What is the difference between encrypting and signing in asymmetric encryption?

When encrypting, you use their public key to write a message and they use their private key to read it.

When signing, you use your private key to write message's signature, and they use your public key to check if it's really yours.

I want to use my private key to generate messages so only I can possibly be the sender.

I want my public key to be used to read the messages and I do not care who reads them

This is signing, it is done with your private key.

I want to be able to encrypt certain information and use it as a product key for my software.

I only care that I am the only one who can generate these.

If you only need to know it to yourself, you don't need to mess with keys to do this. You may just generate random data and keep it in a database.

But if you want people to know that the keys are really yours, you need to generate random data, keep in it a database AND sign it with your key.

I would like to include my public key in my software to decrypt/read the signature of the key.

You'll probably need to purchase a certificate for your public key from a commercial provider like Verisign or Thawte, so that people may check that no one had forged your software and replaced your public key with theirs.

In RSA crypto, when you generate a key pair, it's completely arbitrary which one you choose to be the public key, and which is the private key. If you encrypt with one, you can decrypt with the other - it works in both directions.

So, it's fairly simple to see how you can encrypt a message with the receiver's public key, so that the receiver can decrypt it with their private key.

A signature is proof that the signer has the private key that matches some public key. To do this, it would be enough to encrypt the message with that sender's private key, and include the encrypted version alongside the plaintext version. To verify the sender, decrypt the encrypted version, and check that it is the same as the plaintext.

Of course, this means that your message is not secret. Anyone can decrypt it, because the public key is well known. But when they do so, they have proved that the creator of the ciphertext has the corresponding private key.

However, this means doubling the size of your transmission - plaintext and ciphertext together (assuming you want people who aren't interested in verifying the signature, to read the message). So instead, typically a signature is created by creating a hash of the plaintext. It's important that fake hashes can't be created, so cryptographic hash algorithms such as SHA-2 are used.

So:

• To generate a signature, make a hash from the plaintext, encrypt it with your private key, include it alongside the plaintext.
• To verify a signature, make a hash from the plaintext, decrypt the signature with the sender's public key, check that both hashes are the same.

There are two distinct but closely related problems in establishing a secure communication

1. Encrypt data so that only authorized persons can decrypt and read it.
2. Verify the identity/authentication of sender.

Both of these problems can be elegantly solved using public key cryptography.

I. Encryption and decryption of data

Alice wants to send a message to Bob which no one should be able to read.

• Alice encrypts the message with Bob's public key and sends it over.
• Bob receives the message and decrypts it using his private Key.

Note that if A wants to send a message to B, A needs to use the Public key of B (which is publicly available to anyone) and neither public nor private key of A comes into picture here.

So if you want to send a message to me you should know and use my public key which I provide to you and only I will be able to decrypt the message since I am the only one who has access to the corresponding private key.

II. Verify the identity of sender (Authentication)

Alice wants to send a message to Bob again. The problem of encrypting the data is solved using the above method.

But what if I am sitting between Alice and Bob, introducing myself as 'Alice' to Bob and sending my own message to Bob instead of forwarding the one sent by Alice. Even though I can not decrypt and read the original message sent by Alice(that requires access to Bob's private key) I am hijacking the entire conversation between them.

Is there a way Bob can confirm that the messages he is receiving are actually sent by Alice?

• Alice signs the message with her private key and sends it over. (In practice, what is signed is a hash of the message, e.g. SHA-256 or SHA-512.)
• Bob receives it and verifies it using Alice's public key. Since Alice's public key successfully verified the message, Bob can conclude that the message has been signed by Alice.