the same address no matter which program is used to convert. If you call the one specifying the keysize (say, 256 the BC provider will try to choose a default curve of the right size (for 256, it will be "prime256v1".k.a. A private key in the context of Bitcoin is a secret number that allows bitcoins to be spent. Just as with any other transaction, there is risk of swept transactions to be double-spending. To brute force attack a public key to obtain a public key with 128 bits of entropy will cost at least 100M in electricity at 5 cents per KW-Hr using almost perfectly efficient quantum computers. The private key is only needed to spend the bitcoins, not necessarily to see the value of them. Because bitcoins can only be spent once, when they are spent using a private key, the private key becomes worthless. Some wallets allow private keys to be imported without generating any transactions while other wallets or services require that the private key be swept.
So private key 256 bits, public key bits OR 2561257 bits. Because the private key is the "ticket" that allows someone to spend bitcoins, it is important that these are kept secure. The two bitcoin explorer (bx) commands below replicate statements/results in the site references above. Non-HD wallets generate a new randomly-selected private key for each new address; therefore, if the wallet file is lost or damaged, the user will irretrievably lose all funds received to addresses generated after the most recent backup. It is mostly supposition to arrive at projections for when an mathematical back doors for compromising secp256k1. Not every private key or Bitcoin address has a corresponding mini private key - they have to be generated a certain way in order to ensure a mini private key exists for an address. The seed value should not be confused with the private keys used directly to sign Bitcoin transactions.
Bitcoin is the most excellent canary in the cryptographic coal mine to determine when secp256k1 fails. From, table 1 the elliptic curve subject matters experts assert the strength of a 256-bit secp256k1 private key has the strength of 128 bits of encryption when the associated public key is exposed. Echo "e9873d79c6d87dc0fb6a f da61f20bd67fc233aa33262" bx base58check-encode -v 128 - is the associated uncompressed private key that is encoded using base58 check, also called Wallet Input Format (WIF). This is the same private key in (mainnet) wallet import format: when a WIF private key is imported, it always corresponds to exactly one. Hierarchical Deterministic (HD) Wallet Keys, main article: Hierarchical deterministic wallet. 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.