+ = OTP + QKD = QC. ψ = a. OTP One-Time Pad QKD Quantum Key Distribution QC Quantum Cryptography. θ = 135 o state 1

Transcription

1 Quantum Cryptography Quantum Cryptography Presented by: Shubhra Mittal Instructor: Dr. Stefan Robila Intranet & Internet Security (CMPT-585-) Fall 28 Montclair State University, New Jersey Introduction Deficiencies of classical cryptography Solution: Quantum Cryptography Fundamentals of Quantum Cryptography Quantum Key Distribution (QKD) BB84 without eavesdropping BB84 with eavesdropping Implementation Summary Introduction Deficiencies of Classical Cryptography Quantum cryptography is the single most successful application of Quantum Computing/Information theory. For the first time in history, we can use the forces of nature to implement perfectly secure cryptosystems. Quantum cryptography has been tried experimentally: it works! Distribution of the key is the main problem with classical cryptography. An eavesdropper can passively snoop secret key as its been exchanged. Security relies on unproven mathematical assumptions such as difficulty of factoring last integers. A quantum computer can easily crake all possible classical cryptographic solutions. Classical cryptographic is vulnerable to quantum attacks.

2 Solution: Quantum Cryptography + = OTP + QKD = QC OTP One-Time Pad QKD Quantum Key Distribution QC Quantum Cryptography Concepts of the Quantum Mechanics Light waves are propagated as discrete quanta called photons. They are mass less and have energy, momentum and angular momentum called spin. Spin carries the polarization. If on its way we put a polarization filter, a photon may pass through it or may not. We can use a detector to check of a photon has passed through a filter. Concepts of the Quantum Mechanics Polarization Measurement Measuring a quantum system will alter its state. Example: the Qubit. When observed, the state of a qubit will collapse to either a= or b=. s A photon is an electromagnetic wave. Polarization A photon has a property called polarization, which is the plane in which the electric field oscillates. We can use photons of different polarizations to represent quantum states. ψ = a + b o θ = state o θ = 9 state The polarization basis is the mapping to decide to use for a particular state. Rectilinear : (,) ( o, 9 o ) θ = o state θ = 9 o state Diagonal : (,) (45 o, 35 o ) θ = 45 o state θ = 35 o state

3 Measurement in the Same Measurement in Different Measurement in the same basis does not change the state. Quantum Key Distribution & Protocols Quantum Key Distribution exploits the effects discussed in order to thwart eavesdropping. If an eavesdropper uses the wrong polarization basis to measure the channel, the result of the measurement will be random. QKD Protocols A protocol is a set of rules governing the exchange of message over a channel. There are three main quantum protocols.. BB84 By C. H. Bennett and G. Brassard (984) 2. Entanglement Based QKD proposed by A. K. Ekert (99) 3. B92 Proposed by C. H. Bennett (992) Meet Alice and Bob We have to prevent Eve from eavesdropping on communications between Alice and Bob. Alice Eve Bob

4 BB84 Protocol BB84 was the first security protocol implementing QKD (Quantum Key Distribution). It uses the idea of photon polarization. The Key consists of bits that will be transmitted as photons. Each bit is encoded with a random polarization basis. BB84 Without Eavesdropping (Step-) Alice Select random sequence of bits(,). Alice encoded selected bits with random basis(+, x). Bit BB84 Without Eavesdropping (Step-2) Bob receives the photons and must decode them using a random basis. Bit Some of Bob s basis and resulting bits are correct. BB84 Without Eavesdropping (Step-3) Alice and Bob talk on the telephone: Alice chooses a subset of the bits (the test bits) ) and reveals which basis she used to encode them to Bob. Bob tells Alice which basis he used to decode the same bits. Where the same basis was used, Alice tells Bob what bits he ought to have got. Alice s Bit Alice s Bob s Bob s Bit Test bits The test bits allow Alice and Bob to test whether the channel is secure.

5 BB84 Without Eavesdropping (Step-4) Test bits are removed. Alice tells Bob the basis used for other bits. They agree on common set of bits. Alice s Bit Alice s BB84 With Eavesdropping = / Alice s Bit Alice s Eve s Eve s Bit Bob s Bob s Bob s Bit Test bits Final Key = Bob s Bit Eve s presence can be detected with 2nd bit, where Alice and Bob use the same basis but get different results. After discussion, they discard 3rd and 4th bit. Now Alice and Bob have common set of bits and this final set of bits is the final key. How it works!... How it works! Source:

6 Implementations As of March 27 the longest distance over which quantum key distribution has been demonstrated using optic fibre is 48.7 km, achieved by Los Alamos/NIST using the BB84 protocol. The DARPA Quantum Network, a -node quantum cryptography network, has been running since 24 in Massachusetts, USA. It is being developed by BBN Technologies, Harvard University, Boston University, and QinetiQ. Three companies offering commercial quantum cryptography systems; id Quantique (Geneva), MagiQ Technologies (New York), SmartQuantum (France). Quantum encryption technology provided by the Swiss company id Quantique was used in the Swiss canton (state) of Geneva to transmit ballot results to the capitol in the national election occurring on Oct. 2, 27. The world's first computer network protected by quantum cryptography was implemented in October 28, at a scientific conference in Vienna. Summary Quantum cryptography is a major achievement in security engineering. Quantum cryptography, also known as quantum key distribution, allows us to send encrypted messages the secrecy of which can be guaranteed by allowing an eavesdropper to be detected. Secure messages have been sent over distances in excess of km using quantum cryptography with photons carried by optical fibres. As it gets implemented, it will allow perfectly secure bank transactions, secret discussions for government officials, and well-guarded trade secrets for industry! The next step will be to establish a "quantum network" that could allow quantum cryptography to cover cities and eventually the globe.