Public and private keys, explained with a mailbox (not just "it's like a passwor

[diggler]

However, I've been for quite a while trying to define an important concept, and I think I finally found the correct words to do it.
Anyway, it's one of the points that always comes up in discussions about cryptocurrencies: the comparison between a key pair and a username/password for any online service.

It's a false comparison and it creates confusion.
Imagine, to start, that the public key is something like a mailbox mounted on a wall visible to everyone on the street, with the address showing too. Any person can use that address to send letters inside that box. And what would the private key be in this case? It would be the physical thing that opens that box, and that thing must be kept far away, not even for the mailman!
As for this process with Bitcoin, it works exactly like this too, except that the relationship between these keys is mathematically inverted. Getting the public key starting from the private key is simple. Deriving the private key starting from the public one will never be possible. All the security that exists in this system is based on this single functionality.

The Bitcoin address where you receive BTC is derived from the public key with more hashings to simplify it even further. So, the sequence of operations will be this:
private key -> public key -> address where you receive BTC
All these procedures are absolutely one-directional.

There are countless users who have completely wrong ideas that if you lose the private key that implies you just won't be able to use your address anymore. They think there will always be a way to recover the key, just like you recover a password... That's false, and it will never be possible.

No entity in this system, not even an exchange house or even the developer themself, will have the capacity to recover a private key from a public key or from a BTC address where you receive BTCs.
That total incapacity for recovery only exists if there is personal custody. If you lose your password to an account at an exchange house like Binance or Coinbase, it's a completely different scenario, because those exchange houses have your private key for you, that's what custody means. So, you can recover your account using traditional account recovery methods.

[SeriouslyGiveaway]

The Bitcoin address where you receive BTC is derived from the public key with more hashings to simplify it even further. So, the sequence of operations will be this:
private key -> public key -> address where you receive BTC
All these procedures are absolutely one-directional.

It's absolutely correct. The procedure of creating public key from private key is one-way, and the procedure of generating a Bitcoin public address from its public key is also one-way.

Private key > Public key: through Elliptic Curve Multiplication (one-way)
Public key > Bitcoin address: through a Hashing function (one-way)

There are countless users who have completely wrong ideas that if you lose the private key that implies you just won't be able to use your address anymore. They think there will always be a way to recover the key, just like you recover a password... That's false, and it will never be possible.

I am sorry but I am feeling lost when reading this post because it is confusing and kind of misleading me to a thought like if I lost my Bitcoin private key, I still can access my bitcoin, and it means like I am still safe.

It's untrue.

If you lost your Bitcoin private keys - lost means you lost your original wallet, and did not have any wallet back or can not use any wallet backup you have - so you will certainly not be able to access your bitcoin.

[Cookdata]

The Bitcoin address where you receive BTC is derived from the public key with more hashings to simplify it even further. So, the sequence of operations will be this:
private key -> public key -> address where you receive BTC
All these procedures are absolutely one-directional.

You are right, but there is a small correction to the way you simplify this explanation, Bitcoin are recieved on the address, but this address is not directly from the public key, they are derived from the public key hash which is why we have different types of Bitcoin locking scripts. Among them, we have the old p2pk, p2pkh, p2sh and we have the SegWit scripts. It is these pubkey hashes that are encoded into the address, not the public key.

That total incapacity for recovery only exists if there is personal custody. If you lose your password to an account at an exchange house like Binance or Coinbase, it's a completely different scenario, because those exchange houses have your private key for you, that's what custody means. So, you can recover your account using traditional account recovery methods.

The centralised exchanges are custodial services, they help you manage your coins. You give them the coin, and they give you a platform where you keep records of transactions but most of them are not reliable, they have failed their customers, most of the exchanges have lost funds to hacks, and they don't speak up. We have some that have been bankrupt for years now and are still paying creditors. If you want to avoid these nightmares, use a custodial wallet.

[hugeblack]

No entity in this system, not even an exchange house or even the developer themself, will have the capacity to recover a private key from a public key or from a BTC address where you receive BTCs.

This is true under certain conditions, namely generating a good entropy Private Key and not revealing xpub + ANY Child Private Key.
In short, never share Extended Public Keys (xpub). Create a wallet with good entropy, preferably open-source and ideally airgapped.

Andreas M. Antonopoulos' YouTube channel has better explanations of public and private keys; I highly recommend it instead of relying on online articles.

[Charles-Tim]

That total incapacity for recovery only exists if there is personal custody. If you lose your password to an account at an exchange house like Binance or Coinbase, it's a completely different scenario, because those exchange houses have your private key for you, that's what custody means. So, you can recover your account using traditional account recovery methods.

So, in short, you are insinuating that people should use custodial means to hold their coins? Also this is entirely different from the title of your topic which is about private key and public key explained, and not about in difference to exchanges.

Exchanges have their own downsides which can not make me use exchanges to hold coins.

[Taskford]

That total incapacity for recovery only exists if there is personal custody. If you lose your password to an account at an exchange house like Binance or Coinbase, it's a completely different scenario, because those exchange houses have your private key for you, that's what custody means. So, you can recover your account using traditional account recovery methods.

So, in short, you are insinuating that people should use custodial means to hold their coins? Also this is entirely different from the title of your topic which is about private key and public key explained, and not about in difference to exchanges.

Exchanges have their own downsides which can not make me use exchanges to hold coins.

Maybe he just think about he convenience what those custodial platforms could offer to their users. But he didn't pay any attention on possible trade offs for using those exchange.

Yeah recovery is truly possible with those exchange, but the bigger problem comes if the exchange got suffered for massive hack. Like they lose lots of money and can't afford to pay those people affected with this issue. Also if there's sudden unfair freezing of their account or they decide to rug pull and shutdown their operation.

People should remember that the coins deposited on custodial platforms are always in huge risk. So better use those exchange as gateway for their trading or buying, then best to hold their funds on wallet on which they have full control like non custodial wallets.