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| from sage.all import GF
from pwn import process, remote
from fastecdsa import keys, point
import ast, random
from tss2 import hash_transcript, verify, curve, TARGET
from tqdm import tqdm
from concurrent.futures import ThreadPoolExecutor
sk2, pk2 = keys.gen_keypair(curve)
def connect(i):
io = remote("challs.actf.co", 31302)
return io
def sign(sk, pk, msg):
k, R = keys.gen_keypair(curve)
c = hash_transcript(pk, R, msg)
s = (k - c * sk) % curve.q
return c, s
def establish(io, sk2, pk2):
io.recvuntil(b"my public key: ")
pk_tpl = ast.literal_eval(io.recvline().strip().decode())
pk1 = point.Point(*pk_tpl, curve=curve)
io.sendlineafter(b"x: ", str(pk2.x).encode())
io.sendlineafter(b"y: ", str(pk2.y).encode())
c, s = sign(sk2, pk2, b"foo")
io.sendlineafter(b"c: ", str(c).encode())
io.sendlineafter(b"s: ", str(s).encode())
apk = pk1 + pk2
return apk
def do_sign_get_nonce_R1(io, msg):
io.sendlineafter(b"sign?", msg.hex().encode())
io.recvuntil(b"my nonce: ")
R1_tpl = ast.literal_eval(io.recvline().strip().decode())
R1 = point.Point(*R1_tpl, curve=curve)
return R1
def send_nonce_R2_get_s(io, R2):
io.sendlineafter(b"x: ", str(R2.x).encode())
io.sendlineafter(b"y: ", str(R2.y).encode())
io.recvuntil(b"my share of the signature: ")
s1 = int(io.recvline().strip().decode())
return s1
Zp = GF(curve.q)
ell = 256
messages = [f"message{i}".encode() for i in range(ell)]
with ThreadPoolExecutor(max_workers=32) as executor:
ios = list(tqdm(executor.map(connect, range(ell)), desc="Init", total=ell))
apks = list(
tqdm(
executor.map(establish, ios, [sk2] * ell, [pk2] * ell),
desc="Establish",
total=ell,
)
)
apk = apks[0]
R1 = list(
tqdm(
executor.map(do_sign_get_nonce_R1, ios, messages),
desc="Get nonce",
total=ell,
)
)
print("done, forging signature...")
k2 = [[random.randrange(curve.q), random.randrange(curve.q)] for i in range(ell)]
R2 = [[x * curve.G, y * curve.G] for x, y in k2]
c = [
[hash_transcript(apk, R1[i] + R2[i][b], messages[i]) for b in range(2)]
for i in range(ell)
]
g_func = lambda x, z=0: sum(
[int(Zp(2) ** i / (c[i][1] - c[i][0])) * x[i] for i in range(ell)], z
)
forged_R = g_func(R1, z=point.Point.IDENTITY_ELEMENT)
forged_message = b"flag"
forged_c = hash_transcript(apk, forged_R, forged_message)
bits = [
int(b)
for b in bin((forged_c - g_func([c[i][0] for i in range(ell)])) % curve.q)[
2:
].rjust(256, "0")
][::-1]
chosen_R2 = [R2[i][b] for (i, b) in enumerate(bits)]
with ThreadPoolExecutor(max_workers=32) as executor:
s1 = list(
tqdm(
executor.map(send_nonce_R2_get_s, ios, chosen_R2),
desc="Get signature share",
total=ell,
)
)
signatures = [
(int(c[i][bits[i]]), int(s1[i] + k2[i][bits[i]] - c[i][bits[i]] * sk2))
for i in range(ell)
]
forged_signature = (
forged_c,
(g_func(s1) - forged_c * sk2) % curve.q,
)
print([verify(apk, messages[i], signatures[i]) for i in range(ell)])
print(verify(apk, forged_message, forged_signature))
c, s = forged_signature
io = ios[0]
io.sendlineafter(b"c: ", str(c).encode())
io.sendlineafter(b"s: ", str(s).encode())
io.interactive()
|