be sent to other public addresses using transactions. Because the private key is the "ticket" that allows someone to spend bitcoins, it is important that these are kept secure. For a brute-force attacker such a private key is just as difficult to guess as the fully random 64 character bitcoin private key. The public key is also mathematically derived from your private key, but using reverse mathematics to derive the private key would take the worlds most powerful supercomputer many trillion years to crack. To be valid, the amount of output coins must not exceed the amount of input coins, and to be verified the output address hash is signed by the input address' private key. Wallet import format is the most common way to represent private keys in Bitcoin.
Bitcoin wallet contains one or more private keys, which are saved in the wallet file. The private keys are mathematically related to all. Bitcoin addresses generated for the wallet.
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If a private key controlling unspent bitcoins is compromised or stolen, the value can only be protected if it is immediately spent to a different output which is secure. The seed value should not be confused with the private keys used directly to sign Bitcoin transactions. The private keys are mathematically related to all Bitcoin addresses generated for the wallet. The public key is used to ensure you are the owner of an address that can receive funds. The "link" to Bitcoin initially happens during block generation where a certain amount of Bitcoin is generated and sent to the miner's public address; this is merely a record in the blockchain. Private keys associated with compressed public keys are 52 characters and start with a capital L or K on mainnet (c on testnet).
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