Not exactly true. Elliptic-curve cryptography is used to derive the public key from the private key. However the public key is hashed to get a Bitcoin address. 
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Homework on Public and Private key Cryptography - Questions
- Describe the concept of public and private key with your own words.
A Public Key is the hashed out, algorithmic, computation, representation of the Private Key. A Private Key is a random number generated by a computer and then hashed out via, let’s say, SHA256 in to a Public Key. Private Keys can reveal a Public Key but a Public Key cannot reveal a Private Key. You can go forward but never backwards.
- What 2 use-cases can public key cryptography be used for?
Encryption and Digital Signatures.
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Describe the concept of public and private key with your own words.
–> A (secret) private key is based on a random number and generated by a wallet/computer. The public key is then derived from the private key, and finally, the Bitcoin address is generated from the public key. This is a one-way relationship. It is practically impossible to derive the private key from a public key. -
What 2 use-cases can public key cryptography be used for?
–> The two use cases public key cryptography can be used for are encryption and digital signatures.
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We use elliptic curve cryptography in order to generate a public key from the private key. However we do hash the public key in a particular order to get the public address. If you are interested in more details feel free to message me back. I will provide you with even more details. 
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A private key is basically a random number. It is used to sign transactions. It can also generate a public key which everyone can see it. When we create a bitcoin wallet, we randomly generate a private key, then that private generates a public key, and then that public key generates our bitcoin address. This process cannot be done backward.
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The two use-cases of publics keys are to generate the wallet address and to encrypt messages.
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Its all about digital signature and it being encrypted
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Wallets , sending messages on public forum
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A public key is used to interact with others on the network. A private key is linked to the public key and is necessary to access encrypted data. A digital signature can be used to identify the integrity of the public key. Public keys are used by other users on the Bitcoin network to challenge the ownership of Bitcoin. Bitcoin ownership is proven when the public key is proven to be generated from the private key.
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- Describe the concept of public and private key with your own words.
The two major uses of public key-private key cryptography are:
- Encryption
- Digital Signatures
In both cases the private key must stay secret-private. If this key is revealed, it’s the same as giving away your bitcoins to anyone that wants it. If somebody copies your private key, they have total access to your assets, and can clean you out. To prevent this, the public key is derived by mathematical equations from the private key. You derive/can derive the public key from the private key. But you can’t derive the private key from the public key. This is because of the unidirectional function used to derive the public key from the private key. The public key is public, anybody can see it, and they will “never” be able to figure out your private key from it.
In encryption [of messages], When Alice send a message to Bob, Her message is encrypted with bob’s public key. When Bob receives Alice’s [encrypted] message [encrypted with Bob’s public key], he is able to open it with his private key. Nobody else will be able to see Alice’s message, for anybody else intercepting the message, it will look like gibberish. If Bob loses his private key, he will not be able to decrypt the message. If somebody steals/copies Bob’s private key, they will also be able to decrypt Alice’s message.
Digital signatures are the way bitcoin/crypto use the public/private key to record transactions. With digital signatures, the bitcoin system seeks to verify WHO sent a particular message/transaction. The emphasis here is to confirm that it was indeed Alice that sent a message to Bob. In this scenario, Alice sends a message to Bob, and she puts a digital signature on this message. The concern here is to make sure that the message came from Alice, not the privacy of the info within the message. To make sure that the message is from Alice, Bob analyses the Digital signature in the message, and Alice’s public key, and derives Alice’s private key, confirming that the message came from Alice.
- What 2 use-cases can public key cryptography be used for?
The two major uses of public key cryptography are:
- Encryption
- Digital Signatures
Encryption is used to prevent others from having access to your messages/conversations.
Digital Signatures “are about identification.” It identifies who you are and ensures the integrity of the message you received. This is the way bitcoin benefits from private key-public key cryptography. In bitcoin, there is no central entity that tracks accounts. Instead, each wallet in the network depends on public-private key pairings for security and privacy. Both the wallets and the bitcoin network are built on the public-private keys.
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Describe the concept of public and private key with your own words.
A private key is an random very large number on my computer that verifies my identity, a public key is generated from that private key … with that pulic key i can send a encrypted message to somebody.
What 2 use-cases can public key cryptography be used for?
The public key can be used for encryption of a message ( that means transform the message in a secret cryptografic “puzzle”) and can be used for a digital signature, that means by the public key I can verify the identity of the sender.
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wo totaly clear ! thanks
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The public and private key is used to communicate securely encrypted trough an open network.
A private key is a random large number created on a the computer an the public key is generated from that number. -
Encryption and Digital signatures
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Describe the concept of public and private key with your own words.
an public key is created by private key. everyone can see you public key but you have to ensure you keep your private key safe as it can be used to digitally sign and de-crypt messages. Private key is very large generated random number that is impossibly to guess. -
What 2 use-cases can public key cryptography be used for?
-Keys can be used for encryption or digital signatures. With encryption the key pair can be used to en-crypt and de-crypt messages.With digital signatures (that is used in BTC). The sender signs digitally the message/transaction with private key to ensure receiver authenticity.
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Public and Private keys are used in Cryptography in order to Encrypt messages, and for Digital Signatures. This is accomplished by first generating a public key from a private key.
This public key can then be used by anyone else to encrypt a message meant for that reader only which keeps the message private.
In the second use case someones private key may also be used to sign a message, encrypted or not, so other viewers are able to verify it is from that sender.
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Don’t forget about the digital signatures. They are made with a help of a private key. In bitcoin, a digital signatures can verify that you own the private key without actually revealing. This enables you to spend the funds connected to a public address.
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Your first answer is great answer for the second question. Is there anything you can tell me more about the private and public keys? How are these keys used in order to achieve encryption and digital signatures?
Yes, thank you for the reminder.
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Best answer I have seen so far. Very detailed and on point. Keep up the great work.
I shared you answer on twitter: https://twitter.com/Mauro4897/status/1275788771997282306?s=19
Only to the person who owns the private key of that public key. Otherwise they wouldn’t be able to decrypt it.
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A private key is a “number” that uniquely identifies the person who generated it. No other person will generate this exact unique number. This private key should be secured and kept strictly confidential to the person. The public key is generated based off the private key, and can be propagated to the public for use as proof that the person who gave out the public key, is who they say they are.
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A public key can be used to decrypt a PGP encrypted email sent to others. If the person receiving the email has the public key of the sender, they then have the ability to decrypt the email contents. A public key can also be used to verify authentication and permissions to other systems (ala SSH).
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