Quote from: citb0in on Today at 07:59:07 PM

---snip---

Code:

import time
import os
import sys
import random
import gmpy2
import multiprocessing
from math import log2, sqrt, log
from multiprocessing import Pool, cpu_count

os.system("cls||clear")
t = time.ctime()
sys.stdout.write(f"\033[?25l")
sys.stdout.write(f"\033[01;33m[+]\033[32m KANGAROO: \033[01;33m{t}\n")
sys.stdout.flush()

modulo = gmpy2.mpz(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
Gx = gmpy2.mpz(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
Gy = gmpy2.mpz(0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)
PG = (Gx, Gy)

Z = (0, 0) # zero-point, infinite in real x, y - plane

def add(P, Q, p=modulo):
   Px, Py = P
   Qx, Qy = Q
   if P == Z:
   return Q
   elif Q == Z:
   return P
   elif Px == Qx and (Py != Qy or Py == 0):
   return Z
   elif Px == Qx:
   m = (3 * Px * Px) * gmpy2.invert(2 * Py, p) % p
   else:
   m = (Qy - Py) * gmpy2.invert(Qx - Px, p) % p

   x = (m * m - Px - Qx) % p
   y = (m * (Px - x) - Py) % p
   return (x, y)

def mul2(P, p=modulo):
   Px, Py = P
   if P == Z:
   return Z
   m = gmpy2.f_mod(3 * Px * Px * gmpy2.invert(2 * Py, p), p)
   x = gmpy2.f_mod(m * m - 2 * Px, p)
   y = gmpy2.f_mod(m * (Px - x) - Py, p)
   return (x, y)

def mulk(k, P=PG, p=modulo):
   if k == 0:
   return Z
   elif k == 1:
   return P
   elif k % 2 == 0:
   return mulk(k // 2, mul2(P, p), p)
   else:
   return add(P, mulk((k - 1) // 2, mul2(P, p), p), p)

def X2Y(X, y_parity, p=modulo):
   X_cubed = gmpy2.powmod(X, 3, p)
   X_squared = gmpy2.powmod(X, 2, p)
   tmp = gmpy2.f_mod(X_cubed + 7, p)
   Y = gmpy2.powmod(tmp, gmpy2.f_div(gmpy2.add(p, 1), 4), p)
   if y_parity == 1:
   Y = gmpy2.f_mod(-Y, p)
   return Y

def comparator(A, Ak, B, Bk):
   result = set(A).intersection(set(B))
   if result:
   sol_kt = A.index(next(iter(result)))
   sol_kw = B.index(next(iter(result)))
   HEX = "%064x" % abs(Ak[sol_kt] - Bk[sol_kw])
   dec = int(HEX, 16)
   total_time = time.time() - starttime
   print('\n[+] total time: %.2f sec' % (total_time))
   t = time.ctime()
   print(f"\033[32m[+] PUZZLE SOLVED: {t} \033[0m")
   print(f"\033[32m[+] Private key (dec) : {dec} \033[0m")
   dash_line = '-' * 140
   with open("KEYFOUNDKEYFOUND.txt", "a") as file:
   file.write(f"\n{dash_line}")
   file.write("\n\nSOLVED " + t)
   file.write(f"\nTotal Time: {total_time:.2f} sec")
   file.write("\nPrivate Key (decimal): " + str(dec))
   file.write("\nPrivate Key (hex): " + HEX)
   file.write(f"\n{dash_line}")
   file.close()
   return True
   else:
   return False

def check(P, Pindex, DP_rarity, A, Ak, B, Bk):
   modulo_val = P[0] % DP_rarity
   if modulo_val == 0:
   A.append(gmpy2.mpz(P[0]))
   Ak.append(gmpy2.mpz(Pindex))
   return comparator(A, Ak, B, Bk)
   else:
   return False

# Generate a list of powers of two for faster access
def generate_powers_of_two(hop_modulo):
   return [gmpy2.mpz(1 << pw) for pw in range(hop_modulo)]

def search(thread_id, P, W0, DP_rarity, Nw, Nt, hop_modulo, upper_range_limit, lower_range_limit, result_queue, powers_of_two):
   pid = os.getpid()
   core_number = pid % cpu_count()
   #Random seed Config
   #constant_prefix = b'' #back to no constant
   constant_prefix = b''
   prefix_length = len(constant_prefix)
   length = 8
   ending_length = length - prefix_length
   with open("/dev/urandom", "rb") as urandom_file:
   ending_bytes = urandom_file.read(ending_length)
   random_bytes = constant_prefix + ending_bytes
   print(f"[+] [Core]: {core_number+1:02}, [Random seed]: {random_bytes}")
   random.seed(random_bytes)
   t = [gmpy2.mpz(lower_range_limit + gmpy2.mpz(random.randint(0, upper_range_limit - lower_range_limit))) for _ in range(Nt)]
   T = [mulk(ti) for ti in t]
   dt = [gmpy2.mpz(0) for _ in range(Nt)]
   w = [gmpy2.mpz(random.randint(0, upper_range_limit - lower_range_limit)) for _ in range(Nw)]
   W = [add(W0, mulk(wk)) for wk in w]
   dw = [gmpy2.mpz(0) for _ in range(Nw)]
   Hops, Hops_old = 0, 0
   t0 = time.time()
   # Memoization dictionary
   memo = {}
   solution_found = False # Flag to control the loop
   while not solution_found:
   for k in range(Nt):
   Hops += 1
   pw = T[k][0] % hop_modulo
   if pw not in memo:
   memo[pw] = powers_of_two[pw]
   dt[k] = memo[pw]
   if check(T[k], t[k], DP_rarity, T, t, W, w):
   result_queue.put((thread_id, T[k], t[k], W[k], w[k]))
   solution_found = True # Set flag to exit loop
   break # Exit the for-loop
   t[k] += dt[k]
   T[k] = add(P[int(pw)], T[k])
   if solution_found: # Break the while-loop if solution is found
   break
   for k in range(Nw):
   Hops += 1
   pw = W[k][0] % hop_modulo
   if pw not in memo:
   memo[pw] = powers_of_two[pw]
   dw[k] = memo[pw]
   if check(W[k], w[k], DP_rarity, W, w, T, t):
   result_queue.put((thread_id, T[k], t[k], W[k], w[k]))
   solution_found = True # Set flag to exit loop
   break # Exit the for-loop
   w[k] += dw[k]
   W[k] = add(P[int(pw)], W[k])
   if solution_found: # Break the while-loop if solution is found
   break
   t1 = time.time()
   elapsed_time = t1 - starttime
   if t1 - t0 > 1 and thread_id == 0:
   hops_per_second = (Hops - Hops_old) / (t1 - t0) * cores
   hours, rem = divmod(elapsed_time, 3600)
   minutes, seconds = divmod(rem, 60)
   elapsed_time_str = f"{int(hours):02d}:{int(minutes):02d}:{int(seconds):02d}"
   p_2 = f'{log2(Hops*cores):.2f}'
   print(f'[+] [Hops: 2^{p_2} <-> {hops_per_second:.0f} h/s] [{elapsed_time_str}]', end='\r', flush=True)
   t0 = t1
   Hops_old = Hops
   print('\r[+] Hops:', Hops* cores)
   print('[+] Average time to solve: %.2f sec' % ((time.time()-starttime)))

def main():
   result_queue = multiprocessing.Queue()
   processes = [
   multiprocessing.Process(target=search, args=(i, P, W0, DP_rarity, Nw, Nt, hop_modulo, upper_range_limit, lower_range_limit, result_queue, powers_of_two)) for i in range(cores)
   ]
   for p in processes:
   p.start()
   result = result_queue.get()
   for p in processes:
   p.terminate()

# Configuration for the puzzle
cores = cpu_count()
puzzle = 40
compressed_public_key = "03a2efa402fd5268400c77c20e574ba86409ededee7c4020e4b9f0edbee53de0d4"
kangaroo_power = 3
lower_range_limit = 2 ** (puzzle - 1)
upper_range_limit = (2**puzzle) - 1

DP_rarity = 1 << int(((puzzle - 2*kangaroo_power)/2 - 2))
hop_modulo = ((puzzle - 1) // 2) + kangaroo_power
Nt = Nw = 2**kangaroo_power

# Precompute powers of two for faster access
powers_of_two = generate_powers_of_two(hop_modulo)

print('[+] [Tame and Wild herds are prepared]')

if len(compressed_public_key) == 66:
   X = gmpy2.mpz(compressed_public_key[2:66], 16)
   Y = X2Y(X, gmpy2.mpz(compressed_public_key[:2]) - 2)
else:
   print("[error] pubkey len(66/130) invalid!")

W0 = (X,Y)
starttime = oldtime = time.time()

Hops = 0

P = [PG]
for k in range(255):
   P.append(mul2(P[k]))
print('[+] [P-table prepared]')

print(f"[+] [Using {cores} CPU cores for parallel search]")
print(f"[+] [Puzzle: {puzzle}]")
print(f"[+] [Lower range limit: {lower_range_limit}]")
print(f"[+] [Upper range limit: {upper_range_limit}]")
print(f"[+] [Expected Hops: 2^{log2(2.2 * sqrt(1 << (puzzle-1))):.2f} ({int(2.2 * sqrt(1 << (puzzle-1)))})]")

if __name__ == '__main__':
   main()

Code:

[+] KANGAROO: Tue May 6 12:28:34 2025
[+] [Tame and Wild herds are prepared]
[+] [P-table prepared]
[+] [Using 12 CPU cores for parallel search]
[+] [Puzzle: 40]
[+] [Lower range limit: 549755813888]
[+] [Upper range limit: 1099511627775]
[+] [Expected Hops: 2^20.64 (1631201)]
[+] [Core]: 12, [Random seed]: b'\xfb\xeb|z\x1fF\xa5"'
[+] [Core]: 04, [Random seed]: b'\x10\x86\x08\xe4#\x84#\x90'
[+] [Core]: 07, [Random seed]: b'\xba\x08\xb4\xaa\x0ex;\xb8'
[+] [Core]: 11, [Random seed]: b'\x8a-\xa2T?-L\x03'
[+] [Core]: 02, [Random seed]: b'?\xb8b.&\x86\x0e\x0b'
[+] [Core]: 06, [Random seed]: b'\x7f>\xcb\xd4w\xc7\x0e\xfc'
[+] [Core]: 10, [Random seed]: b'\xc7\xe51Kg\xe9;\xd8'
[+] [Core]: 02, [Random seed]: b'L/E\t\xfb`\x9a\xf6'
[+] [Core]: 08, [Random seed]: b'\xc5\x81\xca\x8aA\xc3\x95\x9c'
[+] [Core]: 10, [Random seed]: b'N!\xc3\x8a\xb2\xf8\x9b\xde'
[+] [Core]: 06, [Random seed]: b'\x0b$\x199\xdb]\xb5G'
[+] [Core]: 03, [Random seed]: b'\xc6=\x94\xf1aE\xf3\xb4'
[+] [Hops: 2^22.21 <-> 2429183 h/s] [00:00:02]
[+] total time: 2.63 sec
[+] PUZZLE SOLVED: Tue May 6 12:28:37 2025
[+] Private key (dec) : 1003651412950
[+] Hops: 6313212
[+] Average time to solve: 2.63 sec