def PolyVerify(ck, pk, m, n1, n2, x, v, pi, commitfunction=Commitment.commit):
G, key = ck
g = G.generator()
p = G.order()
H, BP, BPP = pk
Hscale, Zh, Zb = pi
try:
xi = x.mod_inverse(p)
#print 'Bn path succeeded'
except AttributeError:
#print 'Generic path'
xi = _invert(x, p)
Cleft = reduce(operator.add, [pow(x, i, p) * H[i] for i in xrange(len(H))])
#print 'x=',x
#print Hscale
#print v
#print [xss%p for xss in Hscale]
Cright = commitfunction(ck, Hscale, Zh)
if not Cleft == Cright:
print 'Verification Failed (1)'
return 0
Cleft2 = x * BP - xi * BPP
ppoly = LPoly(Hscale[:n1], mod=p)
npoly = LPoly(Hscale[-n2:], mod=p)
assert len(ppoly) == n1
assert len(npoly) == n2
rv1 = ppoly.eval(pow(x, m, p)) * x
#print 'rv1sc',x
#print 'rv1e ',ppoly.eval(pow(x,m,p))
rv2 = npoly.eval(pow(x, m, p)) * pow(xi, m * n2 + 1, p)
#print 'rv2sc',pow(xi,m*n2+1,p)
#print 'rv2e ',npoly.eval(pow(xi,m,p))
rval2 = (rv1 + rv2 - v) % p
#print 'diff==',(rv1+rv2-v)%p
#print 'rval2=',rval2,ppoly,'=',rv1,npoly,'=',rv2
Cright2 = commitfunction(ck, [rval2], Zb)
if not Cleft2 == Cright2:
print 'Verification Failed (2)'
return 0
print 'Verification successful'
return 1
def test_aio():
nn2 = Bn(50000).random() + 10
nn1 = Bn(50000).random() + 10
m = int(math.sqrt(int(max(nn1, nn2))))
n1 = int(math.ceil(int(nn1 / m))) + 1
n2 = int(math.ceil(int(nn2 / m))) + 1
assert m * n1 >= nn1
assert m * n2 >= nn2
ck = commitment_key_gen(n1 + n2)
G, key = ck
g = G.generator()
p = G.order()
np = [Bn(2**20).random() for c in xrange(nn2)]
h = LPoly(np, deg=-len(np), mod=p)
h.append(0)
np = [Bn(2**20).random() for c in xrange(nn1)]
h = h + LPoly(np, deg=1, mod=p)
#h=LPoly([-3,-2,-1,0,1,2,3,4,5,6,7,8],deg=-3,mod=p)
#h=LPoly([3,0,5],deg=-1,mod=23)
#h=LPoly([100,-10,4,5],deg=8,mod=p)
#h=LPoly([100],deg=1,mod=p)
x0 = p.random()
#print h.pp()
pk, sk = PolyCommit(ck, m, n1, n2, h)
print 'Commit Ok'
v, pi = PolyEval(ck, sk, x0)
#print v,h.eval(x0)
assert v == h.eval(x0)
print 'Eval Ok'
ver = PolyVerify(ck, pk, m, n1, n2, x0, v, pi)
assert ver == 1
#print 'h(x)=',h.pp()
print 'x0=', x0
print 'p=', p
def test_eval():
from numpy import fft
x = LPoly([1], 1)
y = LPoly([0, 1])
assert (y * y).eval(1) == 1
assert x.eval(0) == 0
x = Bn.from_binary(b"10000adadadadada000001").random()
print x
#x=Bn(1)
m = Bn.from_binary(b"10000adadadadadad000001").random()
p = LPoly([1, 1], mod=m)
q = LPoly([1, 1])
q5 = q * q * q * q * q
p5 = p * p * p * p * p
rh = p * p
assert rh == p.fft_mul(p)
assert p5 == q5 #only for small coeffs
assert q5.eval(x) % m == pow(x + 1, 5, m)
assert (p * p * p * p * p).eval(x) % m == pow(
x + 1, 5,
m) #this should not be needed but it might help pin down bugs
assert (p * p * p * p * p).eval(x) == pow(x + 1, 5, m)
assert LPoly([1], -1, 13).eval(5) == 8
assert LPoly([1], -1, 13).eval(Bn(5)) == 8