def dlog(b, a, m):
counter = 0
result = exp(b, 0, m)
while (result != a):
counter = counter + 1
result = exp(b, counter, m)
return counter
def test(a, n):
t, u = 0, n - 1
while u % 2 == 0:
t += 1
u //= 2
x = exp(a, u, n)
if x == 1 or x == n - 1:
return False
for _ in range(t - 1):
x = exp(x, 2, n)
if x == n - 1:
break
else:
return True
def test(a, n):
t, u = 0, n - 1
while (u % 2 == 0):
t += 1 #t >= 1, u is odd, n=1 = 2^t * u
u //= 2 #initialization
x = exp(a, u, n) #initializing x0 = a^u mod n
for _ in range(t - 1): #for i = 1 to t
x_prev = x #xi-1
x = exp(x_prev, 2, n) #xi = (xi-1)^2 mod n
if x == 1 and x_prev != 1 and x_prev != (n - 1): #NSR test
return True
if x != 1: #Fermat test
return True
return False
def test(a, n):
s = n - 1
t = 0
while (s % 2 == 0): #2로 더이상 나누어지지 않을 때까지
s //= 2
t += 1
u = s # a=4 u=5 t=4
x = exp(a, u, n)
for i in range(t): #NSR Test
xx = exp(x, 2, n)
if (xx == 1):
if (exp(x, 1, n) != 1 and exp(x, 1, n) != n - 1):
return True # 확실히 합성수
x = xx
if (xx != 1): # Fermat Test
return True
return False
def test(a, n):
# n-1을 인수분해
t = 0
nn = n - 1
while ((nn % 2) == 0):
t += 1
nn //= 2
u = nn
# print("a : ", a, "n : ", n, "u: ", u, "t: ", t)
# t=1 부터 n까지 a^u를 거듭제곱하면서 NSR test
x_0 = 0
x_i = exp(a, u, n)
for i in range(t):
# print("x_0 : ", x_0, "x_i : ", x_i)
if (x_i == 1 or x_i == (n - 1)):
return False # prime이라는 증거
x_0 = x_i
x_i = exp(x_i, 2, n)
return True # composite이다.
def test(a, n):
y = n - 1
cnt = 0
while (1):
if (y % 2 == 0):
y //= 2
cnt += 1
else:
break
t = cnt
u = y
x_0 = exp(a, u, n)
for i in range(t):
x = exp(x_0, 2, n)
if x == 1 and x_0 != 1 and x_0 != n - 1:
return True
x_0 = x
if x != 1:
return True
return False
def test(a, n):
# 1. 정수 k,q를 찾는다.
while True:
k = 1
q_remain = (n - 1) % (exp(2, k, n))
if q_remain == 0:
q = (n - 1) // (exp(2, k, n))
break
k += 1
# 2. 1 < a < n-1 임의 정수 a 선택
# -> 인수로 이미 a를 받았다.
# 3. 첫 번쨰 조건
if exp(a, q, n) % n == 1:
return False
# 4. 두 번째 조건
for j in range(0, k):
x = exp(2, j, n)
if exp(a, x * q, n) % n == n - 1:
return False
return True
def test(a, n):
# n-1 = (2^t) * u
t = 0
u = n - 1
while u % 2 == 0:
t += 1
u //= 2
# x0 = (a^u) mod n
x = exp(a, u, n)
updated_x = x
# NSR test
for _ in range(t):
updated_x = exp(x, 2, n)
if updated_x == 1 and x != 1 and x != n - 1:
return True
x = updated_x
# Fermat test
if updated_x != 1:
return True
return False
def dlog(b, a, m):
cur = 1
for i in range(1, m):
cur = exp(b, i, m)
if cur == a:
return i
# from tqdm import tqdm # progress bar
from exponentiation import exp
import random
def dlog(b, a, m):
cur = 1
for i in range(1, m):
cur = exp(b, i, m)
if cur == a:
return i
if __name__ == "__main__":
base = 3
modulus = 65537 # 2 ** 16 + 1
expos = [1, 2, 65535]
try:
# for expo in tqdm(expos):
for expo in expos:
powed = exp(base, expo, modulus)
loged = dlog(base, powed, modulus)
print("({},{},{},{},{}),".format(expo, base, powed, loged,
modulus))
assert expo == loged
print(">> All the tests passed <<")
except:
print("expo({}) and loged({}) is not equal".format(expo, loged))
def dlog(a, b, n):
x = 0
for i in range(1,n):
x = exp(a,i,n)
if x == b:
return i