Public key and address difference

[Mhassan38]

I need a convincing and satisfying answer on the difference between public key and address because In the course of studying I'm trying to assume public key is the same as address. Though address is just a way of representing our public key which was derived from our private key using the mathematical elliptical curve multiplication.
Please I need more clarification on it.

[Charles-Tim]

The public key is generated by the private key.

The private key can generate the public key and the address.

The public key can only generate the address.

The address can not generate the public key.

For payment, you will give your bitcoin address to people, not public key.

The bitcoin public key starts from 02 or 03 or the old 04. Bitcoin address starts from 1, 3 or bc1.

[Ruttoshi]

Your wallet address is derived from your public key because public key is very long and cannot be used to recieve bitcoin directly. Therefore, your wallet address is hashed from your public key to make it shorter and easy to share with people, instead of a very long number. You receive bitcoin directly to your address.

https://learnmeabitcoin.com/technical/keys/public-key/hash/

[Hypnotizer]

Well, to clarify your question, let’s first understand what a public key is and what an address is and their usages..

•Public key: a public key is an long alphanumeric character that is generated from a private key using the elliptic curve cryptography and it is a one way process and it is use to allow other users verify the credibility of a signed transaction to the private key and also to generate an address.

• An address: an address is use to recieve bitcoin from other users and it is derived from the public key, when you want to receive  payment or funds from another party, you’ll share your address to them and they will use your address to send you bitcoin. An address is derived from public key through hashing and encoding  processes.

The difference between an address and a public key, in the most simple way is that an address is use to receive  bitcoin while a public key is used for cryptography verification. A public key is generated only once while addresses can be generated multiple times.

[MusaMohamed]

I need a convincing and satisfying answer on the difference between public key and address because In the course of studying I'm trying to assume public key is the same as address. Though address is just a way of representing our public key which was derived from our private key using the mathematical elliptical curve multiplication.
Please I need more clarification on it.

It's the one-way flow like this.

Bitcoin Private Key > Bitcoin Public Key > Bitcoin Address.

You can not do any cryptographic bruteforce to find your Bitcoin public key from your Bitcoin address, or find your Bitcoin private key from your Bitcoin public key.

You have to read two chapters about Keys, and wallets in Mastering Bitcoin book for understanding about these terms more.
https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch04_keys.adoc
https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch05_wallets.adoc

To spend your bitcoins, you need to have Bitcoin private keys.

[stwenhao]

The address can not generate the public key.

Meanwhile in Taproot:

Address: bc1p0xlxvlhemja6c4dqv22uapctqupfhlxm9h8z3k2e72q4k9hcz7vqzk5jj0
Public key: 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

And the same can be done with every other 32-byte Taproot address, which starts with bc1p.

For payment, you will give your bitcoin address to people, not public key.

For Taproot, it is equivalent, because you can convert things between public keys and addresses, and get 1:1 mapping.

So yes, for old address types, there is a difference, but for Taproot, public keys are just encoded as addresses, and as long as spending by key is possible, all Taproot addresses can be cleared. The underlying TapScript doesn't matter, if you know the private key, and can move all coins directly, by making a valid Schnorr signature.

Please I need more clarification on it.

Historically, public keys were hashed, to make addresses out of it, just because they were too long. So, instead of sharing 65 bytes per uncompressed public key, Satoshi hashed it with SHA-256, and got 32 bytes instead. And because it was still too long, he hashed it again, this time with RIPEMD-160, and got 20 bytes instead.

Currently, 160-bit addresses have only 80-bit security, and because the network can get closer and closer to check 2^80 keys in reasonable time, we are getting closer and closer to seeing the first address collisions. Which is why all new address types try to provide at least 128-bit security instead.

[satscraper]

The address can not generate the public key.

Meanwhile in Taproot:

Address: bc1p0xlxvlhemja6c4dqv22uapctqupfhlxm9h8z3k2e72q4k9hcz7vqzk5jj0
Public key: 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

Wait, 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 -is the point G written in SEC format rather than public key relevant to bc1p0xlxvlhemja6c4dqv22uapctqupfhlxm9h8z3k2e72q4k9hcz7vqzk5jj0

For Taproot, it is equivalent, because you can convert things between public keys and addresses, and get 1:1 mapping.

Nope, you cannot get 1:1 mapping for taproot addresses because the operations that convert public keys into the tweaked ones ^{(used to derive a Taproot addresses)} are irreversible, due to the nature of inner operands involved ^{such as hashing, multiplication, and addition on the elliptic curve}.

[j2002ba2]

Currently, 160-bit addresses have only 80-bit security, and because the network can get closer and closer to check 2^80 keys in reasonable time, we are getting closer and closer to seeing the first address collisions. Which is why all new address types try to provide at least 128-bit security instead.

The security of unspent 160 bit addresses is exactly 160 bit. When spent from, barring monumental errors, it drops down to 128 bit.

Collision is kinda useless, what would one do with it?

[JaanusRaim]

It would be much better if the public key would function as the address as well.

There should be only 2 things related to BTC: the private key and the public key (that is the address as well).

[stwenhao]

because the operations that convert public keys into the tweaked ones

You don't have to tweak keys. As you can see, coins were moved from this address. Of course, using untweaked keys is less secure, because if the key-spending path will ever be blocked, then these funds may be confiscated, but here and now, they are spendable by key.

Collision is kinda useless, what would one do with it?

If Lightning Network would work on top of P2SH, or other 160-bit addresses, then one participant could create a collision, where a given script would be spendable by 2-of-2 multisig, and by the attacker alone.

But yes, you are right about 160-bit security: as long as the public key is not revealed, it is the case. When it comes to 80-bit security, it is the case, when two or more participants are trying to get a shared UTXO, and put their coins on the same address.

[Mia Chloe]

I need a convincing and satisfying answer on the difference between public key and address because In the course of studying I'm trying to assume public key is the same as address. Though address is just a way of representing our public key which was derived from our private key using the mathematical elliptical curve multiplication.
Please I need more clarification on it.

To add to what others have said, your public keys are more like an origin where your addresses are generated from which is basically similar to how your child keys to respective addresses are generated from the master keys. Back in the day it was possible to send coins directly to your public keys and there were wallets that supported them.

However you may be able to guess why that is no longer a thing. It was discontinued because it was a total breach of privacy on the network.

[melinoe]

It would be much better if the public key would function as the address as well.

There should be only 2 things related to BTC: the private key and the public key (that is the address as well).

Addresses are shorter, easier to use, and aren't a direct clue to your public key.

So I don't see a problem there.

[Cookdata]

It would be much better if the public key would function as the address as well.

There should be only 2 things related to BTC: the private key and the public key (that is the address as well).

Early versions Bitcoin payments support public key payment, pay to public key P2PK but it was later change because publick key has has more byte, like 33 for compressed keys.

This long byte can be converted  to short version with hash functions of  Repimd160 and Sha256, that's gives 20 bytes but importantly the more reason for the change is to enhance transaction privacy and protection of your public key, there is also risk of sending coin to a wrong public key. If you see a Bitcoin address with 1hMgj..., Bc1q or Bc1p, you will know it's an address but if I paste you a public key, you can't tell its a public key.

If there hasnt been the change of public keys to address before now, maybe we will be more worried about Quantum attack if publick keys are actually visible on scriptpubkeys.

[FortuneFollower]

It would be much better if the public key would function as the address as well.

There should be only 2 things related to BTC: the private key and the public key (that is the address as well).

Early versions Bitcoin payments support public key payment, pay to public key P2PK but it was later change because publick key has has more byte, like 33 for compressed keys.

This long byte can be converted  to short version with hash functions of  Repimd160 and Sha256, that's gives 20 bytes but importantly the more reason for the change is to enhance transaction privacy and protection of your public key, there is also risk of sending coin to a wrong public key. If you see a Bitcoin address with 1hMgj..., Bc1q or Bc1p, you will know it's an address but if I paste you a public key, you can't tell its a public key.

If there hasnt been the change of public keys to address before now, maybe we will be more worried about Quantum attack if publick keys are actually visible on scriptpubkeys.

Quantums are the problem of the future.. I do think when the time comes and they will be there for masses to be used, BTC will be prepared for it.

As of now, it's just a big buzz.

[Cookdata]

It would be much better if the public key would function as the address as well.

There should be only 2 things related to BTC: the private key and the public key (that is the address as well).

Early versions Bitcoin payments support public key payment, pay to public key P2PK but it was later change because publick key has has more byte, like 33 for compressed keys.

This long byte can be converted  to short version with hash functions of  Repimd160 and Sha256, that's gives 20 bytes but importantly the more reason for the change is to enhance transaction privacy and protection of your public key, there is also risk of sending coin to a wrong public key. If you see a Bitcoin address with 1hMgj..., Bc1q or Bc1p, you will know it's an address but if I paste you a public key, you can't tell its a public key.

If there hasnt been the change of public keys to address before now, maybe we will be more worried about Quantum attack if publick keys are actually visible on scriptpubkeys.

a

Quantums are the problem of the future.. I do think when the time comes and they will be there for masses to be used, BTC will be prepared for it.

As of now, it's just a big buzz.

It's a future speculation but we have a present FUD we are dealing with. Some people prefer fake information over truth. If Bitcoin is using P2PK in 2025 with price trading at $90k, they will used that FUD to kill the price. That's going to be a food for content and opportunities to demarket Bitcoin.



https://x.com/coinbureau/status/1991026149661815080

This are the kind of FUD I'm talking about, posted some hours ago.

[FortuneFollower]

It's a future speculation but we have a present FUD we are dealing with. Some people prefer fake information over truth. If Bitcoin is using P2PK in 2025 with price trading at $90k, they will used that FUD to kill the price. That's going to be a food for content and opportunities to demarket Bitcoin.



https://x.com/coinbureau/status/1991026149661815080

This are the kind of FUD I'm talking about, posted some hours ago.

Yeah, that's just crazy.

I am happy to know that the tremblings from such news are not long, unlike dips on something that happens on the overall market

[j2002ba2]

Collision is kinda useless, what would one do with it?

If Lightning Network would work on top of P2SH, or other 160-bit addresses, then one participant could create a collision, where a given script would be spendable by 2-of-2 multisig, and by the attacker alone.

Lightning requires segwit, which means P2WSH, 256 bit (with HTLC). So collision security goes up to 128 bit. When (eventually) using PTLC (taproot), again security is again 128 bit.

AFAIK nobody accepts wrapped lightning commitment P2SH-P2WSH.

[IjawMan]

Please I need more clarification on it.

Here is a thread will be of help to your question. What is the difference between public key and public key hash. you will find it very helpful with what prominent members like pooya87, o_e_l_e_o, BlackHatCoiner, apogio has explained.
 
You can add this to the list to get the satisfying answers you looking for: Public keys and Addresses - Are there striking similarities or difference

[satscraper]

because the operations that convert public keys into the tweaked ones

You don't have to tweak keys.

You have to tweak it to get the correct Taproot address. The relevant steps are shown below. ^{My previous response was related to your statement about "1:1 mapping' "between public keys and addresses" relevant to taproot}.

Regarding sending, yes, you can send from Taproot address provided your wallet supports Taproot. List of relevant wallets can be found here.

[stwenhao]

You have to tweak it to get the correct Taproot address.

If you have to tweak it, then why using untweaked version is valid?

Because as long as it is valid, tweaking is optional. For example:

https://mempool.space/signet/address/tb1pruektj90gg8nysa7yuk07w7ucwlywrf4p02lq3sz49f05xd00djscyt2fw

Address: tb1pruektj90gg8nysa7yuk07w7ucwlywrf4p02lq3sz49f05xd00djscyt2fw
Public key: 021f3365c8af420f3243be272cff3bdcc3be470d350bd5f04602a952fa19af7b65

You don't need to know "internal, tweaked Taproot key". And you don't need TapScript. If you can get the private key for 021f3365c8af420f3243be272cff3bdcc3be470d350bd5f04602a952fa19af7b65, then you can just move the coins, without mining them.

Which means, that tweaking is officially recommended, but it is not obligatory, so it is not enforced everywhere. And as long as it is the case, 1:1 mapping is possible.