How are Electrum addresses connected to my private key?

Question

I've started using Electrum and created my first wallet. I saved the private key seed on a piece of paper.

I also created a new address by going to the Receive tab and clicking "New Address". I successfully used that address to transfer my coins from my exchange, and they show up in Electrum under the Coins tab. I did this twice successfully with 2 different addresses on the same wallet.

What confuses me is this: how did Electrum create a new address? How is that address related to my private key/seed? When I go to Wallet Information the Master Public Key is completely different from the public keys of the addresses I used in the transactions. If I use a different computer, and I enter my seed phrase into Electrum, will it find my coins? If so, how does it do that based on just my private key?

Thanks.

Answer 1

how did Electrum create a new address?

Electrum, and most modern wallets are Hierarchical Deterministic (HD) Wallets. They derive a series of private-keys from the "master private-key".

If you always start with the same seed phrase you get the same master private-key. Electrum uses its own unique method for seed phrases. Most wallets with seed-phrases use a different method described in BIP-39

If you use the same "derivation path", your wallet will always generate the same sequences of private-keys (that is the "deterministic" part) from the master private key.

Different wallet developers sometimes use different derivations-paths. But many of the wallets these developers produce allow the user to specify the derivation-path as part of initial configuration - this allows for compatibility between wallets.

For each private-key there is a public-key. Each public-key corresponds to a Bitcoin-address (in the commonest types of Bitcoin transactions).

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References

• Electrum Seed Phrases

• Bitcoin Improvement Proposal 39

• Deterministic Wallets

• Bitcoin Improvement Proposal 32

• Extended keys