Added tool to test cooperative signing

tools/ed25519raw.py

@@ -0,0 +1,106 @@
+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")

tools/keytool

@@ -0,0 +1,246 @@
+#!/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()