Changes

'''Public-key encryption''' is an asymmetric [[encryption]] method in which 2 complementary keys are used. What gets encrypted by one of the keys can be decrypted only by the other. Generally one key of the pair is kept safe by an individual and the other key is distributed as widely as possible, after which two things can be done.

'''Public-key encryption''' is an asymmetric [[encryption]] method in which 2 complementary keys are used. What gets encrypted by one of the keys can be decrypted only by the other. Generally one key of the pair (the "private key") is kept safe by an individual and the other key (the "public key") is distributed freely, after which two things can be done.

If a message can be decrypted using the widely distributed ("public") key, it proves that the author of the message is the individual that holds the private key. Conversely, if a message is encrypted by the public key, it can only be decrypted by the key that was kept safe (the "private" key), making it possible to send a confidential message to the holder of the private key knowing only the public key. While this is the general principle of operation, many modifications are made in order to ensure practical and quick encryption.

If a message can be decrypted using the widely distributed ("public") key, it proves that the author of the message is the individual that holds the private key. Conversely, if a message is encrypted by the public key, it can only be decrypted by the key that was kept safe (the "private key"), making it possible to send a confidential message to the holder of the private key knowing only the public key. While this is the general principle of operation, many modifications are made in order to ensure practical and quick encryption.

Well-known public-key encryption algorithms include '''Diffie-Hellman''' and '''RSA'''. In Diffie-Hellman, the hardness is based on the [[discrete logarithm]]; in RSA it is [[factoring]].

Well-known public-key encryption algorithms include '''Diffie-Hellman''' and '''RSA'''. In Diffie-Hellman, the hardness is based on the [[discrete logarithm]]; in RSA it is [[factoring]].

* Fred '''encrypts''' the message using his ''private key''. (only fred knows this key)

* Fred '''encrypts''' the message using his ''private key''. (only fred knows this key)

* Fred sends the encrypted message  

* Fred sends the encrypted message  

* George gets the message (so do many other people, it's not important)

* George gets the message (others may as well,but that is not important)

* George '''decrypts''' the message using Fred's ''Public key''.  

* George '''decrypts''' the message using Fred's ''Public key''.  

* Only a message coded with the private key can be decoded wth the public key so George knows it came from Fred.  

* Only a message coded with the private key can be decoded with the public key so George knows it came from Fred.  

Step 2

Step 2

* George drafts a reply and '''encrypts''' it with Fred's ''Public key''.

* George drafts a reply and '''encrypts''' it with Fred's ''Public key''.

* Only Freds ''private key'' can '''decrypt''' the message, so it is secure

* Only Fred's ''private key'' can '''decrypt''' the message, so it is secure

* Fred receives the message and decrypts it  

* Fred receives the message and decrypts it  

* It's a valid message but Fred can't know who sent it, anyone with the public key could send to him.  

* It's a valid message but Fred can't know who sent it, anyone with the public key could send to him. For this reason, George may encrypt the message with his private key as well as Fred's public key, to prove it came from George while ensure only Fred can read it.

This form of public key encryption works best with sets of private and public keys.

This form of public key encryption works best with sets of private and public keys.