**Symmetric and asymmetric encryption**

**Private and public keys**

Notes based on the following video:

https://www.youtube.com/watch?v=HubAvQg6SPM

Let us say that you want to send to your friend an encrypted message saying "Hi". You decide to use the following encryption method, or encryption key: shift each letter by one place in the alphabet. The "Hi" is encrypted to "Ij". You meet your friend in private taking all precautions for eavesdropping, and you tell him that this is the key. You can then go ahead and send encrypted messages to each other. Cryptologists came up 30 years ago with the following method: they used an algorithm (key 1) to encrypt a word and strangely enough the word could not be decrypted by the same algorithm but with another one (let us say key 2). This means that you are free to send key 1 in a standard email message to your friend. Key 1 would be a public key. You just keep key 2 to yourself. In the previous case you cannot say over the internet that you need to shift each letter by one place. This makes it a private key, a key that has to be kept private. Also, in this case you use the same measure, same calculus, same math (metrics) to encrypt and to decrypt, therefore this is symmetric. In the other case you have two different algorithms, and therefore not the same measure (deprivative “a” in asymmetric).

http://science.howstuffworks.com/…/…/quantum-cryptology4.htm

(Excerpts from above link and "previous page")

"To create a photon, quantum cryptographers use LEDs -- light emitting diodes, a source of unpolarized light.

Through the use of polarization filters, we can force the photon to take one state or another -- or polarize it. If we use a vertical polarizing filter situated beyond a LED, we can polarize the photons that emerge: The photons that aren't absorbed will emerge on the other side with a vertical spin ( | )."

"The thing about photons is that once they're polarized, they can't be accurately measured again, except by a filter like the one that initially produced their current spin. So if a photon with a vertical spin is measured through a diagonal filter, either the photon won't pass through the filter or the filter will affect the photon's behavior, causing it to take a diagonal spin. In this sense, the information on the photon's original polarization is lost, and so, too, is any information attached to the photon's spin."

"How do you attach information to a photon's spin?"

"This is where binary code comes into play. Each type of a photon's spin represents one piece of information -- usually a 1 or a 0, for binary code. This code uses strings of 1s and 0s to create a coherent message. For example, 11100100110 could correspond with h-e-l-l-o."

"When Alice sends Bob her photons using an LED, she'll randomly polarize them through either the X or the + filters, so that each polarized photon has one of four possible states: (|), (--), (/) or ( ) [source: Vittorio]. As Bob receives these photons, he decides whether to measure each with either his + or X filter -- he can't use both filters together. Keep in mind, Bob has no idea what filter to use for each photon, he's guessing for each one. After the entire transmission, Bob and Alice have a non-encrypted discussion about the transmission."

"The reason this conversation can be public is because of the way it's carried out. Bob calls Alice and tells her which filter he used for each photon, and she tells him whether it was the correct
or incorrect filter to use. Their conversation may sound a little like this:

Bob: PlusAlice: Correct

Bob: PlusAlice: Incorrect

Bob: XAlice: Correct

Since Bob isn't saying what his measurements are -- only the type of filter he used -- a third party listening in on their conversation can't determine what the actual photon sequence is."