def test_static(self):
# Verify against static test vectors
alpha = [
6808181831819141657160280673506432691407806061837762993142662373500430825792,
4138536697521448323155976179625860582331141320072618244300034508091478437877,
20259243729221075783953642258755031830946498253783650311586175820530608751936,
11227115470523445882235139084890542822660569362938710556861479160600812964997
]
points = [(i, shamirs_poly(i, alpha)) for i in range(0, len(alpha))]
test_points = [
(0,
6808181831819141657160280673506432691407806061837762993142662373500430825792
),
(1,
20544834857245836424258632451520592838797650598216707762192147676147522484985
),
(2,
10833210933219706719196668784844423052753721417299010433393634464005858464330
),
(3,
1259517139202877390892412692306630092142705895884865660519589327528699562575
)
]
assert points == test_points
assert alpha[0] == lagrange(points, 0)
def test_random(self):
# Randomized tests
for _ in range(0, 10):
alpha = [FQ.random() for _ in range(0, 4)]
points = [(FQ(i), shamirs_poly(FQ(i), alpha))
for i in range(0, len(alpha))]
assert alpha[0] == lagrange(points, 0)
assert alpha[0] != lagrange(points[1:], 0)
assert alpha[0] != lagrange(points[2:], 0)
def test_random_small(self):
q = 100003
for _ in range(0, 10):
alpha = [FQ.random(q) for _ in range(0, 4)]
points = [(FQ(i, q), shamirs_poly(FQ(i, q), alpha))
for i in range(0, len(alpha))]
assert alpha[0] == lagrange(points, 0)
assert alpha[0] != lagrange(points[1:], 0)
assert alpha[0] != lagrange(points[2:], 0)
# XXX: scipy's lagrange has floating point precision for large numbers
points_x, points_y = unzip(points)
interpolation = scipy_lagrange([_.n for _ in points_x], [_.n for _ in points_y])
assert int(interpolation.c[-1]) == alpha[0]
def test_fromdocs2(self):
p = 100003
k = 4
a = [FQ.random(p) for _ in range(0, k)] # [6257, 85026, 44499, 14701]
F = lambda i, x: a[i] * (x**i)
X = lambda x: a[0] + F(1, x) + F(2, x) + F(3, x)
# Create the shares
Sx = range(1, 5)
Sy = [X(_) for _ in Sx]
for x, y in zip(Sx, Sy):
z = shamirs_poly(FQ(x, p), a)
assert z == y
# Then recover secret
result = int(scipy_lagrange(Sx, [_.n for _ in Sy]).c[-1]) % p
assert a[0] == result
def test_poly_constraints(self):
I = FQ(14107816444829002666153088737167870815199986768206359534115449255516606414458)
A = [
FQ(17167899297711346731111134130539302906398306115120667361324654931060817769652),
FQ(20692971555607562002131076139518972969954851288604992618106076572794460197154),
FQ(11669314840495787582492056085422064523948780040073924653117253046363337959489),
FQ(15735493254427804666818698471807230275586165984790760178845725782084556556535)
]
S = [
FQ(1),
FQ(14107816444829002666153088737167870815199986768206359534115449255516606414458),
FQ(5067932324814081810415131337916762410698113547031307360925810907599032394672),
FQ(13201723662860499519704937914604513230538757359894370890481138582074383924053)
]
T = [
FQ(17167899297711346731111134130539302906398306115120667361324654931060817769652),
FQ(13947767308050706262790594447202101821284419559667543268525874072511409211876),
FQ(12611939459072476081893406313696501745859572890147944797422704733972764295239),
FQ(1657398546220101661314129991806057074896482894269175421846876999103942041527)
]
result = shamirs_poly(I, A)
assert result == T[-1]
for i in range(0, len(A)):
if i == 0:
r1cs_constraint(1, S[i], 1)
elif i == 1:
r1cs_constraint(I, I, S[i+1])
elif i < (len(A)-1):
r1cs_constraint(I, S[i], S[i+1])
if i == 0:
r1cs_constraint(A[i], S[i], T[i])
else:
r1cs_constraint(A[i], S[i], (T[i] - T[i-1]))