J. Miranda University of Ottawa 21 November 2003 Quantum Cryptography J. Miranda University of Ottawa 21 November 2003

Outline Background info on secure comms Description of current systems Where quantum mechanics fits in Description of BB84 protocol Conclusion -- the topic of discussion is the use of Quantum Mechanics in secure communications systems -- therefore, I’ll be giving you a brief backgrounder on secure comms systems ...

Secure Comms System block diagram for secure comms: A A Encryption Decryption -- 5 components: tx, channel, rx -- the secure part lies with the encryption and decryption boxes -- encryption accomplished by cryptography (difficult mathematical functions) -- 6th component is a most important - the key and is the focus of this presentation -- piece of information required to make it easier to decrypt the data 01101 01101 Transmitter Channel Receiver 01101

Secret-key System the same key is used to encrypt & decrypt -- two types of systems, the first is SECRET-KEY SYSTEM -- disadvantage is getting the key to the receiver how does the key get to the receiver?

Public-key System public key for encryption private key for decryption -- public-key system is a solution to the SECRET-KEY system -- two types of keys, a public key for encrypting and a private key for decrypting -- the weakness in this system is that the public-key and private-key are mathematically related; therefore, it is possible that the private key can be determined via the public key problem is that the keys are mathematically related

Quantum Key Distribution Quantum Mechanics? in both cases, there was a key-distribution problem quantum mechanics is solution Quantum Cryptography Quantum Key Distribution

Qubits states of binary bit: 1,0 states of qubit: |1>,|0> differences between bit & qubit: states of superposition examination for state determination -- a qubit stands for a quantum bit -- analogous to a binary bit -- as a binary bit can have two states (1,0) so can a qubit -- two main differences between bits and qubits -- qubits can also be in a state which is a superposition of the 1 and 0 state -- and bits can be examined to determine the state that they are in, not so for qubits -- quantum mechanics only allows certain information to be determined when examining a qubit

BB84 Protocol linear polarization (+) circular polarization (*) -- returning to quantum key distribution, how is it accomplished? -- several protocols, one of which is the BB84 protocol developed in ..., by... -- in this protocol, an encoding scheme is used to translate a binary 1 or 0 into a quantum state -- bits represented by voltage levels, qubits by polarization of photons -- BB84 protocol requires to encoding schemes to represent the bits

BB84 Protocol Public Comms Channel Quantum Channel -- describing this process requires 3 players: -- Vanessa to send a message -- Powers to receive it -- and Dr. Evil to try to intercept it

BB84 Protocol chooses random Key sequence (100111010110…) for each bit: encoding scheme corresponding state transmits to Austin Powers K bit scheme state 1 + | > * |U> -- there are 5 steps to this protocol to get a random key from Vanessa to Austin -- Step 1, Vanessa is required to generate a random bit sequence, parts of which will become the key -- Step 2 Vanessa will randomly choose an encoding scheme to represent the state of each bit of the number sequence. -- and she transmits the photons individually over the quantum communications channel to Powers

BB84 Protocol + * x photons received guess scheme record & check Vanessa Austin Check + * x photons received guess scheme record & check RAW KEY -- Step 3 is the receipt of the photons by Austin. -- randomly chooses a polarization scheme to examine the photon (by chance, he’ll have chosen some correctly) -- records his choice of alphabet for each photon. -- In Step 4 Austin contacts Vanessa over the public communications channel -- Both Vanessa and Austin then discard those photons to which Austin applied the incorrect alphabet. -- What remains is a sequence of random bits referred to as a raw key which has been transmitted securely from Vanessa to Austin. This is so because Vanessa has transmitted the photons one at a time and they cannot be split nor cloned. Additionally, any attempt at examining the photons while in transit to Austin will modify some of their properties. -- For example, measuring a linearly polarized photon with a diagonal filter will result in a 50% chance that the photon will go through, and if it does, it will have a different polarization when it reaches Austin. Dr. Evil has changed the message. Measuring a horizontally polarized photon with a vertical filter will block that photon and will not allow it to go through to Austin. Again, Dr. Evil has changed the message. This is the secure part of the protocol.

BB84 Protocol final check, reveal a portion of raw key Public Comms Channel raw key = 10111… final check, reveal a portion of raw key error correction & indication of Dr. Evil -- Step 5 is a final check, Vanessa and Austin take a sample of the raw key and over a public communications channel reveal the values that they have, to determine if there were any errors introduced by noise and Dr. Evil eavesdropping -- if the error count is below a given threshold, then what they both have is a key that can be used in a one-time pad encryption system. This key will only be used for one message and a new key will be developed for subsequent messages.

Conclusion secure communications important Quantum Key Distribution = security -- Secure communications systems are in greater demand in today’s digital world. Quantum mechanics can offer greater security in systems that currently in use via Quantum Key Distribution