def test_sub_int(self):
first = 100
second = 337
bg1 = BigNum(first)
self.assertEqual(bg1 - second, BigNum(first - second))
self.assertEqual(second - bg1, BigNum(second - first))
def test_mul_int(self):
first = 10
second = 20
bg = BigNum(first)
self.assertEqual(bg * second, BigNum(first * second))
def generate_pis(self, chi, n):
if chi <= n + 1:
raise ValueError(
"chi should be greater than n + 1, chi=%s n+1=%s" %
(chi, n + 1))
pis = []
prod = BigNum(1)
# prod = (x - w_1) (x - w_2) ... (x - w_{n+1})
for j in range(1, n + 2):
prod = prod * (chi - j)
# denoms[0] = 1 / (w_1 - w_2) (w_1 - w_3) ... (w_1 - w_{n + 1})
# denoms[1] = 1 / (w_2 - w_1) (w_2 - w_3) ... (w_2 - w_{n + 1})
# denoms[n] = 1 / (w_{n+1}- w_1) (w_{n+1} - w_2) ... (w_{n+1} - w_n)
denoms = self.compute_denominators(n + 1)
missing_factor = chi - (n + 1)
ln_plus1 = prod * missing_factor.mod_inverse()
ln_plus1 = ln_plus1 * denoms[n].mod_inverse()
# P_0 is special
pis.append(ln_plus1 - BigNum(1))
two = BigNum(2)
for i in range(1, n + 1):
missing_factor = chi - i
l_i = prod * missing_factor.mod_inverse()
l_i = l_i * denoms[i - 1].mod_inverse()
pis.append(two * l_i + ln_plus1)
return pis
def test_add(self):
first = 100
second = 337
bg1 = BigNum(first)
bg2 = BigNum(second)
self.assertEqual(bg1 + bg2, BigNum(first + second))
def test_mul(self):
first = 10
second = 20
bg1 = BigNum(first)
bg2 = BigNum(second)
self.assertEqual(bg1 * bg2, BigNum(first * second))
def test_eq(self):
first = 100
second = 337
bg1 = BigNum(first)
bg2 = BigNum(second)
self.assertEqual(bg1, BigNum(first))
self.assertNotEqual(bg1, bg2)
def test_sub(self):
first = 100
second = 337
bg1 = BigNum(first)
bg2 = BigNum(second)
self.assertEqual(bg1 - bg2, BigNum(first - second))
self.assertEqual(bg2 - bg1, BigNum(second - first))
def compute_denominators(self, k):
denominators = []
temp = BigNum(1)
for i in range(1, k + 1):
if i == 1:
for j in range(2, k + 1):
elem = i - j
temp = temp * elem
elif i == k:
elem = 1 - k
temp = temp * elem
else:
inverse = BigNum(i - 1 - k)
inverse = inverse.mod_inverse()
elem = i - 1
temp = temp * elem
temp = temp * inverse
denominators.append(temp)
return denominators
def mul_test(self, g1):
# create N - 1 BigNum
bg = [BigNum() for _ in xrange(MAX - 1)]
# get the sum of the BigNums
s = reduce((lambda x, y: x + y), bg)
# Nth element of bg is order + 1 - s, so sum(bg) = order + 1
# so g1 * bg[0] + g1 * bg[1] + ... + g1 * bg[N] == g1 * sum(bg) ==
# == g1 * (order + 1) == g1
bg.append(bg[0].getOrder() + 1 - s)
res = [g1 * e for e in bg]
s = reduce((lambda x, y: x + y), res)
self.assertEqual(s, g1)
def test_neg(self):
num = 10
bg = BigNum(num)
self.assertEqual(-bg, BigNum(-num))
def test_mod_inverse(self):
bg = BigNum()
self.assertEqual(bg * bg.mod_inverse(), BigNum(1))
def test_pow(self):
num = 2
p = 2
bg = BigNum(num)**p
self.assertEqual(bg, BigNum(num**p))
def test_add_int(self):
first = 100
second = 337
bg1 = BigNum(first)
self.assertEqual(bg1 + second, BigNum(first + second))
def test_get_order(self):
order = BigNum(num=0)
self.assertEqual(BigNum.getOrder(), order)
import sys import datetime from libffpy import LibffPy, BigNum n = int(sys.argv[1]) l = LibffPy(n) g2 = l.gen2() g1 = l.gen1() start = datetime.datetime.now() bg = [BigNum() for _ in xrange(n - 1)] end = datetime.datetime.now() print "BigNum creation ellapsed: %s" % (end - start) s = reduce((lambda x,y: x + y), bg) bg.append(bg[0].getOrder() + 1 - s) start = datetime.datetime.now() res = [g2 * e for e in bg] end = datetime.datetime.now() print "G2 Multiplication ellapsed: %s" % (end - start) s = reduce((lambda x,y: x+ y), res) print "Test passed: %s" % (s == g2) start = datetime.datetime.now()
def test_pow(self):
gt = self.libff.pair(self.g1, self.g2)
bg = BigNum(3)
self.assertEqual(gt**bg, gt * gt * gt)