QUANTUM CRYPTOGRAPHY. BCS, Plymouth University, December 1, Professor Kurt Langfeld Centre for Mathematical Sciences, Plymouth University
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1 QUANTUM CRYPTOGRAPHY BCS, Plymouth University, December 1, 2015 Professor Kurt Langfeld Centre for Mathematical Sciences, Plymouth University
2 OUTLOOK: Quantum Physics Essentials: particles and light are the same! Cryptography The 5000 year legacy From the Freemason cipher to Engima Modern cryptography Can you exchange secrets without having met? The quantum leap of mind
3 QUANTUM PHYSICS ESSENTIALS How do we describe Matter & Light? objects(electrons, light, ) theory of evolution Newton laws of mechanics: Assumption: Position & Velocity of the football Where is the football in the future?
4 Historically: We describe electrons, protons, as particles Experiment: 1-electron at a time hit the screen and light as waves: Experiment: Interference [J.D. Norten, Pittsburgh] MIT Physics]
5 Historically: Light & Matter are dferent and described by two completely dferent theories Correct (quantum) theory: Light is made of particles as well (Photons) BOTH evolve according to the same theory: probability to find the particle is a wave theory Where does Newton s theory fall short? Assumption: We can measure position AND velocity [This would explain why we can measure position and velocity of the football]
6 Experiment tells otherwise. electron source 11 electrons "one elctron at a time" TV screen 200 electrons 6,000 electrons 40,000 electrons [Dr Akira Tonomura, Hitachi] 140,000 electrons
7 Quantum Unication: Also explains the wave theory of light Photons interact VERY weakly Many photons at a time each hitting according to probability Intensity!
8 BUT: If we cannot measure position and velocity at the same time, why can we measure position and velocity of the football? Let s be precise: position of the football = centre of mass of particles velocity of the football = average velocity of particles Ehrenfest Theorem of Quantum Mechanics: Averages( expectation values ) obey the the classical laws of physics!
9 CRYPTOGRAPHY HISTORY AND IMPORTANCE Atbash Bible Code (2000 bc): reverted Hebrew alphabet Caesar Cipher (~50 ad): Roman emperor Julius Caesar, unbroken for Centuries Ludendorff Cipher (1st WW) Enigma (2nd WW) [Tony Sale, Codes and Ciphers] [Novel by Robert Harris]
10 What so have all these ciphers in common? Based upon substitution needs a key to inform the substitution Hands-on: the Freemason cipher Gravestone of James Leeson New York 1794 [Jerusalem Lodge No. 4]
11 Decoding Exercise: the Freemason Cipher Gravestone of James Leeson (died 17 Sept 1794) at the Trinity Churchyard, New York Kurt Langfeld PLAIN TEXT:
12 MODERN CRYPTOGRAPHY Modern applications: internet banking, sign electronic documents, bit coin (electronic money), encrypt an , e- health, cloud storage, Exchange of a key is VERY inconvenient Challenge: Can two parties exchange secure messages without having met before? Yes! public key cryptography!
13 RSA - How does it work? Door with a strange lock: two dferent keys One key locks the door Only the OTHER key unlocks the door Bob prepares himself to receive an encrypted message leaves the door open puts ONE key beside the door [public key]
14 Alice wants to send Bob a message that only Bob can read Bob finds his door locked [only he can open it!] Alice is sure that only Bob reads her message Application: Internet Banking
15 Who invented Public Key Cryptography? GCHQ (early 70s): Ellis, Cocks, Williamson (disclosed until 1997) MIT (1997): Rivest, Shamir, Adleman RSA standard What Mathematics is involved? Unlocking a door without the Other key Factorising a prime number but that is easy: 21 = 7 x 3 Can we now break into the Bank of England from the sofa in the living room?
16 What about this number? [200 digits, only 2 factors] Standard Algorithm: 55 years on a 2.2 GhZ Opteron CPU and the winners are: and
17 4,000 years the same idea: substitution ciphers with key Since 1970: Public Key Cryptography, exchange of secret messages with a person who you never met before! approx. 2000: Quantum Cryptography Can we exchange a secret message without encrypting it at all?
18 QUANTUM CRYPTOGRAPHY Photons come in (polarization) states : How do we make photons with a specic polarization? use polarization filters
19 How do we detect photons? use polarization filters again! What the filter is skewed? Either state is equally probable! The information of the original state cannot be recovered!
20 Now, let us encode information:
21 Alice wants to exchange a secret key with Bob and Eve tries to intercept the key Alice prepares a random filter setting and transmits a random bit sequence Remember:
22 Bob prepares a random filter setting and receives: Remember
23 After exchanging the photons, Bob and Alice openly talk about their filter settings The agreed key is: 011. Hands on!
24 Step 1 on the handout: Bob: Step 1: Step 2: a random filter setting; use construct the signal or or or or or
25 Alice: Step 2 on the handout: Alice s bit sequence (signal) Bob: Step 1: Step 2: a random filter setting; use construct the signal or or or or or
26 Alice: Step 3 & 4 on handout: Bob: Step 1: Step 2: Alice s bit sequence (signal) etc a random filter setting; use construct the signal etc or or or or or Step 3: Step 4: copy the signale for all filter settings that match 0 0 etc translate the signal into bi ary code
27 Bob and Alice can unambiguously exchange a key, but can Eve intercept the key? Eve must a filter orientation for detection Eve s randomly chosen filter 50% of the photons are sent to Bob with the wrong information!
28 Alice and Bob can easily detect this by exchanging a checksum Alternatively, Eve could overhear the filter settings, but she would not get the photons anymore! The secret key is openly transmitted Alice and Bob are sure that nobody else has the key!
29 CHANGE OF PARADIGM: 2000 bc - WWII (Enigma): need to meet for key exchange : phone books of public keys; use private key to unlock messages Security hinges on a Maths problem! Since 2000: Open key exchange, but nobody eavesdropped! Guaranteed by the laws of nature (quantum physics)!
30 CHANGE OF PARADIGM: 2000 bc - WWII (Enigma): need to meet for key exchange : phone books of public keys; use private key to unlock messages Security hinges on a Maths problem! Since 2000: Open key exchange, but nobody eavesdropped! Guaranteed by the laws of nature (quantum physics)! Thank you!
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slides available for download at: www.math.cm.is.nagoya-u.ac.jp/~buscemi/crypto.pdf Introduction to Cryptography from ancient ciphers to quantum cryptography ブシェーミ F( 計算機数理科学専攻 )buscemi@is.nagoya-u.ac.jp