def si1(x, n):
"""Return all-0 vector of length n-1 (if x=0) and (x-1)-st unit vector of length n-1 (if 1 <= x < n)."""
if n==1:
return []
elif n==2:
return [x]
else:
b = mpc.lsb(x)
v = si1((x - b) / 2, (n + 1) // 2)
w = mpc.scalar_mul(b, v)
return [b-sum(w)] + [v[i//2]-w[i//2] if i%2==0 else w[i//2] for i in range(n-2)]
def si1(a, n):
"""Return all-0 vector of length n-1 (if a=0) and (a-1)-st unit vector of length n-1 (if 1 <= a < n)."""
if n == 1:
return []
elif n == 2:
return [a]
else:
b = mpc.lsb(a / 2**stype.field.frac_length)
x = si1((a - b) / 2, (n + 1) // 2)
y = mpc.scalar_mul(b, x)
return [b - sum(y)] + [
x[i // 2] - y[i // 2] if i % 2 == 0 else y[i // 2]
for i in range(n - 2)
]
def test_secint(self):
secint = mpc.SecInt()
a = secint(12)
b = secint(13)
c = mpc.run(mpc.output(a * b + b))
self.assertEqual(c, 12 * 13 + 13)
c = mpc.run(mpc.output(a**11 * a**(-6) * a**(-5)))
self.assertEqual(c, 1)
c = mpc.run(mpc.output(a**(secint.field.modulus - 1)))
self.assertEqual(c, 1)
self.assertEqual(mpc.run(mpc.output(secint(12)**73)), 12**73)
c = mpc.to_bits(
mpc.SecInt(0)(0)) # mpc.output() only works for non-empty lists
self.assertEqual(c, [])
c = mpc.run(mpc.output(mpc.to_bits(mpc.SecInt(1)(0))))
self.assertEqual(c, [0])
c = mpc.run(mpc.output(mpc.to_bits(mpc.SecInt(1)(1))))
self.assertEqual(c, [1])
c = mpc.run(mpc.output(mpc.to_bits(secint(0))))
self.assertEqual(c, [
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
])
c = mpc.run(mpc.output(mpc.to_bits(secint(1))))
self.assertEqual(c, [
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
])
c = mpc.run(mpc.output(mpc.to_bits(secint(8113))))
self.assertEqual(c, [
1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
])
c = mpc.run(mpc.output(mpc.to_bits(secint(2**31 - 1))))
self.assertEqual(c, [
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 0
])
c = mpc.run(mpc.output(mpc.to_bits(secint(-1))))
self.assertEqual(c, [
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1
])
c = mpc.run(mpc.output(mpc.to_bits(secint(-2**31))))
self.assertEqual(c, [
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1
])
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(-2**31)))), 0)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(-2**31 + 1)))), 1)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(-1)))), 1)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(0)))), 0)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(1)))), 1)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(2**31 - 1)))), 1)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(5)))), 1)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(-5)))), 1)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(50)))), 0)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secint(-50)))), 0)
self.assertEqual(mpc.run(mpc.output(secint(3)**73)), 3**73)
def test_secfxp(self):
secfxp = mpc.SecFxp()
f = 16
d = mpc.run(mpc.output(secfxp(1) + secfxp(1)))
self.assertEqual(d.frac_length, f)
self.assertEqual(d, 2 * 2**f)
d = mpc.run(mpc.output(secfxp(2**-f) + secfxp(1)))
self.assertEqual(d, 1 + 2**f)
s = [10.7, -3.4, 0.1, -0.11]
ss = [round(v * (1 << f)) for v in s]
self.assertEqual(mpc.run(mpc.output(list(map(secfxp, s)))), ss)
s = [10.5, -3.25, 0.125, -0.125]
x, y, z, w = list(map(secfxp, s))
s2 = [v * v for v in s]
ss2 = [round(v * (1 << f)) for v in s2]
self.assertEqual(mpc.run(mpc.output([x * x, y * y, z * z, w * w])),
ss2)
s2 = [s[0] + s[1], s[0] * s[1], s[0] - s[1]]
ss2 = [round(v * (1 << f)) for v in s2]
self.assertEqual(mpc.run(mpc.output([x + y, x * y, x - y])), ss2)
s2 = [(s[0] + s[1])**2, (s[0] + s[1])**2 + 3 * s[2]]
ss2 = [round(v * (1 << f)) for v in s2]
self.assertEqual(mpc.run(mpc.output([(x + y)**2, (x + y)**2 + 3 * z])),
ss2)
ss2 = [int(s[i] < s[i + 1]) * (1 << f) for i in range(len(s) - 1)]
self.assertEqual(mpc.run(mpc.output([x < y, y < z, z < w])), ss2)
ss2 = int(s[0] < s[1] and s[1] < s[2]) * (1 << f)
self.assertEqual(mpc.run(mpc.output((x < y) & (y < z))), ss2)
ss2 = int(s[0] < s[1] or s[1] < s[2]) * (1 << f)
self.assertEqual(mpc.run(mpc.output((x < y) | (y < z))), ss2)
ss2 = (int(s[0] < s[1]) ^ int(s[1] < s[2])) * (1 << f)
self.assertEqual(mpc.run(mpc.output((x < y) ^ (y < z))), ss2)
ss2 = (int(not s[0] < s[1]) ^ int(s[1] < s[2])) * (1 << f)
self.assertEqual(mpc.run(mpc.output(~(x < y) ^ y < z)), ss2)
s2 = [s[0] < 1, 10 * s[1] < 5, 10 * s[0] == 5]
ss2 = [round(v * (1 << f)) for v in s2]
self.assertEqual(mpc.run(mpc.output([x < 1, 10 * y < 5, 10 * x == 5])),
ss2)
s[3] = -0.120
w = secfxp(s[3])
for _ in range(3):
s2 = s[3] / s[2] + s[0]
self.assertAlmostEqual(mpc.run(mpc.output(w / z + x)).signed(),
s2,
delta=1)
ss2 = round(s2 * (1 << f))
self.assertAlmostEqual(mpc.run(mpc.output(w / z + x)),
ss2,
delta=1)
s2 = ((s[0] + s[1])**2 + 3 * s[2]) / s[2]
self.assertAlmostEqual(mpc.run(mpc.output(
((x + y)**2 + 3 * z) / z)).signed(),
s2,
delta=2)
s2 = 1 / s[3]
self.assertAlmostEqual((mpc.run(mpc.output(1 / w))).signed(),
s2,
delta=1)
s2 = s[2] / s[3]
self.assertAlmostEqual(mpc.run(mpc.output(z / w)).signed(),
s2,
delta=1)
s2 = -s[3] / s[2]
ss2 = round(s2 * (1 << f))
self.assertAlmostEqual(mpc.run(mpc.output(-w / z)), ss2, delta=1)
s2 = s[2] / s[3]
ss2 = round(s2 * (1 << f))
self.assertAlmostEqual(mpc.run(mpc.output(w / z)), ss2, delta=1)
a = mpc._norm(w)
self.assertEqual(mpc.run(mpc.output(mpc.sgn(x))),
int(s[0] > 0) * (1 << f))
self.assertEqual(mpc.run(mpc.output(mpc.sgn(-x))),
-int(s[0] > 0) * (1 << f))
self.assertEqual(mpc.run(mpc.output(mpc.sgn(secfxp(0)))), 0)
ss2 = round(min(s) * (1 << f))
self.assertEqual(mpc.run(mpc.output(mpc.min(x, y, w, z))), ss2)
ss2 = round(min(s[0], 0) * (1 << f))
self.assertEqual(mpc.run(mpc.output(mpc.min(x, 0))), ss2)
ss2 = round(min(0, s[1]) * (1 << f))
self.assertEqual(mpc.run(mpc.output(mpc.min(0, y))), ss2)
ss2 = round(max(s) * (1 << f))
self.assertEqual(mpc.run(mpc.output(mpc.max(x, y, w, z))), ss2)
ss2 = round(max(s[0], 0) * (1 << f))
self.assertEqual(mpc.run(mpc.output(mpc.max(x, 0))), ss2)
ss2 = round(max(0, s[1]) * (1 << f))
self.assertEqual(mpc.run(mpc.output(mpc.max(0, y))), ss2)
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secfxp(1)))), 0 * (2**f))
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secfxp(1 / 2**f)))),
1 * (2**f))
self.assertEqual(mpc.run(mpc.output(mpc.lsb(secfxp(2 / 2**f)))),
0 * (2**f))