
msg = 'fart'
sig = dsa.sign_sha1(priv, msg)
dsa.verify_sha1(pub, sig, msg)
msg = "For those that envy a MC it can be hazardous to your health\nSo be friendly, a matter of life and death, just like a etch-a-sketch\n"
pub = (group, y)
sig = (548099063082341131477253921760299949438196259240, 857042759984254168557880549501802188789837994940)
dsa.verify_sha1(pub, sig, msg)
# brute force value for k
for k in range(0, 2**16):
x = dsa.recover_x_given_sig_k(group, k, sig, msg)
# check using known hash (could also use pubkey = g^x mod p)
if dsa.sha1('%x' % x).hexdigest() == hash_x:
print 'k: 0x%x, x: 0x%x' % (k, x)
break
r = 228998983350752111397582948403934722619745721541,
m = 'd6340bfcda59b6b75b59ca634813d572de800e8f')
]
if __name__ == '__main__':
pub = (group, y)
# check signatures for sanity
for s in sigs:
sig = (s['r'], s['s'])
dsa.verify_sha1(pub, sig, s['msg'])
# look at all pairs for signatures and see if key falls out
for i1, d1 in enumerate(sigs):
for i2, d2 in enumerate(sigs):
if i1 == i2:
continue
m1 = dsa.hash(d1['msg'])
m2 = dsa.hash(d2['msg'])
s1 = d1['s']
s2 = d2['s']
sd = (s1 - s2) % group.q
invsd = rsa.invmod(sd, group.q)
k = (((m1 - m2) % group.q) * invsd) % group.q
x = dsa.recover_x_given_sig_k(group, k, (d1['r'], d1['s']), d1['msg'])
if dsa.sha1('%x' % x).hexdigest() == hash_x:
print 'i1: %d, i2: %d, k: 0x%x, x: 0x%x' % (i1, i2, k, x)
exit(0)
