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mirror of https://github.com/trezor/trezor-firmware.git synced 2024-11-13 19:18:56 +00:00

Added tool to test cooperative signing

This commit is contained in:
Jochen Hoenicke 2017-04-02 17:27:36 +02:00
parent 87b7d0649b
commit 99915f1a63
2 changed files with 352 additions and 0 deletions

106
tools/ed25519raw.py Normal file
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import hashlib
b = 256
q = 2**255 - 19
l = 2**252 + 27742317777372353535851937790883648493
def H(m):
return hashlib.sha512(m).digest()
def expmod(b,e,m):
if e < 0:
raise Exception('negative exponent')
if e == 0: return 1
t = expmod(b,e >> 1,m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x,q-2,q)
d = -121665 * inv(121666)
I = expmod(2,(q-1)>>2,q)
def xrecover(y):
xx = (y*y-1) * inv(d*y*y+1)
x = expmod(xx,(q+3)>>3,q)
if (x*x - xx) % q != 0: x = (x*I) % q
if x % 2 != 0: x = q-x
return x
By = 4 * inv(5)
Bx = xrecover(By)
B = [Bx % q,By % q]
def edwards(P,Q):
x1 = P[0]
y1 = P[1]
x2 = Q[0]
y2 = Q[1]
x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
return [x3 % q,y3 % q]
def scalarmult(P,e):
if e == 0: return [0,1]
Q = scalarmult(P,e>>1)
Q = edwards(Q,Q)
if e & 1: Q = edwards(Q,P)
return Q
def encodeint(y):
bits = [(y >> i) & 1 for i in range(b)]
return bytes([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b>>3)])
def encodepoint(P):
x = P[0]
y = P[1]
bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1]
return bytes([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b>>3)])
def bit(h,i):
return (h[i>>3] >> (i&7)) & 1
def publickey(sk):
h = H(sk)
a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
A = scalarmult(B,a)
return encodepoint(A)
def Hint(m):
h = H(m)
return sum(2**i * bit(h,i) for i in range(2*b))
def signature(m,sk,pk):
h = H(sk)
a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
r = Hint(bytes([h[i] for i in range(b>>3,b>>2)]) + m)
R = scalarmult(B,r)
S = (r + Hint(encodepoint(R) + pk + m) * a) % l
return encodepoint(R) + encodeint(S)
def isoncurve(P):
x = P[0]
y = P[1]
return (-x*x + y*y - 1 - d*x*x*y*y) % q == 0
def decodeint(s):
return sum(2**i * bit(s,i) for i in range(0,b))
def decodepoint(s):
y = sum(2**i * bit(s,i) for i in range(0,b-1))
x = xrecover(y)
if x & 1 != bit(s,b-1): x = q-x
P = [x,y]
if not isoncurve(P): raise Exception("decoding point that is not on curve")
return P
def checkvalid(s,m,pk):
if len(s) != b>>2: raise Exception("signature length is wrong")
if len(pk) != b>>3: raise Exception("public-key length is wrong")
R = decodepoint(s[0:b>>3])
A = decodepoint(pk)
S = decodeint(s[b>>3:b>>2])
h = Hint(encodepoint(R) + pk + m)
if scalarmult(B,S) != edwards(R,scalarmult(A,h)):
raise Exception("signature does not pass verification")

246
tools/keytool Executable file
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#!/usr/bin/env python3
import sys
import binascii
import ed25519raw
import pyblake2
def hex(by):
return str(binascii.hexlify(by), 'ascii')
def combine_keys(pks):
combine = None
for pk in pks:
P = ed25519raw.decodepoint(pk)
if not combine:
combine = P
else:
combine = ed25519raw.edwards(combine, P)
return ed25519raw.encodepoint(combine)
def combine_sig(R, sigs):
s = 0
for si in sigs:
s += ed25519raw.decodeint(si)
s = s % ed25519raw.l
sig = R + ed25519raw.encodeint(s)
return sig
def binom(n, k):
b = 1
for i in range(1, k+1):
b = b * (n - k + i) // i
return b
def compute_mask(combination, m, n):
result = 0
signer = 0
while m > 0:
m = m - 1
n = n - 1
numst = binom(n, m)
while combination >= numst:
combination -= numst
signer = signer + 1
n = n - 1
numst = binom(n, m)
result |= 1 << signer
signer = signer + 1
return result
def createPubkey():
print('Enter randomness: ', end='')
seckey = ed25519raw.H(input().encode('utf-8'))[0:32]
pubkey = ed25519raw.publickey(seckey)
print('Secret Key: %s' % hex(seckey))
print('Public Key: %s' % hex(pubkey))
def combinePubkeys(m,n):
if binom(n,m) > 100:
raise Exception("Too many keys")
pks = []
for i in range(0, n):
print('Enter pubkey %d: ' %i, end='')
pk = binascii.unhexlify(input())
# remove 00 prefix if present
if len(pk) == 33:
pk = pk[1:]
pks.append(ed25519raw.decodepoint(pk))
for i in range(0, binom(n,m)):
mask = compute_mask(i, m, n)
sum = None
for j in range(0, n):
if mask & (1<<j) != 0:
if sum == None:
sum = pks[j]
else:
sum = ed25519raw.edwards(sum, pks[j])
pk = ed25519raw.encodepoint(sum)
print ('Key %02x: %s' % (mask, hex(pk)))
def get_nonce(sk,data,ctr):
h = ed25519raw.H(sk)
b = ed25519raw.b
a = 2**(b-2) + sum(2**i * ed25519raw.bit(h,i) for i in range(3,b-2))
r = ed25519raw.Hint(bytes([h[i] for i in range(b>>3,b>>2)]) + data +
binascii.unhexlify("%08x" % ctr))
R = ed25519raw.scalarmult(ed25519raw.B,r)
return (r, ed25519raw.encodepoint(R))
def phase1(data):
digest = pyblake2.blake2s(data).digest()
print('Digest: %s' % hex(digest))
print('Enter counter (small integer): ', end='')
ctr = int(input())
print('Enter privkey: ', end='')
seckey = binascii.unhexlify(input())
(_, R) = get_nonce(seckey, digest, ctr)
print('Local commit: %s' % hex(R))
def combinePhase1(m):
commits = []
for i in range(0, m):
print('Enter commit %d: ' % i, end='')
commits.append(binascii.unhexlify(input()))
print('Global commit: %s' % hex(combine_keys(commits)))
def phase2(data):
digest = pyblake2.blake2s(data).digest()
print('Digest: %s' % hex(digest))
print('Enter combined commitment: ', end='')
R = binascii.unhexlify(input())
print('Enter combined public key: ', end='')
pk = binascii.unhexlify(input())
print('Enter counter: ', end='')
ctr = int(input())
print('Enter privkey: ', end='')
seckey = binascii.unhexlify(input())
(r, Ri) = get_nonce(seckey, digest, ctr)
h = ed25519raw.H(seckey)
b = ed25519raw.b
a = 2**(b-2) + sum(2**i * ed25519raw.bit(h,i) for i in range(3,b-2))
S = (r + ed25519raw.Hint(R + pk + digest) * a) % ed25519raw.l
print('Local commit: %s' % hex(Ri))
print('Local sig: %s' % hex(ed25519raw.encodeint(S)))
def combinePhase2(m):
sigs = []
print('Enter global commit: ', end='')
R = binascii.unhexlify(input())
for i in range(0, m):
print('Enter sig %d: ' % i, end='')
sigs.append(binascii.unhexlify(input()))
sig = combine_sig(R, sigs)
print('Combined sig: %s' % hex(sig))
def checkSignature(data):
digest = pyblake2.blake2s(data).digest()
print('Digest: %s' % hex(digest))
print('Enter Public Key: ', end='')
pubkey = binascii.unhexlify(input())
print('Enter Sig: ', end='')
sig = binascii.unhexlify(input())
ed25519raw.checkvalid(sig, digest, pubkey)
print('Valid Signature!')
def usage():
print('Usage: keyctl phase options')
print('Phases:')
print(' keyctl create_pub: create single public keys')
print(' keyctl combine_pub m n: create combined public keys')
print(' keyctl ph1 file.bin: compute partial commitment')
print(' keyctl combine_ph1 m: combine commitments')
print(' keyctl ph2 file.bin: compute partial signature')
print(' keyctl combine_ph2 m: combine signatures')
print(' keyctl check_sig file.bin: check signature')
def main():
if len(sys.argv) < 2:
usage()
return 1
func = sys.argv[1]
if func == 'create_pub':
createPubkey()
elif func == 'combine_pub':
m = int(sys.argv[2])
n = int(sys.argv[3])
combinePubkeys(m,n)
elif func == 'ph1':
filename = sys.argv[2]
data = open(filename, 'rb').read()
phase1(data)
elif func == 'combine_ph1':
m = int(sys.argv[2])
combinePhase1(m)
elif func == 'ph2':
filename = sys.argv[2]
data = open(filename, 'rb').read()
phase2(data)
elif func == 'combine_ph2':
m = int(sys.argv[2])
combinePhase2(m)
elif func == 'check_sig':
filename = sys.argv[2]
data = open(filename, 'rb').read()
checkSignature(data)
else:
usage()
def test():
data = sys.argv[1].encode('utf-8')
N = 5
keyset = [1,3,4]
digest = pyblake2.blake2s(data).digest()
print('Digest: %s' % hex(digest))
sks = []
pks = []
nonces = []
commits = []
sigs = []
for i in range(0, N):
print('----- Key %d ------' % (i+1))
seckey = ed25519raw.H(("key%d"%(i+1)).encode('utf-8'))[0:32]
pubkey = ed25519raw.publickey(seckey)
print('Secret Key: %s' % hex(seckey))
print('Public Key: %s' % hex(pubkey))
sks.append(seckey)
pks.append(pubkey)
ctr = 0
(r, R) = get_nonce(seckey, digest, ctr)
print('Local nonce: %s' % hex(ed25519raw.encodeint(r)))
print('Local commit: %s' % hex(R))
nonces.append(r)
commits.append(R)
globalPk = combine_keys([pks[i] for i in keyset])
globalR = combine_keys([commits[i] for i in keyset])
print('-----------------')
print('Global pubkey: %s' %hex(globalPk))
print('Global commit: %s' %hex(globalR))
print('-----------------')
for i in range(0,5):
seckey = sks[i]
pubkey = pks[i]
r = nonces[i]
R = commits[i]
h = ed25519raw.H(seckey)
b = ed25519raw.b
a = 2**(b-2) + sum(2**i * ed25519raw.bit(h,i) for i in range(3,b-2))
S = (r + ed25519raw.Hint(globalR + globalPk + digest) * a) % ed25519raw.l
print('Local sig %d: %s' % (i+1, hex(ed25519raw.encodeint(S))))
commits.append(R)
sigs.append(ed25519raw.encodeint(S))
print('-----------------')
sig = combine_sig(globalR, [sigs[i] for i in [1,3,4]])
print('Global sig: %s' %hex(sig))
ed25519raw.checkvalid(sig, digest, globalPk)
print('Valid Signature!')
if __name__ == '__main__':
test()