Quantum Quantum CryptographyCryptographyCryptographyCryptographyPresented by: Shubhra MittalPresented by: Shubhra MittalInstructor: Dr. Stefan RobilaInstructor: Dr. Stefan RobilaIntranet & Internet Security (CMPTIntranet & Internet Security (CMPT--585585--01)01)Fall 2008Fall 2008Montclair State University, New JerseyMontclair State University, New JerseyQuantum CryptographyQuantum Cryptography IntroductionIntroduction Deficiencies of classical cryptographyDeficiencies of classical cryptography Solution: Quantum CryptographySolution: Quantum Cryptography Fundamentals of Quantum CryptographyFundamentals of Quantum CryptographyQuantum Key Distribution (QKD)Quantum Key Distribution (QKD)Quantum Key Distribution (QKD)Quantum Key Distribution (QKD) BB84 without eavesdroppingBB84 without eavesdropping BB84 with eavesdroppingBB84 with eavesdropping ImplementationImplementation SummarySummaryIntroductionIntroduction Quantum cryptography is the single Quantum cryptography is the single most successful applicationmost successful applicationof of Quantum Computing/Information Quantum Computing/Information theory.theory. For the first time in history, we can For the first time in history, we can use the forces of nature to implement use the forces of nature to implement use the forces of nature to implement use the forces of nature to implement perfectly secureperfectly secure cryptosystems.cryptosystems. Quantum cryptography has been tried Quantum cryptography has been tried experimentally: experimentally: it worksit works!!Deficiencies of Classical CryptographyDeficiencies of Classical Cryptography Distribution of the key is the main problem with classical Distribution of the key is the main problem with classical cryptography.cryptography. An eavesdropper can passively snoop secret key as its An eavesdropper can passively snoop secret key as its been exchanged.been exchanged.Security relies on unproven mathematical assumptions Security relies on unproven mathematical assumptions such as difficulty of factoring last integers.such as difficulty of factoring last integers.Security relies on unproven mathematical assumptions Security relies on unproven mathematical assumptions such as difficulty of factoring last integers.such as difficulty of factoring last integers. A quantum computer can easily crake all possible A quantum computer can easily crake all possible classical cryptographic solutions.classical cryptographic solutions. Classical cryptographic is vulnerable to quantum Classical cryptographic is vulnerable to quantum attacks.attacks.Solution: Quantum CryptographySolution: Quantum Cryptography+ =OTP + QKD = QCOTP – One-Time PadQKD – Quantum Key DistributionQC – Quantum CryptographyConcepts of the Quantum Mechanics…Concepts of the Quantum Mechanics… Light waves are propagated as discrete quanta called Light waves are propagated as discrete quanta called photons.photons. They are mass less and have energy, momentum and They are mass less and have energy, momentum and angular momentum called spin.angular momentum called spin.Spin carries the polarization.Spin carries the polarization.Spin carries the polarization.Spin carries the polarization. If on its way we put a polarization filter, a photon may If on its way we put a polarization filter, a photon may pass through it or may not.pass through it or may not. We can use a detector to check of a photon has passed We can use a detector to check of a photon has passed through a filter.through a filter.Concepts of the Quantum MechanicsConcepts of the Quantum Mechanics MeasurementMeasurement MeasuringMeasuring a quantum system will alter a quantum system will alter its state. Example: the its state. Example: the Qubit.Qubit. When observed, the state of a qubit will When observed, the state of a qubit will collapsecollapse to either to either a=0a=0 or or b=0b=0..ψ = ⋅ + ⋅0 1a bθ = ⇒′θ = ⇒oo0 state 090 state 1 PhotonsPhotons A photon is an electromagnetic wave.A photon is an electromagnetic wave. PolarizationPolarization A photon has a property called polarization, A photon has a property called polarization, which is the plane in which the electric field which is the plane in which the electric field oscillates.oscillates. We can use photons of different We can use photons of different polarizations to represent quantum states.polarizations to represent quantum states.Polarization BasisPolarization BasisThe polarization basis is the mapping to decide to use The polarization basis is the mapping to decide to use for a particular state.for a particular state. Rectilinear BasisRectilinear Basis: (0,1) : (0,1)  (0(0oo, 90, 90oo))θθ= = 00oo state | 0state | 0〉〉θθ= = 00 state | 0state | 0〉〉θθ = 90= 90o o state | 1state | 1〉〉 Diagonal BasisDiagonal Basis: : (0,1) (0,1)  (45(45oo, 135, 135oo))θθ = 45= 45oo state | 0state | 0〉〉θθ = 135= 135o o state | 1state | 1〉〉Measurement in the Same BasisMeasurement in the Same Basis0 0   001 1 111 1 110 0   001 1  1 1 Measurement in the same basis does not change the state.Measurement in Different BasisMeasurement in Different Basis00110010100 1101Quantum Key Distribution & ProtocolsQuantum Key Distribution & Protocols Quantum Key Distribution exploits the effects Quantum Key Distribution exploits the effects discussed in order to thwart eavesdropping.discussed in order to thwart eavesdropping.If an eavesdropper uses the wrong polarization basis to If an eavesdropper uses the wrong polarization basis to measure the channel, the result of the measurement will measure the channel, the result of the measurement will be random.be random. QKD ProtocolsQKD Protocols A protocol is a set of rules governing the exchange of A protocol is a set of rules governing the exchange of message over a channel.message over a channel. There are three main quantum protocols. There are three main quantum protocols. 1.1. BB84 By C. H. Bennett and G. Brassard (1984)BB84 By C. H. Bennett