snip
You keep reciting the definition of "
uniform distribution" like a mantra, but you don't understand that this is precisely the argument that's sinking you.
Nobody questions that
the H160 is uniform. What
I question is your lack of strategic vision. In a uniform distribution, each key has the same probability. Therefore, there's no logical reason to choose a sequential scan that prevents you from looking at the last 35% of the range. If everything is uniform, skipping based on a signal (prefix) is a way to optimize the scan, not to change the key's probability.
You say that a continuous scan of X% is "
identical" to my prefix scan.
False. In your continuous 65% scan, if the key is in the remaining 35%, your probability is ZERO.
In my prefix scan, I cover 100% of the range in a skipping fashion. If the key lies within that 35% you're ignoring, my method can find it because it doesn't have an arbitrary exclusion zone.
You talk about "
basic computer science" but you ignore the fact that the world's most advanced search algorithms, like Google or AI, don't use flat sequential scans; they use heuristics. My method isn't magic; it's resource optimization. Your insistence that
sequential is better because it's simpler is why you're stuck in theory while others are advancing in practice.
So you can keep trying to lecture on
independent events, but the reality of the puzzle is simple:
coverage is key. Your "guillotine" blinds you to the 35% potential success rate because of an obsession with continuity that contributes nothing to finding the key.
If my "
magic theory" bothers you so much, it's because it exposes that your clean method is simply a quick way to give up on a third of the puzzle. The forum isn't polluted with technical debate; It becomes tainted by the arrogance of those who prefer to be right on paper rather than have a real chance of finding the key.
Keep your perfect scan; I'll stick with the method that doesn't force me to ignore the treasure if it falls outside your comfort zone.
I know it's a uniform distribution, I know what independent events are, but this is about
search heuristics, not a
statistics exam, which is based on an infinite assumption where questions are
averaged. Remember, you're looking for a
single, discrete event (
the private key), not how many prefixes are in 2^256.
edit:Since you like AI as you demonstrated in other threads, I asked him to modify the code for the comparison of the 3 methods: one with fixed cutoff, one with random stop, and another with prefixes (before you attack the AI fallacy, the math is the same no matter where the code was taken from, it's just for demonstration purposes):
import hashlib
import random
import time
import math
import statistics
# === CONFIGURATION ===
TOTAL_SIZE = 100_000
RANGE_SIZE = 4_096
PREFIX_LENGTH = 3
SIMULATIONS = 2000
# Bitcoin secp256k1 order
SECP_ORDER = int("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16)
def generate_h160(data):
"""Generates RIPEMD160(SHA256(data)) hash."""
h = hashlib.new('ripemd160', str(data).encode('utf-8'))
return h.hexdigest()
def get_shuffled_blocks(total_blocks):
blocks = list(range(total_blocks))
random.shuffle(blocks)
return blocks
# --- SEARCH METHODOLOGIES ---
def fixed_65_search(dataset, block_size, target_hash, block_order):
"""Simulates a static 65% cutoff strategy."""
checks = 0
cutoff = int(block_size * 0.65)
for block_idx in block_order:
start = block_idx * block_size
for i in range(start, start + cutoff):
if i >= len(dataset): break
checks += 1
if generate_h160(dataset[i]) == target_hash:
return {"checks": checks, "found": True}
return {"checks": checks, "found": False}
def random_stop_search(dataset, block_size, target_hash, block_order):
"""Simulates a random stop strategy within each block."""
checks = 0
for block_idx in block_order:
start = block_idx * block_size
stop_point = random.randint(1, block_size)
for i in range(start, start + stop_point):
if i >= len(dataset): break
checks += 1
if generate_h160(dataset[i]) == target_hash:
return {"checks": checks, "found": True}
return {"checks": checks, "found": False}
def prefix_heuristic_search(dataset, block_size, prefix_len, target_hash, block_order):
"""Simulates the dynamic prefix-based jumping strategy (Heuristic)."""
target_prefix = target_hash[:prefix_len]
checks = 0
for block_idx in block_order:
start = block_idx * block_size
end = min(start + block_size, len(dataset))
for i in range(start, end):
checks += 1
current_hash = generate_h160(dataset[i])
if current_hash == target_hash:
return {"checks": checks, "found": True}
if current_hash.startswith(target_prefix):
break
return {"checks": checks, "found": False}
def run_experiment():
results = {
"fixed_65": {"found": 0, "dead_zone_hits": 0, "checks": []},
"random_stop": {"found": 0, "dead_zone_hits": 0, "checks": []},
"prefix_heuristic": {"found": 0, "dead_zone_hits": 0, "checks": []}
}
total_blocks = math.ceil(TOTAL_SIZE / RANGE_SIZE)
dead_zone_threshold = int(RANGE_SIZE * 0.65)
total_keys_in_dead_zone = 0
print(f"Starting {SIMULATIONS} simulations...")
for _ in range(SIMULATIONS):
offset = random.randint(0, SECP_ORDER - TOTAL_SIZE)
dataset = [offset + i for i in range(TOTAL_SIZE)]
# Select a hidden target key
target_idx = random.randint(0, TOTAL_SIZE - 1)
target_hash = generate_h160(dataset[target_idx])
# Verify if key is located in the 35% trailing 'Dead Zone'
is_in_dead_zone = (target_idx % RANGE_SIZE) >= dead_zone_threshold
if is_in_dead_zone:
total_keys_in_dead_zone += 1
block_order = get_shuffled_blocks(total_blocks)
# Run Search Models
f65 = fixed_65_search(dataset, RANGE_SIZE, target_hash, block_order)
rnd = random_stop_search(dataset, RANGE_SIZE, target_hash, block_order)
pre = prefix_heuristic_search(dataset, RANGE_SIZE, PREFIX_LENGTH, target_hash, block_order)
# Record Statistics
for res, key in zip([f65, rnd, pre], results.keys()):
if res["found"]:
results[key]["found"] += 1
results[key]["checks"].append(res["checks"])
if is_in_dead_zone:
results[key]["dead_zone_hits"] += 1
print("\n" + "="*60)
print("SEARCH STRATEGY ANALYSIS: THE DEAD ZONE CHALLENGE")
print("="*60)
print(f"Total Simulations: {SIMULATIONS}")
print(f"Keys located in the 35% Dead Zone: {total_keys_in_dead_zone}")
print("-" * 60)
header = f"{'Method':<18} | {'Total Success':<15} | {'Dead Zone Hits':<15} | {'DZ Efficiency'}"
print(header)
print("-" * len(header))
for name, data in results.items():
dz_eff = (data["dead_zone_hits"] / total_keys_in_dead_zone * 100) if total_keys_in_dead_zone > 0 else 0
print(f"{name:<18} | {data['found']:<15} | {data['dead_zone_hits']:<15} | {dz_eff:>12.2f}%")
print("\n[Resource Efficiency]")
for name, data in results.items():
avg_checks = statistics.mean(data["checks"]) if data["checks"] else 0
print(f"{name:<18}: {avg_checks:,.0f} average checks per find")
if __name__ == '__main__':
run_experiment()
test 1
SEARCH STRATEGY ANALYSIS: THE DEAD ZONE CHALLENGE
============================================================
Total Simulations: 1000
Keys located in the 35% Dead Zone: 344
------------------------------------------------------------
Method | Total Success | Dead Zone Hits | DZ Efficiency
----------------------------------------------------------------------
fixed_65 | 656 | 0 | 0.00%
random_stop | 503 | 73 | 21.22%
prefix_heuristic | 618 | 139 | 40.41%
[Resource Efficiency]
fixed_65 : 33,868 average checks per find
random_stop : 26,736 average checks per find
prefix_heuristic : 32,257 average checks per find
test 2
============================================================
SEARCH STRATEGY ANALYSIS: THE DEAD ZONE CHALLENGE
============================================================
Total Simulations: 1000
Keys located in the 35% Dead Zone: 346
------------------------------------------------------------
Method | Total Success | Dead Zone Hits | DZ Efficiency
----------------------------------------------------------------------
fixed_65 | 654 | 0 | 0.00%
random_stop | 535 | 74 | 21.39%
prefix_heuristic | 654 | 151 | 43.64%
[Resource Efficiency]
fixed_65 : 32,656 average checks per find
random_stop : 26,068 average checks per find
prefix_heuristic : 32,430 average checks per find
test 3
============================================================
SEARCH STRATEGY ANALYSIS: THE DEAD ZONE CHALLENGE
============================================================
Total Simulations: 2000
Keys located in the 35% Dead Zone: 697
------------------------------------------------------------
Method | Total Success | Dead Zone Hits | DZ Efficiency
----------------------------------------------------------------------
fixed_65 | 1303 | 0 | 0.00%
random_stop | 1001 | 126 | 18.08%
prefix_heuristic | 1239 | 305 | 43.76%
[Resource Efficiency]
fixed_65 : 33,029 average checks per find
random_stop : 26,330 average checks per find
prefix_heuristic : 31,815 average checks per find
test 4
============================================================
SEARCH STRATEGY ANALYSIS: THE DEAD ZONE CHALLENGE
============================================================
Total Simulations: 5000
Keys located in the 35% Dead Zone: 1721
------------------------------------------------------------
Method | Total Success | Dead Zone Hits | DZ Efficiency
----------------------------------------------------------------------
fixed_65 | 3279 | 0 | 0.00%
random_stop | 2559 | 296 | 17.20%
prefix_heuristic | 3165 | 789 | 45.85%
[Resource Efficiency]
fixed_65 : 33,069 average checks per find
random_stop : 25,639 average checks per find
prefix_heuristic : 32,178 average checks per find
The 65% cutoff method is a guillotine that leaves you blind to 35% of the puzzle. The random stop is inefficient chaos. The prefix method is the only engineering strategy that balances coverage speed with the real possibility of finding the key anywhere within the range.
As you can see, statistically they may seem similar, but that doesn't change the fact that the prefix method doesn't leave a gap due to an arbitrary cutoff, nor does it leave it to the chaos of randomness.
Is it clear that the prefix method is the most effective for searching when we have limited resources?
What do you prefer now: relying on the fixed cutoff and risking that the target is in the unexplored 35%?
Leaving it to chance, with a random stop?
Or using prefixes, with a margin of error of less than 1/N distributed across 100% of the range?
As you can see, my method doesn't break the rules of mathematics; it doesn't affect the uniform distribution or the independence of events.
It's simply an intelligent approach, which should be valued instead of attacked by egocentric purists who don't grasp the essence of what I'm saying. They only see statistics and numbers, forgetting that
WE'RE LOOKING FOR A SINGLE TARGET.
