user117238: 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.

user13866: 
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).

References

Electrum Seed Phrases

Bitcoin Improvement Proposal 39

Deterministic Wallets

Bitcoin Improvement Proposal 32

Extended keys



117238: <p>I've started using Electrum and created my first wallet. I saved the private key seed on a piece of paper.</p>
<p>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.</p>
<p>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?</p>
<p>Thanks.</p>
 13866: <blockquote>
<p>how did Electrum create a new address?</p>
</blockquote>
<p>Electrum, and most modern wallets are Hierarchical Deterministic (HD) Wallets. They derive a series of private-keys from the &quot;master private-key&quot;.</p>
<p>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</p>
<p>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.</p>
<p>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.</p>
<p>For each private-key there is a public-key. Each public-key corresponds to a Bitcoin-address (in the commonest types of Bitcoin transactions).</p>
<hr />
<p>References</p>
<ul>
<li><p><a href="https://electrum.readthedocs.io/en/latest/seedphrase.html" rel="noreferrer">Electrum Seed Phrases</a></p>
</li>
<li><p><a href="https://en.bitcoin.it/wiki/BIP_0039" rel="noreferrer">Bitcoin Improvement Proposal 39</a></p>
</li>
<li><p><a href="https://en.bitcoin.it/wiki/Deterministic_wallet" rel="noreferrer">Deterministic Wallets</a></p>
</li>
<li><p><a href="https://en.bitcoin.it/wiki/BIP_0032" rel="noreferrer">Bitcoin Improvement Proposal 32</a></p>
</li>
<li><p><a href="https://learnmeabitcoin.com/technical/extended-keys" rel="noreferrer">Extended keys</a></p>
</li>
</ul>
