pollard rho minus 1

pollard_rho.py

@@ -47,7 +47,7 @@ if __name__ == '__main__':
     N2 = 1191515026104746183243378937330489098579 # ~2.5 часа
     N3 = 74048093444435937986114388960912781233885985702403356033834092312625704192350369 # слишком большое, не считает
 
-    number = N2
+    number = N1
 
     fact = rho_pollard(number)
     print(f"Первые 5 записей:")

pollard_rho_minus_1.py

@@ -0,0 +1,66 @@
+# (p-1)-алгоритм полларда, реализация _rho_minus_1_pollard из интернета
+import time
+from math import gcd
+from utils import is_prime
+
+def primes(B):
+    primes_list = []
+    is_prime = [True] * (B + 1)
+    is_prime[0] = is_prime[1] = False
+    for p in range(2, B + 1):
+        if is_prime[p]:
+            primes_list.append(p)
+            for i in range(p * p, B + 1, p):
+                is_prime[i] = False
+    return primes_list
+
+def _rho_minus_1_pollard(n, 
+                         B_start=100, 
+                         B_step=10, B_max=1000000000000):
+    B = B_start
+    while B <= B_max:
+        a = 2
+        for p in primes(B):
+            pp = 1
+            while pp * p <= B:
+                pp *= p
+            a = pow(a, pp, n)
+            g = gcd(a - 1, n)
+            if 1 < g < n:
+                return g, B
+        B *= B_step
+    return None, B_max
+
+def rho_minus_1_pollard(n):
+    factors, stack = [], [n]
+    while stack:
+        current = stack.pop()
+        if current == 1: continue
+        if is_prime(current):
+            factors.append(current)
+            continue
+
+        divisor, _ = _rho_minus_1_pollard(current)
+        if divisor is None:
+            factors.append(current)
+            continue
+
+        stack.append(divisor)
+        stack.append(current // divisor)
+
+    return sorted(factors)
+
+if __name__ == '__main__':
+    start_time = time.time()
+
+    N1 = 13611197472111783959
+    N2 = 1191515026104746183243378937330489098579
+    N3 = 74048093444435937986114388960912781233885985702403356033834092312625704192350369
+
+    number = N2
+
+    factors = rho_minus_1_pollard(number)
+    print(f"Факторизация числа {number}: {factors}")
+
+    elapsed_time = time.time() - start_time
+    print(f"Общее время работы программы: {elapsed_time} секунд.")

pollard_rho_minus_1_slow.py

@@ -0,0 +1,68 @@
+# (p-1)-алгоритм полларда, реализация _rho_minus_1_pollard из презентации препода
+import time
+from math import gcd, log as ln
+from utils import is_prime
+import random
+
+def primes(B):
+    primes_list = []
+    is_prime = [True] * (B + 1)
+    is_prime[0] = is_prime[1] = False
+    for p in range(2, B + 1):
+        if is_prime[p]:
+            primes_list.append(p)
+            for i in range(p * p, B + 1, p):
+                is_prime[i] = False
+    return primes_list
+
+def _rho_minus_1_pollard(n, 
+                         B_start=100, 
+                         B_step=10, B_max=1000000000000):
+    B = B_start
+    while B <= B_max:
+        a = random.randint(2, n - 1)
+        d = gcd(a, n)
+        if d >= 2: return d
+        for p in primes(B):
+            l = int(ln(n)/ln(p))
+            a = pow(a, p**l, n)
+        d = gcd(a-1, n)
+        if not (d == 1 or d == n): 
+            return d
+        B *= B_step
+        
+    return None
+
+def rho_minus_1_pollard(n):
+    factors, stack = [], [n]
+    while stack:
+        current = stack.pop()
+        if current == 1: continue
+        if is_prime(current):
+            factors.append(current)
+            continue
+
+        divisor = _rho_minus_1_pollard(current)
+        if divisor is None:
+            factors.append(current)
+            continue
+
+        stack.append(divisor)
+        stack.append(current // divisor)
+
+    return sorted(factors)
+
+if __name__ == '__main__':
+    start_time = time.time()
+
+    N1 = 13611197472111783959
+    N2 = 1191515026104746183243378937330489098579
+    N3 = 74048093444435937986114388960912781233885985702403356033834092312625704192350369
+
+    number = N2
+
+    factors = rho_minus_1_pollard(number)
+    print(f"Факторизация числа {number}: {factors}")
+
+    elapsed_time = time.time() - start_time
+    print(f"Общее время работы программы: {elapsed_time} секунд.")