mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-11-22 15:38:11 +00:00
Added tool to test cooperative signing
This commit is contained in:
Jochen Hoenicke
parent
87b7d0649b
commit
99915f1a63
106
tools/ed25519raw.py
Normal file
106
tools/ed25519raw.py
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import hashlib
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b = 256
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q = 2**255 - 19
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l = 2**252 + 27742317777372353535851937790883648493
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def H(m):
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return hashlib.sha512(m).digest()
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def expmod(b,e,m):
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if e < 0:
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raise Exception('negative exponent')
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if e == 0: return 1
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t = expmod(b,e >> 1,m)**2 % m
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if e & 1: t = (t*b) % m
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return t
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def inv(x):
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return expmod(x,q-2,q)
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d = -121665 * inv(121666)
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I = expmod(2,(q-1)>>2,q)
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def xrecover(y):
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xx = (y*y-1) * inv(d*y*y+1)
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x = expmod(xx,(q+3)>>3,q)
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if (x*x - xx) % q != 0: x = (x*I) % q
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if x % 2 != 0: x = q-x
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return x
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By = 4 * inv(5)
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Bx = xrecover(By)
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B = [Bx % q,By % q]
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def edwards(P,Q):
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x1 = P[0]
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y1 = P[1]
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x2 = Q[0]
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y2 = Q[1]
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x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
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y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
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return [x3 % q,y3 % q]
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def scalarmult(P,e):
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if e == 0: return [0,1]
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Q = scalarmult(P,e>>1)
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Q = edwards(Q,Q)
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if e & 1: Q = edwards(Q,P)
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return Q
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def encodeint(y):
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bits = [(y >> i) & 1 for i in range(b)]
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return bytes([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b>>3)])
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def encodepoint(P):
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x = P[0]
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y = P[1]
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bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1]
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return bytes([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b>>3)])
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def bit(h,i):
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return (h[i>>3] >> (i&7)) & 1
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def publickey(sk):
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h = H(sk)
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a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
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A = scalarmult(B,a)
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return encodepoint(A)
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def Hint(m):
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h = H(m)
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return sum(2**i * bit(h,i) for i in range(2*b))
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def signature(m,sk,pk):
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h = H(sk)
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a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
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r = Hint(bytes([h[i] for i in range(b>>3,b>>2)]) + m)
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R = scalarmult(B,r)
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S = (r + Hint(encodepoint(R) + pk + m) * a) % l
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return encodepoint(R) + encodeint(S)
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def isoncurve(P):
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x = P[0]
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y = P[1]
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return (-x*x + y*y - 1 - d*x*x*y*y) % q == 0
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def decodeint(s):
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return sum(2**i * bit(s,i) for i in range(0,b))
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def decodepoint(s):
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y = sum(2**i * bit(s,i) for i in range(0,b-1))
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x = xrecover(y)
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if x & 1 != bit(s,b-1): x = q-x
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P = [x,y]
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if not isoncurve(P): raise Exception("decoding point that is not on curve")
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return P
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def checkvalid(s,m,pk):
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if len(s) != b>>2: raise Exception("signature length is wrong")
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if len(pk) != b>>3: raise Exception("public-key length is wrong")
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R = decodepoint(s[0:b>>3])
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A = decodepoint(pk)
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S = decodeint(s[b>>3:b>>2])
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h = Hint(encodepoint(R) + pk + m)
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if scalarmult(B,S) != edwards(R,scalarmult(A,h)):
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raise Exception("signature does not pass verification")
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246
tools/keytool
Executable file
246
tools/keytool
Executable file
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#!/usr/bin/env python3
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import sys
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import binascii
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import ed25519raw
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import pyblake2
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def hex(by):
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return str(binascii.hexlify(by), 'ascii')
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def combine_keys(pks):
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combine = None
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for pk in pks:
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P = ed25519raw.decodepoint(pk)
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if not combine:
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combine = P
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else:
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combine = ed25519raw.edwards(combine, P)
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return ed25519raw.encodepoint(combine)
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def combine_sig(R, sigs):
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s = 0
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for si in sigs:
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s += ed25519raw.decodeint(si)
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s = s % ed25519raw.l
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sig = R + ed25519raw.encodeint(s)
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return sig
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def binom(n, k):
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b = 1
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for i in range(1, k+1):
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b = b * (n - k + i) // i
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return b
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def compute_mask(combination, m, n):
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result = 0
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signer = 0
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while m > 0:
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m = m - 1
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n = n - 1
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numst = binom(n, m)
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while combination >= numst:
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combination -= numst
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signer = signer + 1
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n = n - 1
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numst = binom(n, m)
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result |= 1 << signer
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signer = signer + 1
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return result
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def createPubkey():
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print('Enter randomness: ', end='')
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seckey = ed25519raw.H(input().encode('utf-8'))[0:32]
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pubkey = ed25519raw.publickey(seckey)
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print('Secret Key: %s' % hex(seckey))
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print('Public Key: %s' % hex(pubkey))
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def combinePubkeys(m,n):
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if binom(n,m) > 100:
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raise Exception("Too many keys")
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pks = []
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for i in range(0, n):
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print('Enter pubkey %d: ' %i, end='')
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pk = binascii.unhexlify(input())
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# remove 00 prefix if present
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if len(pk) == 33:
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pk = pk[1:]
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pks.append(ed25519raw.decodepoint(pk))
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for i in range(0, binom(n,m)):
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mask = compute_mask(i, m, n)
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sum = None
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for j in range(0, n):
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if mask & (1<<j) != 0:
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if sum == None:
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sum = pks[j]
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else:
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sum = ed25519raw.edwards(sum, pks[j])
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pk = ed25519raw.encodepoint(sum)
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print ('Key %02x: %s' % (mask, hex(pk)))
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def get_nonce(sk,data,ctr):
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h = ed25519raw.H(sk)
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b = ed25519raw.b
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a = 2**(b-2) + sum(2**i * ed25519raw.bit(h,i) for i in range(3,b-2))
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r = ed25519raw.Hint(bytes([h[i] for i in range(b>>3,b>>2)]) + data +
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binascii.unhexlify("%08x" % ctr))
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R = ed25519raw.scalarmult(ed25519raw.B,r)
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return (r, ed25519raw.encodepoint(R))
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def phase1(data):
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digest = pyblake2.blake2s(data).digest()
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print('Digest: %s' % hex(digest))
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print('Enter counter (small integer): ', end='')
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ctr = int(input())
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print('Enter privkey: ', end='')
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seckey = binascii.unhexlify(input())
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(_, R) = get_nonce(seckey, digest, ctr)
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print('Local commit: %s' % hex(R))
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def combinePhase1(m):
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commits = []
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for i in range(0, m):
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print('Enter commit %d: ' % i, end='')
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commits.append(binascii.unhexlify(input()))
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print('Global commit: %s' % hex(combine_keys(commits)))
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def phase2(data):
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digest = pyblake2.blake2s(data).digest()
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print('Digest: %s' % hex(digest))
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print('Enter combined commitment: ', end='')
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R = binascii.unhexlify(input())
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print('Enter combined public key: ', end='')
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pk = binascii.unhexlify(input())
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print('Enter counter: ', end='')
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ctr = int(input())
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print('Enter privkey: ', end='')
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seckey = binascii.unhexlify(input())
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(r, Ri) = get_nonce(seckey, digest, ctr)
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h = ed25519raw.H(seckey)
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b = ed25519raw.b
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a = 2**(b-2) + sum(2**i * ed25519raw.bit(h,i) for i in range(3,b-2))
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S = (r + ed25519raw.Hint(R + pk + digest) * a) % ed25519raw.l
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print('Local commit: %s' % hex(Ri))
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print('Local sig: %s' % hex(ed25519raw.encodeint(S)))
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def combinePhase2(m):
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sigs = []
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print('Enter global commit: ', end='')
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R = binascii.unhexlify(input())
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for i in range(0, m):
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print('Enter sig %d: ' % i, end='')
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sigs.append(binascii.unhexlify(input()))
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sig = combine_sig(R, sigs)
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print('Combined sig: %s' % hex(sig))
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def checkSignature(data):
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digest = pyblake2.blake2s(data).digest()
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print('Digest: %s' % hex(digest))
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print('Enter Public Key: ', end='')
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pubkey = binascii.unhexlify(input())
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print('Enter Sig: ', end='')
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sig = binascii.unhexlify(input())
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ed25519raw.checkvalid(sig, digest, pubkey)
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print('Valid Signature!')
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def usage():
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print('Usage: keyctl phase options')
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print('Phases:')
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print(' keyctl create_pub: create single public keys')
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print(' keyctl combine_pub m n: create combined public keys')
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print(' keyctl ph1 file.bin: compute partial commitment')
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print(' keyctl combine_ph1 m: combine commitments')
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print(' keyctl ph2 file.bin: compute partial signature')
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print(' keyctl combine_ph2 m: combine signatures')
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print(' keyctl check_sig file.bin: check signature')
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def main():
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if len(sys.argv) < 2:
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usage()
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return 1
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func = sys.argv[1]
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if func == 'create_pub':
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createPubkey()
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elif func == 'combine_pub':
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m = int(sys.argv[2])
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n = int(sys.argv[3])
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combinePubkeys(m,n)
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elif func == 'ph1':
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filename = sys.argv[2]
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data = open(filename, 'rb').read()
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phase1(data)
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elif func == 'combine_ph1':
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m = int(sys.argv[2])
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combinePhase1(m)
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elif func == 'ph2':
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filename = sys.argv[2]
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data = open(filename, 'rb').read()
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phase2(data)
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elif func == 'combine_ph2':
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m = int(sys.argv[2])
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combinePhase2(m)
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elif func == 'check_sig':
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filename = sys.argv[2]
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data = open(filename, 'rb').read()
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checkSignature(data)
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else:
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usage()
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def test():
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data = sys.argv[1].encode('utf-8')
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N = 5
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keyset = [1,3,4]
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digest = pyblake2.blake2s(data).digest()
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print('Digest: %s' % hex(digest))
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sks = []
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pks = []
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nonces = []
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commits = []
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sigs = []
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for i in range(0, N):
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print('----- Key %d ------' % (i+1))
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seckey = ed25519raw.H(("key%d"%(i+1)).encode('utf-8'))[0:32]
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pubkey = ed25519raw.publickey(seckey)
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print('Secret Key: %s' % hex(seckey))
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print('Public Key: %s' % hex(pubkey))
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sks.append(seckey)
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pks.append(pubkey)
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ctr = 0
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(r, R) = get_nonce(seckey, digest, ctr)
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print('Local nonce: %s' % hex(ed25519raw.encodeint(r)))
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print('Local commit: %s' % hex(R))
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nonces.append(r)
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commits.append(R)
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globalPk = combine_keys([pks[i] for i in keyset])
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globalR = combine_keys([commits[i] for i in keyset])
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print('-----------------')
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print('Global pubkey: %s' %hex(globalPk))
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print('Global commit: %s' %hex(globalR))
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print('-----------------')
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for i in range(0,5):
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seckey = sks[i]
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pubkey = pks[i]
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r = nonces[i]
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R = commits[i]
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h = ed25519raw.H(seckey)
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b = ed25519raw.b
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a = 2**(b-2) + sum(2**i * ed25519raw.bit(h,i) for i in range(3,b-2))
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S = (r + ed25519raw.Hint(globalR + globalPk + digest) * a) % ed25519raw.l
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print('Local sig %d: %s' % (i+1, hex(ed25519raw.encodeint(S))))
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commits.append(R)
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sigs.append(ed25519raw.encodeint(S))
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print('-----------------')
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sig = combine_sig(globalR, [sigs[i] for i in [1,3,4]])
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print('Global sig: %s' %hex(sig))
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ed25519raw.checkvalid(sig, digest, globalPk)
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print('Valid Signature!')
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if __name__ == '__main__':
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test()
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