BR Academy
Intro to Blockchain: How It Works and Why It Matters
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Keys, Wallets, and Ownership·Lesson 12 of 25·10 min

Addresses and Derivation

The Concept

You now know that a private key produces a public key through a one-way mathematical function. An address is one more step removed: it's a shortened, checksummed, human-shareable representation of a public key — similar in spirit to how a bank account number is a short, practical stand-in for your full account identity at the bank. Addresses are designed to be easy to copy, paste, and read aloud, and most formats include a built-in checksum that catches typos, so a single mistyped character gets flagged as invalid rather than silently sending funds to the wrong place.

Here's the part that makes modern wallets so convenient: a single seed phrase doesn't just produce one private key — it produces an entire tree of key pairs (and therefore addresses) through a process called hierarchical deterministic (HD) derivation. "Hierarchical" means the keys branch out like a family tree from one root; "deterministic" means the exact same seed phrase, run through the exact same derivation process, always produces the exact same tree of keys, every time, on any compatible wallet software, forever.

This is why restoring a wallet on a brand-new phone with nothing but your 24-word backup regenerates every address you ever used — not because the new device "looked up" your history anywhere, but because it recalculates the identical mathematical tree from the identical seed. It's also why one seed phrase can often manage addresses across multiple different blockchains: the derivation path simply branches differently depending on which chain's key format is requested.

This also explains a practical habit most wallets encourage: generating a fresh receiving address for each new payment rather than reusing one address forever. Because addresses are cheap and effectively unlimited — a single seed can derive millions of them — there's no reason to reuse one, and doing so trades away a small amount of privacy for no real benefit. Anyone who can see that the same address received two separate payments can link those transactions as belonging to the same owner; a new address per payment breaks that link, even though every one of those addresses still ultimately traces back to, and is recoverable from, the exact same 24 words.

Address formats also differ visibly by chain, which is worth recognizing on sight. A Bitcoin address might start with "1", "3", or "bc1" depending on its type; an Ethereum-style address is a 42-character string starting with "0x". These aren't arbitrary — each prefix or format encodes information about which derivation rules and checksum scheme produced it, which is part of how wallets and explorers catch an address pasted for the wrong network before funds are sent somewhere unrecoverable.

There's a standardized naming scheme behind "derivation path" that's worth recognizing even if you never type one yourself: paths like m/44'/0'/0'/0/0 show up in wallet settings and recovery documentation. Reading left to right, m is the master key, 44' signals the standard (BIP-44) being used, the next number identifies which blockchain's branch you're in (0 for Bitcoin, 60 for Ethereum, and so on — a registry maintained so wallets agree on the mapping), the next distinguishes accounts if you've created more than one within the same wallet, and the final numbers step through individual receiving and change addresses. You don't need to memorize these, but recognizing the shape of a derivation path helps when a wallet's advanced settings mention "custom derivation" — usually only relevant if you're recovering funds in an unusual wallet that used a nonstandard path.

This standardization is also precisely why "wallet" is really a misleading word for what these apps do. They don't store coins at all — no blockchain has a concept of coins sitting inside a particular piece of software. What a wallet genuinely stores (or, in the case of a well-designed wallet, merely holds temporarily in memory after being regenerated from your seed) is the key material needed to derive addresses and sign transactions on your behalf. Losing the app is a non-event if you still have the seed phrase; losing the seed phrase with no other backup is unrecoverable, regardless of how many devices had the app installed. That asymmetry is the single most important practical fact this module has been building toward.

Worked Example

Trace the derivation path conceptually, as a chain of narrowing steps:

  1. Seed phrase (12–24 words) → mathematically converts into a single large number, the seed.
  2. Master key → the seed generates one root key pair, the top of the tree.
  3. Chain-specific branch → the master key derives a branch of child keys dedicated to a specific blockchain (for example, a Bitcoin branch and a separate Ethereum branch from the same root).
  4. Individual address → within that branch, each further derivation step produces one specific, usable address — the first address you see in your wallet, the second, the third, and so on.

Because every step from seed to final address is a pure mathematical function with no randomness and no external lookup, running the exact same seed phrase through the exact same four steps on a different device, a year later, reproduces the exact same final address. That's the guarantee that makes "write down 24 words" an adequate backup for a wallet that might contain dozens of addresses across several chains.

Exercise

Compare two addresses you're shown from the same wallet (same format, visibly different characters). Without looking anything up, explain in your own words why they look completely random and unrelated to each other, yet both regenerate deterministically and exactly from the same 24-word seed phrase on any compatible wallet. Then write one sentence describing what would happen if you restored that same seed phrase on a different wallet app that used an incompatible derivation standard — would you expect to see the same addresses, and why or why not?

Recap

  • An address is a short, checksummed, shareable stand-in for a public key — not a separately stored secret.
  • Addresses are derived, not individually stored — hierarchical deterministic derivation turns one seed phrase into an entire reproducible tree of keys and addresses, cheaply enough that fresh addresses per payment cost nothing and improve privacy.
  • The seed phrase is the one secret that regenerates every address and key you've ever used on that wallet, which is exactly why protecting it (previous lesson) matters so much.

Resources

Module quiz

6 questions · pass mark 70% · retake any time

1. What is a public key?
2. Why must you keep your private key secret?
3. What is the difference between a custodial and non-custodial wallet?
4. What is a blockchain address?
5. What is key derivation?
6. What should you do if you lose your private key?
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