Public and Private Key

TLS is using digital certificates for authentication. Use of digital certificates for authentication is based on properties of Public/Private Key Pair. This page contains necessary background information on properties of Public/Private Key Pair.

There are algorithms that allow to generate random pair of keys with following two properties:

1. It is impractical task (in terms of amount of efforts and needed computer time) to try to recover one key in the pair when only another key in the pair is known.
2. If some message is encrypted with one key of the pair, it can only be decrypted back with another key of the pair.

Typically, person or entity will generate one such random pair of keys and make one key publicly known and publicly associated with person's or entity's name. The second (matching) key is kept secret to allow person or entity to decrypt messages encrypted with public key or to confirm person's or entity's identity by proving ownership of the matching secret key.

The first property allows one to make one key of the pair known to the public without risking that anybody will be able to recover the second (private) key of the pair (which is kept secret). Recovering one key by known another key, typically, amounts to resolving mathematical problem that does not have analytical solution or fast numerical algorithm that leads to solution. The amount of needed computer time grows exponentially with key length increase. The key should be long enough to make the task impractical. Two known mathematical problems are:

• finding prime divisors of large integers and
• finding discrete logarithm in large finite fields

The second property allows to use the pair for:

• Encryption: anyone can encrypt message with the public key but only the owner of the matching private key can decrypt the message.
• Authentication: anybody can encrypt random message (authentication challenge) with the public key, but only the owner of the matching private key can return decrypted message (valid authentication response) back to sender to confirm his/her identity via association with public key of the pair.
• Digital signature: one can calculate check-sum (hash or digest) of the message, encrypt check-sum with his/her private key and then send message out with "encrypted check-sum" (digital signature) attached. Anyone who has public key of the signer can decrypt and verify check-sum confirming both (1) that message was sealed by the owner of the matching private key and (2) that message was not changed since it was sealed.