Quantum Information for Quantum Cats (11)

Secure Random Number Sharing with BB84 Protocol

Suppose Alice sends N quantum states that encode N bits with randomly varied coding mode, and Bob receives and decodes them with randome sequences of decoding modes. After the completion of the process, they communicate the encoding and decoding modes, and take up M bits that accidentally have encoded and decoded in the same mode.

If there is nothing in between Alice and Bob, those M bits should match 100%. If Eve is in action in between them, there would be mismatch among those M bits with certain probaility (which in fact occur in 75% chance).

In a form of itemized listing, we have the following situation.
(1) Alice sends sequence of bits in random mixture of Up-Down and Right-Left modes.

(2) Bob also uses random mixture of Up-Down and Right-Left modes in the decoding and reconstruct the sequence of bits.

(3) After the communication through classical channel, they take up only those bits for which encoding and decoding modes conincides.

(4) Those selected bits agree with 100% chance when there is no eavesdropping, and they represent shared random numbers.

(5) If there are disagreements in the shared bits, that is a sign of the existence of Eve.

So there should be two dintinct periods in their quantum communication: The one in which they check their shared data in open channel to detect Eve, and another in which data are shared assuming the absence of Eve. With proper misture of these two periods, a reliable random number sharing is achieved which is secure to the eavesdropping.

If this shared sequence of random number is used for the secret key for Caesar code, for example, Alice and Bob achieves perfect encryption which is unbreakable. This method is called "BB84 protocol" after its inventors Bennet and Brassard of Bell Laboratory of International Business Machines.