Created
July 12, 2018 06:16
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Pollard's Rho algorithm
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| from argparse import ArgumentParser | |
| import numpy as np | |
| gcd_table = {} | |
| def gcd(a, b): | |
| while a % b != 0: | |
| a, b = b, a % b | |
| return b | |
| bound = 10000 | |
| def b_gcd(u, v): | |
| """ | |
| binary gcd (not mine) | |
| """ | |
| if u in gcd_table: | |
| table = gcd_table.get(u) | |
| if v in table: | |
| return table[v] | |
| elif u < bound: | |
| gcd_table[u] = {} | |
| if u == v: | |
| return u | |
| elif u == 0: | |
| return v | |
| elif v == 0: | |
| return u | |
| # u is even | |
| elif u & 1 == 0: | |
| # v is even | |
| if v & 1 == 0: | |
| b = 2*gcd(u >> 1, v >> 1) | |
| if u < bound: gcd_table[u][v] = b | |
| return b | |
| # v is odd | |
| else: | |
| b = gcd(u >> 1, v) | |
| if u < bound: gcd_table[u][v] = b | |
| return b | |
| # u is odd | |
| elif u & 1 != 0: | |
| # v is even | |
| if v & 1 == 0: | |
| b = gcd(u, v >> 1) | |
| if u < bound: gcd_table[u][v] = b | |
| return b | |
| # v is odd and u is greater than v | |
| elif u > v and v & 1 != 0: | |
| b = gcd((u-v) >> 1, v) | |
| if u < bound: gcd_table[u][v] = b | |
| return b | |
| # v is odd and u is smaller than v | |
| else: | |
| b = gcd((v-u) >> 1, u) | |
| if u < bound: gcd_table[u][v] = b | |
| return b | |
| def pollards_rho(n, g, x=2, brent=False, output=True, rand=False): | |
| if rand: | |
| n_64 = min(n, 2**64-1) | |
| a = np.random.randint(1, n_64-3) | |
| b = np.random.randint(1, n_64-1) | |
| print(a, b) | |
| x = a | |
| y = b | |
| else: | |
| y = x | |
| cycle_size = 2 | |
| d = 1 | |
| latex = output | |
| iteration = 0 | |
| if latex: | |
| print("\\hline \n %d & %d & %d & %d \\\\" % (iteration, x, y, d)) | |
| while d == 1: | |
| if brent: | |
| count = 1 | |
| while count <= cycle_size and d <= 1: | |
| x = g(x) % n | |
| d = b_gcd(abs(x - y), n) | |
| count += 1 | |
| cycle_size *= 2 | |
| y = x | |
| else: | |
| x = g(x) % n | |
| y = g(g(y)) % n | |
| d = b_gcd(abs(x - y), n) | |
| # count += 1 | |
| # cycle_size *= 2 | |
| iteration += 1 | |
| if latex: | |
| print("\\hline \n %d & %d & %d & %d \\\\" % (iteration, x, y, d)) | |
| elif output: | |
| print("At iteration %d" % iteration) | |
| print("x = %d" % x) | |
| print("y = %d" % y) | |
| print("d = %d" % d) | |
| print() | |
| if iteration % 100 == 0: | |
| print(iteration) | |
| if d == n: | |
| print("Unsuccessful") | |
| return False | |
| return d, iteration | |
| if __name__ == "__main__": | |
| ap = ArgumentParser() | |
| ap.add_argument("-n", dest="n", type=int, default=10403) | |
| ap.add_argument("-x", dest="x", type=int, default=2) | |
| ap.add_argument("-o", dest="output", type=bool, default=False) | |
| ap.add_argument("-r", "--rand", dest="rand", type=bool, default=False) | |
| ap.add_argument("-c", "--cycle_alg", type=str, | |
| choices=["brent", "floyd"], default="floyd") | |
| args = ap.parse_args() | |
| result = pollards_rho(args.n, lambda x: (x*x + 1), x=args.x, | |
| brent=(args.cycle_alg == "brent"), output=args.output, rand=args.rand) | |
| print(result) |
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