private key is a long, random number that is to remain secret (hence, “private”) which is used to derive - via a one-way function - a public key which can be shown publicly. the public key, if lost can be restored from the private key, but never the other way around
encryption & digital signatures
Private key is a number that generates a public key. The private key is just that - private, and used for DEcryption. The public key is for anyone to see and generated by the private key. Public key is used for ENcryption purposes. This hash function is a one way function; private to public, but never the reverse.
Digital signature and encryption.
To keep a conversation secret messages can be encrypted. For it a private key is generated that further generates a public key. This public key then be used to encrypt messages and only person who has access to the private key can decrypt them.
Digital signatures as used in Bitcoin.
Public and Private Keys is key when it comes to securely exchange data between two parties.
The Private key is randomly generated long string which is held by the owner in safe place where nobody can get hold of it, because it is used to encrypt and decrypt data. The data can be anything eg transactions, messages, accounts etc. From the Private Key one can create unique hashed version of it which is called Public Key.
The Public Key is shared with whoever needs to encrypt or decrypt data with the owner of the keys.
Public key cryptography can be used to send/receive data securely or it can be used to sign data or verifying ownership
Encryption is useful for sending messages directly between users. Using someone’s public key anyone can encrypt data offline and then send the data to the owner of the public key. That person and only that person can then decipher that data with their corresponding private key.
Digital signatures is useful for verifying identity. This is also the primary role of public and private keys in the bitcoin blockchain. Users can only send bitcoin by signing the message with their private key. Anyone can see that the message belongs to that user by checking it against their public key.
The privete key is a randomly generated number, with which we will generate the public key (this cannot be done in reverse), with the public key anyone can encrypt data which will be accessible only for the ones who have the private key.
The 2 use-cases that it can be used for are, encryption and signature.
The public and private keys are key pair values used to encrypt and sign messages or transactions. User computer generates a private key for user A that should be kept secret. The private key is used as input in a special program to generate the public key of user A. User A shares his/her public key with others users who should use the public key of user A to encrypt message sent to user A the user.
User A can decrypt the message using its associated private key.
It is impossible to obtain the private key based public key
A digital signature is used to authenticate the sender of the message or transaction. When a user A sends message to other user, user A signs message with digital signature. The public key together with bitcoin address is sent to other user. When message from user A is received, the receiver uses the public key and digital signature to validate that the sender is user A
use case #1 : Sending encrypted message
use case #2 : Bitcoin transaction
A private key is an extremely large number so large it would be infeasible for another entity to generate the same large number at a whim. The private key is used as a variable within a hashing function to derive a public key that cannot be reverse engineered.
f(private key) = public key
These two numbers the private and public keys can be used for encryption and Digital signatures.
If a message is encrypted with a public key it can only be deciphered by its associated private key. Ex: party A encrypts a message with party B’s public key. Only Party B’s private key will unlock the message.
If a message is encrypted by a private key after hashing this is called a digital signature. The digital signature can then be attached to the message. As the digital signature was encrypted using a specified private key it can be unlocked via the public key revealing the hash. This ability to unlock the encryption proves the provenance of the message. If the original message ran through the same hashing algorithm matches the public key revealed hash then the message is untampered.
1.) With “private key” possible to encrypt the data but with “public key” possible decrypt
So the owner by generating “private key” also gets “public key” for sharing with who needs
2.) Use-cases of public-key cryptography:
a) for security from the public/spectators, to encrypt the data transferred between the owner of “private key” and the entity with “public key”, so no one else can see what data been sent.
b) signature in the network is a nice method to prove for the owner of “private key” to the public/network(which can see the “public key”) about his action
1.this concept describe the use of secret key as a signature to decrypt any public key generated from the originating private key. this allows you send a message in an encrypted manner through a public domain by creating a public key from the private key that can only be decrypted by the private key of the recipient.
2.encryption and digital signature
This concept is analogous to a shareable lock that can only be opened by the lock sharer’s own key:
Public key - acts as a lock that can be shared with others in public to use to lock (a.k.a. encrypt or garble up) the message/data before sharing (that’s what a wallet address is for).
Private key - a key that can unlock that shared lock to see the actual message (a.k.a. decrypt).
Public & Private Key Encryption is also known as Asymmetric Encryption.
Use-case #1 - Digital signatures to secure users’ shared documents so only the receiver can open it.* to verify that the document comes from the creator and no one else.
{* securing a document can be done just by applying a password to the document.}
Use-case #2 - Email encryption by PGP protocol so only the receiver can see the sent email.
Digital signature is a way of signing a message using a private key so that others can verify you are the one that wrote the message using your public key. 
Woops haha I just realized that mistake. Thanks for the correction!
Homework on Public and Private Keys - Questions
Public key allows someone to send their public key in an open, insecure channel. Having a friend’s public key allows you to encrypt messages to them. Your private key is used to decrypt messages encrypted to you.
Encrypt messages and verify digital signatures.
Private key is a random number generated by my computer. The Puiblic key is derived from the private key and it is intended to be seen by everyone. The private key is to be kept safe or “private”. We can never go from the public key to the private key, it is one way only, from the Private to the Public. The Private key is also the digital signature, and the Public Key is for encrypting a message.
One case is for encryption and the other one is for Digital Signature.
Thank you for the help!
1 private key is randomly created by a computer, i can use it send, sign messages or transactions.
public keys is derived from the private key. the other way around is not possible. public keys can be used to communicate where i want to receive something. can also be used for encrypting messages. Never loose it
2 public key cryptography can be use for encryption (of messages or transactions) and digital signatures
The private key is a randomly generated number by your computer that you keep as your key and the public key that is made is based of off the private key that was generated by your computer.
The 2 use-cases that public key cryptography can be used for is sending encrypted messages and sending cryptocurrency.