def shanks_worst_tests(numOfTests: int, numOfBits: list, randSeed=0):
seed(randSeed)
total_steps_class_list, times_clasic_list, total_memory_clasic = [], [], []
total_steps_grumpy_list, times_grumpy_list, total_memory_grumpy = [], [], []
for bits in numOfBits:
time_clas, time_grumpy = [], []
steps_clas, steps_grumpy = [], []
mem_clas, mem_grumpy = [], []
print("Started: ", bits)
if bits >= 50:
numOfTests = 50
elif bits >= 40:
numOfTests = 100
for iter in range(numOfTests):
p, g, exp, h = gnp.worst_shanks_numbers(bits)
t = timer()
x_c, small_clas, giant_clas, mem_c = shanks_classic(g, h, p, p - 1)
steps_clas.append(small_clas + giant_clas)
mem_clas.append(mem_c)
passed_time = (timer() - t) * 1000
time_clas.append(passed_time)
t = timer()
x_c, oper, mem_c = shanks_two_grumpys_one_baby(g, h, p, p - 1)
if x_c != exp:
print("NG")
steps_grumpy.append(oper)
mem_grumpy.append(mem_c)
passed_time = (timer() - t) * 1000
time_grumpy.append(passed_time)
print(
f"Avg steps clasic:{avg(steps_clas) / ceil(sqrt(p)):.4f} -- Avg steps grumpy:{avg(steps_grumpy) / ceil(sqrt(p)):.4f}"
)
print(
f"Avg memory clasic:{avg(mem_clas) / ceil(sqrt(p)):.4f} -- Avg memory grumpy:{avg(mem_grumpy) / ceil(sqrt(p)):.4f}"
)
print(
f"Avg time clasic:{avg(time_clas):.4f} -- Avg time grumpy:{avg(time_grumpy):.4f}"
)
total_steps_class_list.append(avg(steps_clas) / ceil(sqrt(p)))
total_steps_grumpy_list.append(avg(steps_grumpy) / ceil(sqrt(p)))
times_clasic_list.append(avg(time_clas))
times_grumpy_list.append(avg(time_grumpy))
total_memory_clasic.append(avg(mem_clas) / ceil(sqrt(p)))
total_memory_grumpy.append(avg(mem_grumpy) / ceil(sqrt(p)))
print(f"Finished: {bits}\n")
print(
f"Avg steps clasic:{avg(total_steps_class_list):.4f} -- Avg steps grumpy:{avg(total_steps_grumpy_list):.4f}"
)
print(
f"Avg memory clasic:{avg(total_memory_clasic):.4f} -- Avg memory grumpy:{avg(total_memory_grumpy):.4f}"
)
print(
f"Avg time clasic:{avg(times_clasic_list):.4f} -- Avg time grumpy:{avg(times_grumpy_list):.4f}"
)
def shanks_interleved(g, h, p, ordin):
n = ceil(sqrt(ordin))
e = 1
u = pow(g, p - n - 1, p)
s = h
baby, giant = {e:0}, {s:0}
# lista = {e:0, s:0}
for j in range(1, n + 1):
e = (e * g) % p
if e == h:
return j, 2 * j + 1, getsizeof(baby) + getsizeof(giant) #getsizeof(lista)
else:
i = giant.get(e, None)
# i = lista.get(e, None)
if i:
return (j + i*n) % ordin, 2 * j + 1, getsizeof(baby) + getsizeof(giant) #getsizeof(lista)
else:
baby[e] = j
# lista[e] = j
s = (s * u) % p
i = baby.get(s, None)
# i = lista.get(s, None)
if i:
return (j*n + i) % ordin, 2 * (j + 1), getsizeof(baby) + getsizeof(giant)#getsizeof(lista)
else:
giant[s] = j
# lista[s] = j
return None
def shanks_centered(g, h, p, ordin):
n = ceil(sqrt(ordin))
K = ordin // 2
small_steps = 1
e = pow(g, K, p)
lista = {e: 0}
for j in range(1, n):
e = (e * g) % p
if e == h:
return K + j, small_steps, 0
else:
lista[e] = j
small_steps += 1
u = pow(g, p - n - 1, p)
s = pow(g, n, p)
ep = em = h
for i in range(0, n):
try:
j = lista[em]
return j + K - i * n, small_steps, 2 * (i + 1)
except KeyError:
try:
j = lista[ep]
return K + j + i * n, small_steps, 2 * (i + 1)
except KeyError:
ep = (ep * u) % p
em = (em * s) % p
return None
def shanks_order_unkown(g, h, p):
rad_p = ceil(sqrt(p - 1))
n = 100
lista_n = []
while n < rad_p:
lista_n.append(n)
n *= 10
lista_n.append(rad_p)
last_n = 1
e = 1
lista = {e: 0}
for n in lista_n:
for j in range(last_n, n + 1):
e = (e * g) % p
if e == h:
return j
lista[e] = j
u = pow(g, p - n - 1, p)
l = h
for i in range(0, n + 1):
try:
j = lista[l]
return i * n + j
except KeyError:
l = (l * u) % p
last_n = n + 1
return None
def primes_up_to_B(B: int):
a = [1] * B
for i in range(2, ceil(sqrt(B))):
if a[i]:
for j in range(i * i, B, i):
a[j] = 0
return [i for i in range(len(a)) if a[i] == 1][2:]
def shanks_two_grumpys_one_baby(g, h, p, ordin):
n = ceil(sqrt(ordin))
m = ceil(n/2)
u = pow(g, m, p)
s = pow(g, p - (m + 1) - 1, p)
b = 1
giant1 = h
giant2 = pow(h, 2, p)
babys, giants1, giants2 = {b: 0}, {giant1: 0}, {giant2: 0}
for i in range(1, n + 1):
b = (b * g) % p
if b == h:
return i, 3 * (i - 1) + 1, getsizeof(babys) + getsizeof(giants1) + getsizeof(giants2)
else:
j = giants1.get(b, None)
if j:
return (i - j * m) % ordin, 3 * (i - 1) + 1, getsizeof(babys) + getsizeof(giants1) + getsizeof(giants2)
else:
j = giants2.get(b, None)
if j:
r = (i + j * (m + 1)) // 2
l = ordin // 2
for _ in range(3):
if pow(g, r, p) == h:
return r, 3 * (i - 1) + 1, getsizeof(babys) + getsizeof(giants1) + getsizeof(giants2)
r += l
else:
babys[b] = i
giant1 = (giant1 * u) % p
j = babys.get(giant1, None)
if j:
return (j - i * m) % ordin, 3 * (i - 1) + 2, getsizeof(babys) + getsizeof(giants1) + getsizeof(giants2)
else:
j = giants2.get(giant1, None)
if j:
return (i * m + j * (m + 1)) % ordin, 3 * (i - 1) + 2, getsizeof(babys) + getsizeof(giants1) + getsizeof(giants2)
else:
giants1[giant1] = i
giant2 = (giant2 * s) % p
j = babys.get(giant2, None)
if j:
r = (j + i * (m + 1)) // 2
l = ordin // 2
for _ in range(3):
if pow(g, r, p) == h:
return r, 3 * i , getsizeof(babys) + getsizeof(giants1) + getsizeof(giants2)
r += l
else:
j = giants1.get(giant2, None)
if j:
return (j * m + i * (m + 1)) % ordin, 3 * i, getsizeof(babys) + getsizeof(giants1) + getsizeof(giants2)
else:
giants2[giant2] = i
return None
def worst_shanks_numbers(numOfBits: int):
prime = get_primes(numOfBits, 1)[0]
while prime < 10:
prime = get_primes(numOfBits, 1)[0]
generator = artmod.generator_Zp(prime)
n = math.ceil(artmod.sqrt(prime - 1))
exp = n * (n - 1)
if exp >= prime - 1:
exp = n * (n - 2)
h = pow(generator, exp, prime)
return prime, generator, exp, h
def shanks_classic_better_avg(g, h, p, ordin):
n = ceil(sqrt(ordin/2))
e = 1
lista = {e: 0}
for j in range(1, n):
e = (e * g) % p
if e == h:
return j, j, 0, getsizeof(lista)
else:
lista[e] = j
u = pow(g, p - n - 1, p)
e = h
for i in range(0, 2 * n):
try:
j = lista[e]
return i * n + j, n, i + 1, getsizeof(lista)
except KeyError:
e = (e * u) % p
return None
def shanks_classic_binary_search(g, h, p, ordin):
n = ceil(sqrt(ordin))
small_steps = 1
e = 1
lista = [(e,0)]
for j in range(1, n):
e = (e * g) % p
if e == h:
return j, small_steps, 0, getsizeof(lista)
else:
lista.append((e,j))
small_steps += 1
lista.sort(key=lambda x: x[0])
u = pow(g, p - n - 1, p)
e = h
for i in range(0, n):
j = find_index(lista, e)
if j != None:
return i * n + j, small_steps, i + 1, getsizeof(lista)
else:
e = (e * u) % p
return None
def shanks_classic(g, h, p, ordin):
n = ceil(sqrt(ordin))
e = 1
lista = {e: 0}
dict_limit = 1.15 * (10 ** 10)
for j in range(1, n):
if getsizeof(lista) > dict_limit:
return None, None, None, None
e = (e * g) % p
if e == h:
return j, j, 0, getsizeof(lista)
else:
lista[e] = j
u = pow(g, p - n - 1, p)
e = h
for i in range(0, n):
try:
j = lista[e]
return i * n + j, n, i + 1, getsizeof(lista)
except KeyError:
e = (e * u) % p
return None
def optim_factors(ordin):
factori = [pow(x, e) for x, e in factorint(ordin).items()]
factori.sort()
if len(factori) == 1:
return Shanks_ordin_cunoscut(g, h, p, ordin)
if len(factori) == 2:
l = ceil(sqrt(factori[1]))
m = ceil(sqrt(factori[0]))
else:
fact_1 = reduce(mul, factori[:-1])
if fact_1 > factori[-1]:
l = ceil(sqrt(fact_1))
m = ceil(sqrt(factori[-1]))
else:
l = ceil(sqrt(factori[-1]))
m = ceil(sqrt(fact_1))
return l, m
def shanks_classic_with_memory(g, h_values, p, ordin):
n = ceil(sqrt(ordin))
small_steps = 1
e = 1
lista = {e: 0}
for j in range(1, n):
e = (e * g) % p
lista[e] = j
small_steps += 1
u = pow(g, p - n - 1, p)
exponents, giant_steps_list = [], []
for h in h_values:
e = h
for i in range(0, n):
try:
j = lista[e]
exponents.append(i * n + j)
giant_steps_list.append(i + 1)
break
except KeyError:
e = (e * u) % p
return exponents, small_steps, giant_steps_list, getsizeof(lista)
return exponents[-1] % (p - 1), t_cong, it
if __name__ == '__main__':
i = 0
ts, tts = [], []
its = []
seed(42)
for q in range(5):
for _ in range(500):
ok = 1
while ok:
ok = 0
p, g, exponent, h = logarithm_test_numbers(15, safe=False)
x = 2**ceil(log2(p - 1))
B = ceil(exp(1 / sqrt(2) * sqrt(log(x) * log(log(x)))) / 2)
# print(L(p), shanks_complex(p))
primesB = primes_up_to_B(B)
max_equations = primes_upto(B) + 5
# print(B, max_equations, p)
t = timer()
x, ta, it = SELD_lect11(g, h, p, B, max_equations, primesB, 42)
ts.append((timer() - t) * 1000)
its.append(it)
if x == exponent:
# print("DA")
i += 1
else:
if pow(g, x, p) != h:
print("Nu")
avg_ts = avg(ts)
from aritmetica_modulara import sqrt, extended_euclid, avg
from math import gcd, ceil, floor
import random as rand
from functools import partial
from sys import getsizeof
A = (sqrt(5) - 1) / 2
def found_match(g, h, p, a_x, a_y, b_x, b_y):
u = (a_x - a_y) % (p - 1)
v = (b_y - b_x) % (p - 1)
if v == 0:
return None
d, s, t = extended_euclid(v, p - 1)
if d == 1:
return (u * s) % (p - 1)
else:
# print("D: ",d)
w = ((u * s) % (p - 1)) // d
sol_pos = [w] + [(w + k * ((p - 1) // d)) % (p - 1)
for k in range(1, d)]
for sol in sol_pos:
if pow(g, sol, p) == h:
return sol
return None
def hash_function(num, r):
return floor(((A * num) % 1) * r) + 1
def test_pollard(numOfTests: int,
listOfBits: list,
contests: dict,
img_path: str,
rand_seeds=[0]):
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from itertools import cycle
marker = cycle(rand.sample(Line2D.markers.keys(), len(contests)))
plt.tight_layout(pad=0.05)
times = [[[0 for _ in rand_seeds] for _ in contests] for _ in listOfBits]
times_avg = [[0 for _ in contests] for _ in listOfBits]
iterations = [[[0 for _ in rand_seeds] for _ in contests]
for _ in listOfBits]
iterations_avg = [[0 for _ in contests] for _ in listOfBits]
for ind_b, bits in enumerate(listOfBits):
print("Bits: ", bits)
tests = num_of_tests(bits, numOfTests)
print("Nr of tests: ", tests)
p_set = set()
print("Seed: ", end='')
for ind_s, seed in enumerate(rand_seeds):
rand.seed(seed)
print(seed, end=', ')
distinct_primes = number_of_distinct_primes(bits)
for _ in range(tests):
p, g, exp, h = logarithm_test_numbers(bits, safe=False)
p_iter = 0
while p in p_set and len(
p_set) < distinct_primes - 1 and p_iter < 10**2:
p, g, exp, h = logarithm_test_numbers(bits, safe=False)
p_iter += 1
p_set.add(p)
bit_seed = rand.randint(1, seed)
for ind_c, c in enumerate(contests):
t = timer()
x, iter = pollard_rho(g,
h,
p,
cycle=c[0],
func=c[1],
rand_seed=bit_seed)
if x != exp:
print("WRONG " + c[0] + " " + c[1])
times[ind_b][ind_c][ind_s] += (timer() - t) * 1000
iterations[ind_b][ind_c][ind_s] += iter
for ind_c, c in enumerate(contests):
iterations[ind_b][ind_c][ind_s] /= tests
times[ind_b][ind_c][ind_s] /= tests
print()
for ind_c, c in enumerate(contests):
iterations_avg[ind_b][ind_c] = avg(
iterations[ind_b][ind_c]) / ceil(sqrt(p))
times_avg[ind_b][ind_c] = avg(times[ind_b][ind_c])
print(
f"Cycle: {c[0]}, function: {c[1]}, itertions: {iterations_avg[ind_b][ind_c]:.4f}, time: {times_avg[ind_b][ind_c]:.3f}"
)
print()
plt.figure(0)
for ind_c, c in enumerate(contests):
the_times = [t[ind_c] for t in times_avg]
plt.plot(listOfBits,
the_times,
marker=next(marker),
label=c[0] + '_' + c[1])
plt.legend()
plt.ylabel("Milisecunde")
plt.xlabel("biti")
# plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
plt.yscale('log')
plt.savefig(img_path + '/pollard_time.png', bbox_inches='tight')
plt.figure(1)
print("The avg number of iterations: ", end='')
avgits = []
for ind_c, c in enumerate(contests):
the_iterations = [it[ind_c] for it in iterations_avg]
avg_c = avg(the_iterations)
print(c[0] + '-' + c[1] + f": {avg_c:.4f}", end=' ')
avgits.append(avg_c)
plt.plot(listOfBits,
the_iterations,
marker=next(marker),
label=c[0] + '_' + c[1])
plt.legend()
plt.ylabel("Iteratii")
plt.xlabel("biti")
# plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
plt.yscale('log')
plt.savefig(img_path + '/pollard_iter.png', bbox_inches='tight')
plt.show()
return avgits
def test_pollard_dellays(numOfTests: int,
listOfBits: list,
contests: dict,
img_path: str,
rand_seeds=[0]):
iterations = [[[0 for _ in rand_seeds] for _ in contests]
for _ in listOfBits]
iterations_avg = [[0 for _ in contests] for _ in listOfBits]
lambs = [[[0 for _ in rand_seeds] for _ in contests] for _ in listOfBits]
lambs_avg = [[0 for _ in contests] for _ in listOfBits]
mus = [[[0 for _ in rand_seeds] for _ in contests] for _ in listOfBits]
mus_avg = [[0 for _ in contests] for _ in listOfBits]
for ind_b, bits in enumerate(listOfBits):
print("Bits: ", bits)
tests = num_of_tests(bits, numOfTests)
print("Nr of tests: ", tests)
p_set = set()
print("Seed: ", end='')
for ind_s, seed in enumerate(rand_seeds):
rand.seed(seed)
print(seed, end=', ')
distinct_primes = number_of_distinct_primes(bits)
for _ in range(tests):
p, g, exp, h = logarithm_test_numbers(bits, safe=False)
p_iter = 0
while p in p_set and len(
p_set) < distinct_primes - 1 and p_iter < 10**2:
p, g, exp, h = logarithm_test_numbers(bits, safe=False)
p_iter += 1
p_set.add(p)
bit_seed = rand.randint(1, seed)
for ind_c, c in enumerate(contests):
x, iter, lamb, mu = pollard_rho(g,
h,
p,
cycle=c[0],
func=c[1],
rand_seed=bit_seed)
if x != exp:
print("WRONG " + c[0] + " " + c[1])
iterations[ind_b][ind_c][ind_s] += iter
lambs[ind_b][ind_c][ind_s] += lamb
mus[ind_b][ind_c][ind_s] += mu
for ind_c, c in enumerate(contests):
iterations[ind_b][ind_c][ind_s] /= tests
lambs[ind_b][ind_c][ind_s] /= tests
mus[ind_b][ind_c][ind_s] /= tests
print()
for ind_c, c in enumerate(contests):
iterations_avg[ind_b][ind_c] = avg(
iterations[ind_b][ind_c]) / ceil(sqrt(p))
lambs_avg[ind_b][ind_c] = avg(lambs[ind_b][ind_c]) / ceil(sqrt(p))
mus_avg[ind_b][ind_c] = avg(mus[ind_b][ind_c]) / ceil(sqrt(p))
print(
f"Cycle: {c[0]}, function: {c[1]}, itertions: {iterations_avg[ind_b][ind_c]:.4f}, lambs: {lambs_avg[ind_b][ind_c]:.4f} mus: {mus_avg[ind_b][ind_c]:.4f}, "
f"rho: {lambs_avg[ind_b][ind_c] + mus_avg[ind_b][ind_c]:.4f} delay: {iterations_avg[ind_b][ind_c]/(lambs_avg[ind_b][ind_c] + mus_avg[ind_b][ind_c]):.4f}"
)
print()
for ind_c, c in enumerate(contests):
the_iterations = avg([it[ind_c] for it in iterations_avg])
the_lambs = [lamb[ind_c] for lamb in lambs_avg]
the_mus = [mu[ind_c] for mu in mus_avg]
the_rhos = avg([x + y for x, y in zip(the_lambs, the_mus)])
print(
f"Cycle: {c[0]}, function: {c[1]}, itertions_avg: {the_iterations:.4f}, rho: {the_rhos:.4f}, delays {the_iterations/the_rhos:.4f}"
)
def test_shanks_clasic_inter_grumpy(numOfTests: int,
numOfBits: list,
randSeeds=[0]):
total_steps_class_list, times_clasic_list, total_memory_clasic = [], [], []
total_steps_inter_list, times_inter_list, total_memory_inter = [], [], []
total_steps_grumpy_list, times_grumpy_list, total_memory_grumpy = [], [], []
for bits in numOfBits:
seed_steps_class_list, seed_times_clasic_list, seed_total_memory_clasic = [], [], []
seed_steps_inter_list, seed_times_inter_list, seed_total_memory_inter = [], [], []
seed_steps_grumpy_list, seed_times_grumpy_list, seed_total_memory_grumpy = [], [], []
print("Started: ", bits)
if bits >= 50:
numOfTests = 50
elif bits >= 40:
numOfTests = 100
elif bits >= 30:
numOfTests = 500
for s in randSeeds:
seed(s)
time_clas, time_inter, time_grumpy = [], [], []
steps_clas, steps_inter, steps_grumpy = [], [], []
mem_clas, mem_inter, mem_grumpy = [], [], []
for iter in range(numOfTests):
p, g, exp, h = gnp.logarithm_test_numbers(bits, False)
t = timer()
x_c, small_clas, giant_clas, mem_c = shanks_classic(
g, h, p, p - 1)
steps_clas.append(small_clas + giant_clas)
mem_clas.append(mem_c)
passed_time = (timer() - t) * 1000
time_clas.append(passed_time)
t = timer()
x_c, oper, mem_c = shanks_interleved(g, h, p, p - 1)
if x_c != exp:
print("NI")
steps_inter.append(oper)
mem_inter.append(mem_c)
passed_time = (timer() - t) * 1000
time_inter.append(passed_time)
t = timer()
x_c, oper, mem_c = shanks_two_grumpys_one_baby(g, h, p, p - 1)
if x_c != exp:
print("NG")
steps_grumpy.append(oper)
mem_grumpy.append(mem_c)
passed_time = (timer() - t) * 1000
time_grumpy.append(passed_time)
seed_steps_class_list.append(avg(steps_clas) / ceil(sqrt(p)))
seed_steps_inter_list.append(avg(steps_inter) / ceil(sqrt(p)))
seed_steps_grumpy_list.append(avg(steps_grumpy) / ceil(sqrt(p)))
seed_times_clasic_list.append(avg(time_clas))
seed_times_inter_list.append(avg(time_inter))
seed_times_grumpy_list.append(avg(time_grumpy))
seed_total_memory_clasic.append(avg(mem_clas) / ceil(sqrt(p)))
seed_total_memory_inter.append(avg(mem_inter) / ceil(sqrt(p)))
seed_total_memory_grumpy.append(avg(mem_grumpy) / ceil(sqrt(p)))
print(
f"Avg steps clasic:{avg(seed_steps_class_list):.4f} -- Avg steps inter:{avg(seed_steps_inter_list):.4f} -- Avg steps grumpy:{avg(seed_steps_grumpy_list):.4f}"
)
print(
f"Avg memory clasic:{avg(seed_total_memory_clasic):.4f} -- Avg memory inter:{avg(seed_total_memory_inter):.4f} -- Avg memory grumpy:{avg(seed_total_memory_grumpy):.4f}"
)
print(
f"Avg time clasic:{avg(seed_times_clasic_list):.4f} -- Avg time inter:{avg(seed_times_inter_list):.4f} -- Avg time grumpy:{avg(seed_times_grumpy_list):.4f}"
)
total_steps_class_list.append(avg(seed_steps_class_list))
total_steps_inter_list.append(avg(seed_steps_inter_list))
total_steps_grumpy_list.append(avg(seed_steps_grumpy_list))
times_clasic_list.append(avg(seed_times_clasic_list))
times_inter_list.append(avg(seed_times_inter_list))
times_grumpy_list.append(avg(seed_times_grumpy_list))
total_memory_clasic.append(avg(seed_total_memory_clasic))
total_memory_inter.append(avg(seed_total_memory_inter))
total_memory_grumpy.append(avg(seed_total_memory_grumpy))
print(f"Finished: {bits}\n")
print(
f"Avg steps clasic:{avg(total_steps_class_list):.4f} -- Avg steps inter:{avg(total_steps_inter_list):.4f} -- Avg steps grumpy:{avg(total_steps_grumpy_list):.4f}"
)
print(
f"Avg memory clasic:{avg(total_memory_clasic):.4f} -- Avg memory inter:{avg(total_memory_inter):.4f} -- Avg memory grumpy:{avg(total_memory_grumpy):.4f}"
)
print(
f"Avg time clasic:{avg(times_clasic_list):.4f} -- Avg time inter:{avg(times_inter_list):.4f} -- Avg time grumpy:{avg(times_grumpy_list):.4f}"
)
def L(x):
x = 2**ceil(log2(x))
return exp(sqrt(2) * sqrt(log(x) * log(log(x))))