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Galactic_Lottery

A Python script that attempts to find a private key corresponding to a set of Bitcoin addresses associated with Satoshi Nakamoto. It leverages a combination of cryptographic operations and a Bloom filter to demonstrate the near-impossibility of brute-forcing a Bitcoin key.

How It Works

  1. Libraries and Modules

    • hashlib for SHA-256 and RIPEMD-160 hashing.
    • base58 for Base58 encoding.
    • bitarray for implementing a Bloom filter.
    • secp256k1 for elliptic curve cryptography (via Python bindings).
    • KeyDatabase (custom) for importing known Satoshi keys.

  2. hash_key() Function

    • Accepts a public key (in bytes), applies SHA-256, then RIPEMD-160, returning the resulting 20-byte hash.
    • Mirrors part of Bitcoin’s standard address derivation process.

  3. private_key_to_wif() Function

    • Takes a 32-byte private key, prefixes with 0x80 (for mainnet), optionally adds 0x01 for compressed keys, then appends a 4-byte checksum (double SHA-256).
    • The result is encoded in Base58 to produce the standard Wallet Import Format (WIF).

  4. create_bloom_filter() Function

    • Builds a Bloom filter from the known Satoshi keys, using a configurable false-positive rate to size the filter and determine the number of hash functions.
    • Allows quick membership testing before performing a final set check.

  5. try_keys() Function

    • Continuously generates random private keys (via libsecp256k1).
    • Extracts the compressed public key, hashes it, and consults the Bloom filter for a possible match.
    • If potentially present, checks against the final set of Satoshi keys.
    • Prints progress on a single line (updates in place) and terminates if a matching key is (improbably) found.

  6. main() Function

    • Loads Satoshi’s known keys, converts them into byte format, and inserts them into both a Python set and the Bloom filter.
    • Invokes try_keys() to begin the brute-force process.
    • Continues indefinitely unless a match is discovered (which is extraordinarily unlikely).

Limitations and Considerations

  • Huge Key Space: The private key space is (2^{256}), an unfathomably large number, rendering success virtually impossible.
  • High Resource Usage: Even with Bloom filter optimizations, this brute-force approach is CPU-intensive—and can make your computer quite warm.
  • Ethical & Legal Implications: Attempting to recover keys without permission is ethically and legally questionable.

Improbability of Finding a Matching Key

  • 256-bit Entropy: There are approximately (10^{77}) possible private keys—more than the estimated atoms in the observable universe.
  • Uniform Distribution: Bitcoin private keys are generated with secure randomness, minimizing the chance of accidental collisions.
  • Robust Cryptography: The secp256k1 curve, SHA-256, and RIPEMD-160 are specifically chosen for their resistance to known attacks.
  • Probability: Even billions of attempts per second are negligible against (2^{256}).
  • Time & Resources: A successful match in our lifetimes (or the universe’s) is practically zero.

Usage

  1. Clone or Download 
    git clone https://github.com/YourUserName/Galactic_Lottery.git
  2. Install Dependencies
   pip install secp256k1 base58 bitarray