# Public Key Encryption

Imagine Alice wants something valuable shipped to her. Because it’s valuable, she wants to make sure it arrives securely (i.e. hasn’t been opened or tampered with) and that it’s not a forgery (i.e. it’s actually from the sender she’s expecting it to be from and nobody’s pulling the old switcheroo).

One way she can do this is by providing the sender (let’s call him Bob) with a high-security box of her choosing. She provides Bob with this box, and something else: a padlock, but a padlock without a key. Alice is keeping that key all to herself. Bob can put items in the box then put the padlock onto it. But once the padlock snaps shut, the box cannot be opened by anyone who doesn’t have Alice’s private key.

Here’s the twist though: Bob also puts a padlock onto the box. This padlock uses a key Bob has published to the world, such that if you have one of Bob’s keys, you know a box came from him because Bob’s keys will open Bob’s padlocks (let’s imagine a world where padlocks cannot be forged even if you know the key). Bob then sends the box to Alice.

In order for Alice to open the box, she needs two keys: her private key that opens her own padlock, and Bob’s well-known key. If Bob’s key doesn’t open the second padlock, then Alice knows that this is not the box she was expecting from Bob, it’s a forgery.

This bidirectional guarantee around identity is known as mutual authentication.

## Example

The `Box` class uses the given public and private (secret) keys to derive a shared key, which is used with the nonce given to encrypt the given messages and to decrypt the given ciphertexts. The same shared key will be generated from both pairing of keys, so given two keypairs belonging to Alice (pkalice, skalice) and Bob (pkbob, skbob), the key derived from (pkalice, skbob) will equal that from (pkbob, skalice).

This is how the system works:

    import nacl.utils
    from nacl.public import PrivateKey, Box

    # generate the private key which must be kept secret
    skbob = PrivateKey.generate()

    # the public key can be given to anyone wishing to send
    # Bob an encrypted message
    pkbob = skbob.public_key

    # Alice does the same and then
    #     sends her public key to Bob and Bob his public key to Alice
    skalice = PrivateKey.generate()
    pkalice = skalice.public_key

    # Bob wishes to send Alice an encrypted message
    # So Bob must make a Box with his private key and Alice's public key
    bob_box = Box(skbob, pkalice)

    # This is our message to send, it must be a bytestring as Box will
    #   treat is as just a binary blob of data.
    message = b"Kill all humans"

    # This is a nonce, it *MUST* only be used once, but it is not considered
    #   secret and can be transmitted or stored alongside the ciphertext. A
    #   good source of nonce is just 24 random bytes.
    nonce = nacl.utils.random(Box.NONCE_SIZE)

    # Encrypt our message, it will be exactly 40 bytes longer than the original
    #   message as it stores authentication information and nonce alongside it.
    encrypted = bob_box.encrypt(message, nonce)

    # Alice creates a second box with her private key to decrypt the message
    alice_box = Box(skalice, pkbob)

    # Decrypt our message, an exception will be raised if the encryption was
    #   tampered with or there was otherwise an error.
    plaintext = alice_box.decrypt(encrypted)

## Reference

class `nacl.public.``PublicKey`(public_key, encoder)

  The public key counterpart to an Curve25519 `PrivateKey` for encrypting messages.

  Parameters:

  - public_key (bytes) – Encoded Curve25519 public key.
  - encoder – A class that is able to decode the `public_key`.

class `nacl.public.``PrivateKey`(private_key, encoder)

  Private key for decrypting messages using the Curve25519 algorithm.

  Warning

  This must be protected and remain secret. Anyone who knows the value of your `PrivateKey` can decrypt any message encrypted by the corresponding `PublicKey`

  Parameters:

  - private_key (bytes) – The private key used to decrypt messages.
  - encoder – A class that is able to decode the `private_key`.

  `public_key`

    An instance of `PublicKey` that corresponds with the private key.

  classmethod `generate`()

    Generates a random `PrivateKey` object

    Returns: | An instance of `PrivateKey`.

class `nacl.public.``Box`(private_key, public_key)

  The Box class boxes and unboxes messages between a pair of keys

  The ciphertexts generated by `Box` include a 16 byte authenticator which is checked as part of the decryption. An invalid authenticator will cause the decrypt function to raise an exception. The authenticator is not a signature. Once you’ve decrypted the message you’ve demonstrated the ability to create arbitrary valid message, so messages you send are repudiable. For non-repudiable messages, sign them after encryption.

  Parameters:

  - private_key – An instance of `PrivateKey` used to encrypt and decrypt messages
  - public_key – An instance of `PublicKey` used to encrypt and decrypt messages

  classmethod `decode`(encoded, encoder)

    Decodes a serialized `Box`.

    Returns: | An instance of `Box`.

  `encrypt`(plaintext, nonce, encoder)

    Encrypts the plaintext message using the given nonce and returns the ciphertext encoded with the encoder.

    Warning

    It is VITALLY important that the nonce is a nonce, i.e. it is a number used only once for any given key. If you fail to do this, you compromise the privacy of the messages encrypted.

    Parameters:

    - plaintext (bytes) – The plaintext message to encrypt.
    - nonce (bytes) – The nonce to use in the encryption.
    - encoder – A class that is able to decode the ciphertext.

    Returns: | An instance of `EncryptedMessage`.

  `decrypt`(ciphertext, nonce, encoder)

    Decrypts the ciphertext using the given nonce and returns the plaintext message.

    Parameters:

    - ciphertext (bytes) – The encrypted message to decrypt.
    - nonce (bytes) – The nonce to use in the decryption.
    - encoder – A class that is able to decode the plaintext.

    Return bytes: | The decrypted plaintext.