Private key vs public key: how keys and addresses fit together

What is a private key?#

A private key is the private half of a key pair: the part that can create signatures other people can verify with the public key ^[1]. In Bitcoin it is simply a 256-bit number, chosen from a range set by the secp256k1 elliptic curve that covers nearly all of the 2²⁵⁶ possible values ^[3]. Ethereum also uses elliptic-curve (ECDSA) keys; ethereum.org describes a private key as 64 hexadecimal characters that can be encrypted with a password ^[2].

The number is generated at random by your wallet software. That randomness is the whole point: the range is so large that nobody can find your key by guessing. Ethereum’s documentation puts the stakes plainly: you never really hold cryptocurrency, you hold private keys, and the funds are always on the ledger ^[2].

How is a public key made from the private key?#

The wallet feeds the private key into an elliptic-curve function (the developer docs call it point()) that turns a large integer into a point on the curve: that point is the public key ^[3]. The calculation is deterministic, so the same private key always gives the same public key, and the public key never needs to be stored separately ^[6].

Crucially, the function runs only one way. ethereum.org states that you can derive public keys from a private key, but you cannot derive a private key from public keys ^[2]. That asymmetry is what lets you publish one half and keep the other secret.

From secret number to shareable address

Private key vs public key: what is the difference in practice?#

Bitcoin addresses keep the public key hidden until the first time coins sent to that address are spent ^[6].

A handy way to remember it: the private key is like the pen only you can sign with, the public key is the sample signature others compare against, and the address is the label on your mailbox. Ethereum’s plain-language glossary uses similar images, calling a private key “like a PIN for your account” and a public key “like an email address for money” ^[7].

What is an address, and why not just use the public key?#

An address is the string you actually hand out. In classic Bitcoin addresses, the public key is hashed and then encoded with a version number, the hash and an error-detecting checksum to catch typos ^[6]. The hash shortens the key, makes it easier to copy, and adds protection against unforeseen problems that might one day let someone reconstruct private keys from public key data ^[6].

Newer Bitcoin addresses start with bc1 and use the Bech32 format. BIP 173 chose an alphabet that leaves out easily confused characters such as “1”, “b”, “i” and “o” in the data part, and a checksum that will always detect an error affecting up to four characters ^[8]. Ethereum addresses are built differently: take the last 20 bytes of the Keccak-256 hash of the public key and put 0x in front ^[2].

If an “Ethereum address” you are given has a different length, stop and check it before sending anything.

How does a signature prove ownership without revealing the key?#

A signature is a value that could only reasonably have been created by someone holding the private key behind a given public key ^[1]. When you spend bitcoin from a standard address, your wallet supplies your full public key and a signature over the transaction; nodes check that the public key hashes to the address and that the signature matches ^[6].

1. Your wallet builds a transaction

   It lists which coins to spend, who receives them and how much.

2. It signs with your private key

   The signature covers the important parts of the transaction, so nobody can change the amount or destination afterwards ^[6].

3. It attaches your public key

   Nodes need it to check the signature; the private key never leaves your wallet.

4. Every node verifies

   If the key does not match the address or the signature does not match the key, the transaction is rejected.

This is the mechanism the Bitcoin whitepaper describes in its first technical section: each owner transfers a coin by digitally signing a hash of the previous transaction and the public key of the next owner ^[9]. For the full journey of a payment, see how Bitcoin transactions work.

Where do seed phrases fit in?#

Modern wallets rarely make one key at a time. Under the hierarchical deterministic (HD) design, a single root seed creates a whole tree of child keys, and that seed is the only thing you need to back up to rebuild every key the wallet made ^[3]. BIP 39 turns the seed’s randomness into a list of words: 128 bits of randomness plus a 4-bit checksum become 12 words, and 256 bits plus 8 checksum bits become 24 words, each word drawn from a list of 2,048 ^[10].

Because the phrase can regenerate every private key, treat it exactly like a private key. Our guide to seed phrases covers safe storage.

Should you reuse the same address?#

You can, but it costs privacy. All Bitcoin transactions are stored publicly, so anyone can see the balance and history of any address; bitcoin.org says this is one reason addresses should only be used once ^[5]. The developer guide adds that if a public key is reused, others can easily track how much a person receives and spends, and recommends new addresses for payments and for change ^[6]. The whitepaper gave the same advice in 2008: use a new key pair for each transaction ^[9]. Most wallets now generate a fresh address for you automatically.

What mistakes do beginners make here?#

• Sharing the private key to “receive” money

  To get paid you only ever share an address. Anyone asking for your private key or recovery phrase so they can send you funds is attempting theft.

• Storing keys or seed phrases as screenshots

  ethereum.org warns that screenshots can sync to cloud storage, where hackers look for them ^[4]. Write the phrase down offline instead.

• Assuming an address is a username

  An address is derived from a key, not registered to a name. Sending to a mistyped or wrong-network address can lose funds permanently.

• Thinking the wallet app “holds” the coins

  Coins stay on the blockchain. The app manages keys. Delete the app without a backup and the keys, not the coins, are what you lose.

• Confusing public key with address

  They are related but different: the address is a hash of the public key. Wallet screens usually show only addresses.

Frequently asked questions#

The bottom line#

The private key is the only part that must stay secret. The public key and the address are built from it in one-way steps, which is why you can safely publish them and still be the only person able to sign.

Keep the seed phrase and keys offline, share addresses freely, and let your wallet create a fresh address for each payment. Next, follow those signatures into the ledger in how Bitcoin transactions work, or read about custodial vs self-custody wallets.

Sources#