def conv_mul_mod(a, b, n, q):
if len(a) < n:
a = extend(a, n)
if len(b) < n:
b = extend(b, n)
c = np.zeros(n)
for i in range(n):
for j in range(n):
k = mod(i + j, n)
c[k] = mod(c[k] + a[i] * b[k - i], q)
return c
def poly_egcd(a, b, q):
a = mod(a, q)
b = mod(b, q)
r0 = a
r1 = b
x1 = y0 = np.array([0])
y1 = x0 = np.array([1])
while r1.any():
k, _ = poly_divmod(r0, r1, q)
r0, r1 = poly_update_egcd(r0, r1, k, q)
x0, x1 = poly_update_egcd(x0, x1, k, q)
y0, y1 = poly_update_egcd(y0, y1, k, q)
return reduce(r0), reduce(x0), reduce(y0)
def poly_divmod(a, b, q):
n = deg(a)
d = deg(b)
a = mod(a, q)
b = mod(b, q)
b = b[:d + 1]
r = a[:n + 1]
e = deg(r)
k = np.zeros(n + 1)
while e >= d and not (e == 0 and r[0] == 0):
temp = np.zeros(e - d + 1)
temp[e - d] = mod(r[e] * inverse_mod(b[d], q), q)
k = add_mod(k, temp, q)
r = subtract_mod(r, poly_mul_mod(temp, b, q), q)
e = deg(r)
return k, r
def poly_mul_mod(a, b, q):
n = deg(a)
m = deg(b)
c = np.zeros(n + m + 1)
ac = np.zeros(n + m + 1)
bc = np.zeros(n + m + 1)
ac[:n + 1] = a[:n + 1]
bc[:m + 1] = b[:m + 1]
for i in range(deg(a) + 1):
c += ac[i] * bc
c = mod(c, q)
bc = np.roll(bc, 1)
return c
from addition import add
from subtraction import sub
from multiplication import multi
from division import div
from modulo import mod
print ("a=6, b=4")
print ("sum:", add(6, 4))
print ("difference:", sub(6, 4))
print ("product:", multi(6, 4))
print ("quotient:", div(6, 4))
print ("remainder:", mod(6, 4))
def add_mod(a, b, q):
return mod(add(a, b), q)
def subtract_mod(a, b, q):
return mod(subtract(a, b), q)
def center_lift(a, q):
a = mod(a, q)
a[a > q / 2] = a[a > q / 2] - q
return np.array(a)