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TheTank20andWitherOrNot
f7427792e3
* Add Wither's gists as references * remove broken ones --------- Co-authored-by: WitherOrNot <damemem@gmail.com>
12 KiB
12 KiB
In [ ]:
# Windows 7 Retail/GVLK, public key ID 170
pubkey_data = {
"field": {
"modulus": 886368969471450739924935101400677,
"ec_base_order": 886368969471450710152985728350703,
"k3_minpoly": [
4,
1,
0,
1
],
"k6_minpoly": [
2,
0,
1
]
},
"h1_bases": [
1,
3,
8,
15,
15,
15,
31,
3,
3,
3,
3,
3,
7,
63
],
"curve": {
"a": 26392827536965106777121445123290,
"b": 372325368096095544195525883520589
},
"points": [
{
"x": [
365236101742748463929673543888206,
858097895593939865996182272259769,
148438159087534462792506738986740
],
"y": [
776418047571862972603801173382237,
873677028107508092012208744232957,
622138327043805563266794621920098
]
},
{
"x": [
940136574680879136511599445781,
566978253317108608042529258054523,
176284220413545220121710961573292
],
"y": [
828856809691743749590800150937649,
225146018128364550960496522448712,
348601659612301002638949468744847
]
},
{
"x": [
733747358623171948496764545320051,
728506535527490173098593825125337,
82462451162574422717677160727098
],
"y": [
416331132638004657079841565104549,
366794872410090667339979925100938,
154519017608105570119249112044121
]
},
{
"x": [
849718119860311390685018324089317,
69736499980142833460080381132368,
72139323263966224829624934948858
],
"y": [
122550620604034160835298121626961,
232865179257577260620478614346661,
96495922331236902442197840422963
]
},
{
"x": [
737949449696062407373114808812927,
526576673882551145431025311648593,
577710732700754839750249914833193
],
"y": [
245977198113437420529250724111432,
316396368275232555978824338443046,
755792900000892204654488821885538
]
},
{
"x": [
712586405875738967442641545880322,
615445286425878710157557053762371,
734183236086095230968388017605820
],
"y": [
851284376759840359812981263306021,
769237654873203944088649987250083,
359324880331507581802773028306633
]
},
{
"x": [
579665839598807564349118802507078,
793103874095793223248478622956780,
502860226530799804560661048077280
],
"y": [
526775274489316486107329470634542,
828721161962151275145535457964404,
204415317809040518371881977645416
]
},
{
"x": [
804790447447351785544412956578788,
119046642031064430140912082580578,
475159529884254928674792290619954
],
"y": [
458245266057063984580129835988070,
338411981227059768831710308435687,
577923375329917551735757167190702
]
},
{
"x": [
448295070796654878810211055051604,
482910785083759911781193909334072,
795628820954832750108065551162801
],
"y": [
417757375223493128894380427308216,
755520039102173573177271365439537,
863842006193777913816171128026446
]
},
{
"x": [
663389221842281261857262032548436,
846447543951704162020988219326272,
686142287698732386980948449542167
],
"y": [
769015970121598916167134609518482,
738460771147019950148429256265493,
613009789239563486872501072748270
]
},
{
"x": [
23530113060362511985797534739195,
718131004725002854064127778364823,
140870968646848990835780066321375
],
"y": [
641031697928634900295866764583620,
295544383156746469642549388283327,
133766761871461067699690599056442
]
},
{
"x": [
7518354584460889742005963384331,
340825540582760123772991939806390,
525549834323799848592419044187971
],
"y": [
585295007893871934790357000030208,
117490751031779271453224407217079,
838852298106199238437827740364400
]
},
{
"x": [
806036388470182281562651653929939,
266085928879449679004785507000719,
201474020142460453395308745398496
],
"y": [
573468377549807523205344415925956,
667459718759242575444856430313959,
226975716159080217447594275999935
]
},
{
"x": [
794167987155642331621801361756614,
809201520617560616339201020039820,
198696155869194654384403079624544
],
"y": [
725959545288387914551997303844726,
49262476800238214847233993847181,
537326577113493149345527624223733
]
}
],
"pairing_val": [
[
242940802691096077821709859741616,
178851543248946074944443141484182,
802059826004050667481466713086225
],
[
701042518368651902930590425782509,
265571225406900742458432149860962,
699432283102586243018242179516873
]
]
}In [ ]:
p = pubkey_data["field"]["modulus"]
a = pubkey_data["curve"]["a"]
b = pubkey_data["curve"]["b"]
order = pubkey_data["field"]["ec_base_order"]
h1_bases = list(map(lambda x: x+1, pubkey_data["h1_bases"]))
KCHARS = "BCDFGHJKMPQRTVWXY2346789"
def decode_pkey(k):
k = k.replace("-", "")
out = 0
for c in k:
out *= 24
out += KCHARS.index(c)
return out
K = GF(p)
Kx.<x> = K[]
K3.<u> = K.extension(Kx(pubkey_data["field"]["k3_minpoly"]))
K3y.<y> = K3[]
K6.<t> = K3.extension(K3y(pubkey_data["field"]["k6_minpoly"]))
E = EllipticCurve(K, [a, b])
E6 = EllipticCurve(K6, [a, b])
Qi = [E6(K3(point["x"]) * t^-2, K3(point["y"]) * t^-3) for point in pubkey_data["points"]]
# pairing_val = e_m(P, S)
pairing_val = K6([K3(pubkey_data["pairing_val"][0]), K3(pubkey_data["pairing_val"][1])])
assert is_prime(p)
assert len(h1_bases) == len(Qi)
assert h1_bases[0] == 2
assert pairing_val^order == 1In [ ]:
pkey_chars = "33PXH-7Y6KF-2VJC9-XBBR8-HVTHH"
# pkey = HASH(M)
# HASH is a currently unknown hash function
pkey = decode_pkey(pkey_chars)
# h1_coeffs = H1(M)
# During validation, coeffs must be found by a search that i havent implemented
# h1_coeffs = [1, 0, 7, 1, 4, 15, 9, 1, 1, 0, 2, 1, 0, 19]
# 10 bits unknown, 30 bits product ID, 1 bit unknown (upgrade?)
key_data = (342 << 31 | 918500000 << 1 | 0)
h1_coeffs = [1]
for i in range(len(h1_bases) - 1):
h1_coeffs.append(key_data % h1_bases[i + 1])
key_data //= h1_bases[i + 1]
print(h1_coeffs)
# H2(M) = E.lift_x(HASH(M) % p)
T = E6(E.lift_x(pkey % p))
Q = sum(map(lambda x: x[0] * x[1], zip(h1_coeffs, Qi)))
test_pairing = T.tate_pairing(Q, order, 6, q=p)
print(test_pairing == pairing_val or test_pairing == 1/pairing_val)
key_data = 0
for i in range(len(h1_bases) - 1, 0, -1):
key_data *= h1_bases[i]
key_data += h1_coeffs[i]
print(h1_bases[i], h1_coeffs[i], key_data)
pid = (key_data & ((1 << 31) - 1)) >> 1