How Bitcoin Private Keys, Public Keys, and Addresses Actually Work
A Bitcoin private key is simply a 256-bit random number from which a public key is mathematically derived using the Elliptic Curve Digital Signature Algorithm (ECDSA) on the secp256k1 curve. The public key can be stored in either uncompressed (65 bytes) or compressed (33 bytes) form, with compressed keys now being the modern standard required by Segregated Witness. To make private keys easier to handle, wallets encode them in Wallet Import Format (WIF) using Base58Check encoding, with most wallets defaulting to the compressed variant. A Bitcoin address is a hash of the public key — not the public key itself — meaning users share only the address to receive funds. Security depends entirely on the randomness of the private key, as a weak or guessable key can be cracked in seconds with no recovery option available.
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