pollard rho

.gitignore

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+__pycache__
+var61.txt

pollard_rho.py

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+import random
+import time
+from math import gcd
+from utils import is_prime
+
+log = []
+
+def logger(i, x, y, gcd):
+    global log
+    if len(log) > 10: log = log[:5] + log[-5:]
+    log.append(f'iter = {i}, a = {x}, b = {y}, gcd(x-y, n) = {gcd}')
+
+def _rho_pollard(N):
+    x = random.randint(1, N - 1)
+    y, i, stage = 1, 0, 2
+    while gcd(N, abs(x - y)) == 1:
+        if i == stage:
+            y = x
+            stage <<= 1
+        x = (x * x + 1) % N
+        i += 1
+        logger(i, x, y, 1)
+
+    d = gcd(N, abs(x - y))
+    return d
+
+def rho_pollard(N):
+    factors, stack = [], [N]
+    while stack:
+        current = stack.pop()
+        if current == 1: continue
+        if is_prime(current):
+            factors.append(current)
+            continue
+
+        divisor = _rho_pollard(current)
+
+        stack.append(divisor)
+        stack.append(current // divisor)
+
+    return sorted(factors)
+
+if __name__ == '__main__':
+    start_time = time.time()
+
+    N1 = 13611197472111783959 # менее секунды
+    N2 = 1191515026104746183243378937330489098579 # ~2.5 часа
+    N3 = 74048093444435937986114388960912781233885985702403356033834092312625704192350369 # слишком большое, не считает
+
+    number = N2
+
+    fact = rho_pollard(number)
+    print(f"Первые 5 записей:")
+    for e in log[:5]: print(e)
+    print(f"Последние 5 записей:")
+    for e in log[-5:]: print(e)
+
+    print(f"\nФакторизация числа {number}: {fact}")
+
+    elapsed_time = time.time() - start_time
+    print(f"Общее время работы программы: {elapsed_time} секунд.")
+
+# ЧИСЛО 1
+# Первые 5 записей:
+# iter = 1, a = 5329095354621087087, b = 1, gcd(x-y, n) = 1
+# iter = 2, a = 3783727702130089265, b = 1, gcd(x-y, n) = 1
+# iter = 3, a = 7095258768956724187, b = 3783727702130089265, gcd(x-y, n) = 1  
+# iter = 4, a = 12321744609163004701, b = 3783727702130089265, gcd(x-y, n) = 1 
+# iter = 5, a = 12323988029058238822, b = 12321744609163004701, gcd(x-y, n) = 1
+# Последние 5 записей:
+# iter = 139741, a = 4060051924514528227, b = 13218681676865582158, gcd(x-y, n) = 1
+# iter = 139742, a = 5345059737904245033, b = 13218681676865582158, gcd(x-y, n) = 1
+# iter = 139743, a = 260418000338173485, b = 13218681676865582158, gcd(x-y, n) = 1 
+# iter = 139744, a = 6264061095634053, b = 13218681676865582158, gcd(x-y, n) = 1   
+# iter = 139745, a = 2327761422004049427, b = 13218681676865582158, gcd(x-y, n) = 1
+
+# Факторизация числа 13611197472111783959: [2978457007, 4569882137]
+# Общее время работы программы: 0.1660001277923584 секунд.
+
+# ЧИСЛО 2
+# Первые 5 записей:
+# iter = 1, a = 108874332809547025907597843044982083159, b = 1, gcd(x-y, n) = 1
+# iter = 2, a = 1097955600928184726703035165824138374896, b = 1, gcd(x-y, n) = 1
+# iter = 3, a = 488285885718394315847189711962319835985, b = 1097955600928184726703035165824138374896, gcd(x-y, n) = 1
+# iter = 4, a = 401360566326618042671847881691355213222, b = 1097955600928184726703035165824138374896, gcd(x-y, n) = 1
+# iter = 5, a = 1156594234894495846629254317716430429392, b = 401360566326618042671847881691355213222, gcd(x-y, n) = 1
+# Последние 5 записей:
+# iter = 6760246676, a = 924157203270482170564225956282613146461, b = 508819885811370882496826690334047716214, gcd(x-y, n) = 1
+# iter = 6760246677, a = 948491128612786337471979266549113961972, b = 508819885811370882496826690334047716214, gcd(x-y, n) = 1
+# iter = 6760246678, a = 1132206947658731453064263670716458783892, b = 508819885811370882496826690334047716214, gcd(x-y, n) = 1
+# iter = 6760246679, a = 320645645670504982689398810315637415969, b = 508819885811370882496826690334047716214, gcd(x-y, n) = 1
+# iter = 6760246680, a = 1089717013392774221300379814430702238408, b = 508819885811370882496826690334047716214, gcd(x-y, n) = 1
+
+# Факторизация числа 1191515026104746183243378937330489098579: [28078932453784161973, 42434484575433608423]
+# Общее время работы программы: 9818.221776247025 секунд.

utils.py

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+def is_prime(N):
+    if N < 2:
+        return False
+    for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]:
+        if N % p == 0: return N == p
+    d = N - 1
+    s = 0
+    while d % 2 == 0:
+        d >>= 1
+        s += 1
+    for a in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]:
+        if a >= N: continue
+        x = pow(a, d, N)
+        if x == 1 or x == N - 1: continue
+        for _ in range(s - 1):
+            x = pow(x, 2, N)
+            if x == N - 1: break
+        else: return False
+    return True