If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Public key encryption

On the Internet, two computers often want to exchange secure data with each other. When I type my password into the Khan Academy login screen, I want my computer to send that data safely to the Khan Academy servers. I do not want to worry that an attacker might be monitoring my Internet traffic and watching the password go across the wires.
Illustrator of an attacker stealing password data. A laptop is shown with a browser and a password input field. An arrow goes from the laptop to a server. Above the arrow, there's a pouch that contains the text "Be3tP@ssw0rd3ver" and a smiling attacker looking at the text.
Symmetric encryption techniques rely on both the sender and receiver using the same key to encrypt and decrypt the data. How can my computer and the Khan Academy server exchange the key securely? If an attacker can see my password go across the wires, then they can also see an encryption key!
Illustrator of an attacker stealing an encryption key. A laptop is shown with a browser and a password input field. An arrow goes from the laptop to a server. Above the arrow, there's a pouch that contains the text "TOP_SECRET_KEY" and a smiling attacker looking at the text.
Public key encryption to the rescue! It's an asymmetric encryption technique which uses different keys for encryption and decryption, allowing computers over the Internet to securely communicate with each other.
Let's step through the high-level process of public key encryption.

Step 1: Key generation

Each person (or their computer) must generate a pair of keys that identifies them: a private key and a public key.
You can generate a pair below, using the same RSA algorithm that's used by your computer:
Did you notice it takes a few seconds to generate the keys? That's due to the math involved. The keys are generated by multiplying together two incredibly large primes. The algorithm repeatedly generates random large numbers and checks if they're prime, until it finally finds two random large primes. All that checking for primes can take a while, and these keys are only 512 bits long. The current nationally recommended key length is 2048, or even 3072 bits.

Step 2: Key exchange

The sending and receiving computers exchange public keys with each other via a reliable channel, like TCP/IP. The private keys are never exchanged.
Key exchange diagram with a laptop and a server. The laptop screen shows a browser with a password input field. An arrow goes from the server to the laptop and is labeled with "SERVER_PUBLIC_KEY". Under that, an arrow goes from the laptop to the server and is labeled with "CLIENT_PUBLIC_KEY."

Step 3: Encryption

The sending computer encrypts the secret data using the receiving computer's public key and a mathematical operation.
The power of public key encryption is in that mathematical operation. It's a "one-way function", which means it's incredibly difficult for a computer to reverse the operation and discover the original data. Even the public key cannot be used to decrypt the data.
You can try it out below, with the public key you generated above:

Step 4: Sending encrypted data

The sender can now safely transmit the encrypted data over the Internet without worry of onlookers.
Key exchange diagram with a laptop and a server. The laptop screen shows a browser with a password input field. An arrow goes from the server to the laptop and is labeled with string of encrypted text. An attacker looks unhappily at the text.

Step 5: Decryption

Now the receiver can decrypt the message, using their private key. That's the only key that can be used to decrypt the message (in the world!).
Try it out below, with the encrypted message and private key from above:
Once you successfully decrypt the message, try decrypting it with the public key. It won't work; only the private key can decrypt it.

But how is that possible?

It may sound too good to be true; that it's possible to encrypt something with one key that can only then be decrypted by a different key. For a long time, mathematicians weren't sure if it was possible, but fortunately they discovered a way in the 1970s.
The math of the one-way function relies on prime numbers, the difficulty of factoring large primes, and modular arithmetic. If you'd like to dig deeper into the math, check out the Khan Academy tutorials on modern cryptography.
Fortunately, all of us can use and benefit from public key cryptography without needing to understand the complicated math behind it. In fact, we likely use public key cryptography everyday as we use computers and the Internet. Just imagine, what would the world be without it?

🙋🏽🙋🏻‍♀️🙋🏿‍♂️Do you have any questions about this topic? We'd love to answer—just ask in the questions area below!

Want to join the conversation?

  • hopper cool style avatar for user Alex Ewart
    Is all data sent on the internet due to regulations automatically encrypted?
    When getting other's public keys, generating private keys, and decrypting data, when does all this happen, because I now know that my computer does this but I have no idea when it is all this going on. Is it like when I type in someone's email address? Is the address a public key? If so, is the email address like a way humans can remember the public key like domain names instead of typing IP addresses?
    Does every computer have its own designated keys, or do they change like IP addresses?
    Hope this is not too confusing to answer.
    (5 votes)
    • blobby green style avatar for user Abhishek Shah
      This is a great question!

      All data sent over the Internet is not encrypted. Only if you use certain protocols like HTTPS will it be encrypted. There is no regulation requiring all data to be encrypted.

      A person's email address is not a public key. Every computer has the ability to create its own keys, but when you get a new computer, it doesn't magically already exist. You have to generate it. Once it's generated, keys don't change. You can always generate a new set of keys though.

      One way I find it easy to think about is the following:

      Think about your home. If someone sends you mail, do they need a key to your home to put it inside? No, they could just slide it under the door or put into your mailbox. When you reach home, you can unlock your home and read the mail.

      This is why as users we don't have to generate keys with our own computers. In some sense, we just send mail to servers by slipping it underneath their doors (via a public key encryption) and they can read it via a private key decryption.

      I hope this helps!
      (5 votes)
  • piceratops seed style avatar for user ronanmacg
    When I encrypt something using my public key, eg "Hi" it seems like it can have many different encrypted forms. How is this possible?
    (3 votes)
  • sneak peak yellow style avatar for user Hello there
    Why are the discussions now locked?
    (5 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user sebastian nielsen
    I don't get how the private and public key looks like a mess. Shouldn't the private and public key just be a number? Then what is all those symbols doing in the private and public key?

    -----END RSA PRIVATE KEY-----

    P.s. I went through the math but at no point is it mentioned how this strange looking key was derived.
    (3 votes)
  • leaf red style avatar for user Gamar
    What I wanna know is: The whole public key process, how it really works in a real life situation.

    The receiver shares their public key so the sender can encrypt with it, and then it decrypts it with it’s private key, the only thing that can decrypt it...
    But in what way does this process happen?

    Do they need eachothers public keys for the entire process until TCP/IP disconnection?
    Does every step in the communication require another key?
    Do you always have the same public key on your machine or when does it change?
    (3 votes)
    • starky ultimate style avatar for user KLaudano
      A common scenario is for a party to publish their RSA public key. Then, when someone communicates with that party, they create an AES key and encrypt it with the RSA public key. The encrypted AES key is sent over to the party who then decrypts it with their RSA private key. After that, the remaining messages are encrypted with the AES key for the rest of the session.

      AES encryption is used to encrypt the majority of the messages as it is significantly faster than RSA encryption.
      (2 votes)
  • blobby green style avatar for user Becca
    They both are false in the story I read
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Aland Soran
    In step 1, it is mentioned that the generated keys are only 512 bits long. However, using a character counter, I counted the first key generated and it was 824 characters. How is that 512 bits? am I misunderstanding something?
    (2 votes)
    • stelly blue style avatar for user Evan Lewis
      Great question! The reason for this is the difference between bits and characters. In a computer, a character is represented as a byte (or 8 bits). So, if a key is 512 bits long, that does not mean it is 512 characters long.

      The 512 bits refers to the length of the binary representation of the key. When this binary sequence is encoded as text (for example, using Base64 encoding, which is common for keys), it will indeed be longer than 512 characters.
      (1 vote)
  • leaf green style avatar for user Song Liu
    Are the public and private keys fixed or dynamic for a device connected to internet? Should one of the keys change result in another one change accordingly? Thanks.
    (2 votes)
    • blobby green style avatar for user Abhishek Shah
      A device can have multiple public-private key pairs. When connecting to a device over the Internet, the key pairs are usually fixed, but it's possible for it to be dynamic. The public key for a server can be found in its web certificate (over HTTPS), and the private key is secret.

      Also, keys form a pair, changing one of the keys changes the pair and hence the other one should change accordingly.

      Hope this helps!
      (0 votes)
  • hopper cool style avatar for user Alex Ewart
    So data sent to your computer is encrypted in a randomly generated code? How does a computer decrypt the sent data? Do you decide your own private key? How do passwords play into this, because at first I thought that your own password was a key and now I am not sure.
    (1 vote)
    • blobby green style avatar for user Abhishek Shah
      It's great you are thinking about this!

      Passwords are generally used for authentication, not encryption. Authentication seeks to prove who you are. Encryption seeks to hide a message. They are not equivalent.

      As you observed, you can't decrypt the sent data unless you have the right keys. Hence, in protocols like HTTPS where they use public key encryption, the first thing to do is establish the keys. Only then can you decrypt the data.

      I hope this helps and feel free to ask more!
      (1 vote)
  • blobby green style avatar for user colton.horrell
    How does this subject work.
    (1 vote)
    Default Khan Academy avatar avatar for user