How are Electrum addresses connected to my private key? 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 &quot;New Address&quot;. 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.
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 &quot;master private-key&quot;.
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 &quot;derivation path&quot;, your wallet will always generate the same sequences of private-keys (that is the &quot;deterministic&quot; 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).

References

Electrum Seed Phrases

Bitcoin Improvement Proposal 39

Deterministic Wallets

Bitcoin Improvement Proposal 32

Extended keys