Quantum Cryptography - Quantum Coin Tossing
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Based on Research paper by Brazzard 1982.
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Quantum Cryptography - Quantum Coin Tossing
- 1. Quantum cryptography :Public key distribution and coin tossing Research : Charles H. Bennett & Gilles Brassard Present by : Ruwan Ranganath Senarathne
- 2. Outline Quantum Cryptography Essential properties of polarized photons Quantum public key distribution Quantum coin tossing BB84 Protocol Q & A
- 4. Cryptography • The Art of Writing or Solving Codes. • Classical Cryptography > Modern Cryptography > Number Theory based Public Key Cryptography • One Time Pad • Key Generation and Key Distribution
- 5. Background ● Conventional cryptosystems such as ENIGMA, DES, RSA ● Digital communications in principle can always be passively monitored or copied ● Unless the key,used once only and long as clear text ● Computational complexity is not well enough understood ● Quantum Computers can use Shor’ Algorithm to break
- 6. Quantum cryptography uses photons to transmit a key. Quantum cryptology depends on physics, not mathematics. Heisenberg's Uncertainty Principle & Photon Polarization Quantum key distribution protocols Quantum Cryptography QC = QKD + OTP
- 7. Background ● Conventional Computing - Bits ● Quantum Computing – Quantum Bits or Qubits (/ kju b t/)ˈ ː ɪ ● Qubit could be a Photon, Electron, Nucleus.. ● In a Quantum State particle can achieve a “Superposition” ● Quantum Computers can overcome todays computational limitations
- 8. Essential properties of polarized photons • Photons - Photons are the fundamental particle of light. – wave function : An individual photon can be described as having right or left circular polarization, or a superposition of the two. • The foundation of quantum physics is the unpredictability factor. – Heisenberg's Uncertainty Principle : • Photon polarization – polarization filters, photon to take one state or another -- or polarize it. • Rectilinear basis (0 and 90 degrees) • Diagonal basis (45 and 135 degrees)
- 9. • Heisenberg uncertainty principle : - states that certain pairs of physical properties are related in such a way that measuring one property prevents the observer from simultaneously knowing the value for other. • Principle of photon polarization: - tells that an eavesdropper cannot copy unknown Qubits Explanation
- 11. QKD Protocols • A protocol is a set of rules governing the exchange of messages over a channel. • A security protocol is a special protocol designed to ensure security properties are met during communications. • There are three main security protocols for QKD:BB84, B92, and Entanglement-Based QKD.
- 12. Eve • Unique property gain knowledge about eve trying get the key • By using quantum superposition/entanglement and transmitting information in quantum states , a communication system can be implemented which can detect eavesdropping. • If the level of eavesdropping is below threshold , a key is produced guarantying the secure communication otherwise no secure key is possible and communication is aborted
- 13. BB84 Communication Protocol ● BB84 is a quantum key distribution scheme developed by Charles Bennett and Gilles Brassard in 1984. ● It is the first quantum cryptography protocol ● Use Photon polarization ● four different non-orthogonal quantum states via a quantum channel to transmit the qubits ● A device called a polarizer allows us to place a photon in a particular polarization. A Pockels Cell can be used too. ● The polarization basis is the mapping we decide to use for a particular state
- 16. ● Let us suppose she uses the vertical and the +45 o polarisations for encoding the 0" and the horizontal and -45 o polarisations to encode the 1" ● Bob then randomly uses either a polarizer for diagonal polarisations or one in the horizontal/vertical basis and records his choice and the polarization he measures ● Bob tells Alice on the public channel the sequence of analyzers he used during the transmission, but not his results ● Alice compares Bob's sequence with hers and tells him which bits correspond to the photons she sent ● these compatible bits are used for the shared key
- 17. BB84 with eavesdropping • If an eavesdropper Eve tries to tap the channel, this will automatically show up in Bob’s measurements. • In those cases where Alice and Bob have used the same basis, Bob is likely to obtain an incorrect measurement: Eve’s measurements are bound to affect the states of the photons. • As Eve intercepts Alice’s photons, she has to measure them with a random basis and send new photons to Bob.` • The photon states cannot be cloned (non-clone ability). • Eve’s presence is always detected: measuring a quantum system irreparably alters its state.
- 18. Quantum coin tossing ➔ First discussed ‘Coin Flipping by Telephone’ by Manuel Blum, 1983 ➔ Two unknown party communicate without third party
- 19. Quantum coin tossing ( cont>._)
- 20. Coin Tossing (Cont>._) ● Alice choose random basis ( Rectilinear ) and sequece of random bits ( 1000 should be enough ) . ● Use the polarization and send to Bob ● Bob use polarizer for each bit ● Two tables Rectilinear and diagonal photon table ● Polarizer can loss some photons ● Bob Make his guess ● Alice says if bob wins and tell her basis and ● Send entire bit sequece over classical channel ● Bob verify no cheating by providing his tables
- 21. Current Arguments QKD is not Public key Cryptography Eve can sabotage quantum channel to force Alice and Bob use classical channel Expensive for longer keys
- 22. Thank you.
Notas del editor
- “the coding and decoding of secret messages.” The basic idea is to modify a message so as to make it unintelligible to anyone but the intended recipient. Cryptosystem (Cipher System) – method of disguising messages so that only certain people can read them Cryptography – Art of creating and using Cryptosystems Cryptanalysis – Art of breaking Cryptosystems Cryptology – study of Cryptography and Cryptosystems
- based on a mixture of guesswork and mathematics relies heavily on the complexity of factoring integers To prove the computation security of public key cryptosystem
- Via quantum channel to transmit the bits of Alice's random key
- In a Quantum State particle can achieve a “Superposition” – Its Exist in multiple ways simultaneously
- It's impossible to know both an object's position and velocity -- at the same time. Through the use of polarization filters, we can force the photon to take one state or another -- or polarize it.
- due to non-cloning algorithm.
- • We will only discuss BB84 here.
- • Unique property of quantum cryptography is the ability of two communicating users to detect the presence of third party trying to gain knowledge of the key.
- Let us suppose she uses the vertical and the +45 o polarisations for encoding the \0" and the horizontal and -45 o polarisations to encode the \1" bob then randomly uses either a polarizer for diagonal polarisations or one in the horizontal/vertical basis and records his choice and the polarization he measures (Fig. 1 and Table I). The probability of using the wrong analyzer and therefore obtaining a random result is 50%
- horizontal and -45 o polarisations to encode the \1" Bob then randomly uses either a polarizer for diagonal polarisations or one in the horizontal/vertical basis and records his choice and the polarization he measures Bob tells Alice on the public channel the sequence of analyzers he used during the transmission, but not his results Alice compares Bob's sequence with hers and tells him which bits correspond to the photons she sent these compatible bits are used for the shared key
- come to agree on a winner and a loser in such a way that each party has exactly 50 percent chance of winning
- Alice choose random basis ( Rectilinear ) and sequence of random bits ( 1000 should be enough ) . Use the polarization and send to Bob Bob use polarizer for each bit Two tables Rectiliear and diagonal photon table Polarizer can loss some photons Bob Make his guess Alice says if bob wins and tell her basis and Send entire bit sequece over classical channel Bob verify no cheating by providing his tables Alice Cheating If cheat on step 3 , she need to say diagonal, bobs table probabilistic behavior of the photons after they left her hands If cheat on step 1 , Sending mixture of diagonal and rectilinear , or polarized neither both basis , she will not be able to agree bobs out put. Bob to cheat - Bob would need to guess Alice’s basis with probability greater than 1 / 2.
- Alice Cheating If cheat on step 3 , she need to say diagonal, bobs table probabilistic behavior of the photons after they left her hands If cheat on step 1 , Sending mixture of diagonal and rectilinear , or polarized neither both basis , she will not be able to agree bobs out put.