David Evanshttp://www.cs.virginia.edu/~evans
CS551: Security and PrivacyUniversity of VirginiaComputer Science
Lecture 14:Blocking and Catching Photons
April 22, 2023 University of Virginia CS 551 2
Menu
• Visual Cryptography– Identify your pictures– Work in groups to think about problem on manifest
• Quantum Cryptography• Quantum Computing• Midterm Wednesday• Office Hours: Tuesday 3-4:30
– Will not answer questions about anything except the Dumpster Document
April 22, 2023 University of Virginia CS 551 3
Visual Cryptography
• Can we quickly do a lot of XORs without a computer?
• Yes:
0:
1:
Key Ciphertext Key Ciphertext
.5 probability .5 probability
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Key + Ciphertext Key Ciphertext Key Ciphertext
+ +
+ +
= 0
= 1
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Perfect Cipher? Key Ciphertext Key Ciphertext
.5 probability .5 probability
Plaintext0
1
April 22, 2023 University of Virginia CS 551 6
Perfect Cipher Key Ciphertext Key Ciphertext
.5 probability .5 probability
Plaintext0
1
P (C = | M = 0) = .5 P (C = | M = 1) = .5
P (C = | M = 0) = .5 P (C = | M = 1) = .5
Yes!=
=
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Show Demo
April 22, 2023 University of Virginia CS 551 8
Quantum Cryptography
April 22, 2023 University of Virginia CS 551 9
Quantum Physics for Dummies
• Light behaves like both a wave and a particle at the same time
• A single photon is in many states at once• Can’t observe its state without forcing it into
one state• Schrödinger’s Cat
– Put a live cat in a box with cyanide vial that opens depending on quantum state
– Cat is both dead and alive at the same time until you open the box
April 22, 2023 University of Virginia CS 551 10
Heisenberg’s Uncertainty Principle
“We cannot know, as a matter of principle, the present in all its details.”
Werner Heisenberg, 1920sIf you can’t know all the details about something you can’t copy it.Bits are easy to copy; photons are impossible to copy.
April 22, 2023 University of Virginia CS 551 11
Quantum Cash
Stephen Wiesner, late 60s:“I didn’t get any support from my thesis advisor – he showed no interest in it at all. I showed it to several other people, and they all pulled a strange face, and went straight back to what they were already doing.”
(Quoted in Singh, The Code Book)
April 22, 2023 University of Virginia CS 551 12
Photons have “spin”:
V H +45º -45º
Photon Polarity
Vertical filter:100% of V photons 50% of +45º photons (become V photons) 50% of -45º photons (become V photons) 0% of H photonsHorizontal filter:100% of H photons 50% of +45º photons (become H photons) 50% of -45º photons (become H photons) 0% of V photons
April 22, 2023 University of Virginia CS 551 13
Photon Stream
Vertical filter:100% of V photons 50% of +45º photons (become V photons) 50% of -45º photons (become V photons) 0% of H photons
Can’t tell differencebetween V and +45ºand –45º photons
April 22, 2023 University of Virginia CS 551 14
Quantum Cash
First Photon Bank
$10000
$10000
$10000
$10000
In Light We Trust
Unique ID258309274917392
Spinning Photons
Richard Feynman, Safecracker, Father of Quantum Computing
April 22, 2023 University of Virginia CS 551 15
Bank Verifies Bill
Unique ID258309274917392
Spinning Photons
First Photon BankID Amount Photons… … …258309274917392 $10000 V-45H+45+45V
… … …
Bank aligns filters according to expected values. If photons onbill all pass through filters, the bill is valid.
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Counterfeiting Quantum Cash• To copy a bill, need to know the
photons.• Counterfeiter can guess, but loses
information. Physics says there is no way to measure the spins without knowing them!
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Perfect Security?• Bill photons: V (¼), +45 (¼), -45 (¼), H (¼)• Guess V-filter: passes 100% of V photons, ½ of
+45 and ½ of -45– p (M = V | passes V filter) =
.25 / (.25 + (.5 * .25) + (.5 * .25)) = .25/.5 = .5If photon passes, counterfeiter can guess it is a V photon, right ½ of the time. If photon doesn’t pass, guess it’s a H photon, right ½ of the time.
– p (M = +45 | passes V filter) = .25• Actually a bit more complicated – can guess
some photons wrong, and 50% chance bank won’t notice.
April 22, 2023 University of Virginia CS 551 18
Guessing One +45º Photon• Passes through V-filter (.5)
– Counterfeiter guesses V-photon– Passes through Banks +45 filter (.5)– .25 chance of getting it right
• Doesn’t passes through V-filter (.5)– Counterfeiter guesses H-photon– Passes through Banks +45 filter (.5)– .25 chance of getting it right
• Probability of not getting caught = .5• Forge bill with 6 photons = 1/26; use more
photons for more valuable bills.
April 22, 2023 University of Virginia CS 551 19
Quantum Key Distribution• Charles Bennett (1980s)• Use quantum physics to transmit a key with
perfect secrecy• Alice sends a stream of random photons• Bob selects random filters to try and guess
photons• After, they communicate over insecure
channel to figure out which bits were transmitted correctly
April 22, 2023 University of Virginia CS 551 20
Quantum Key Distribution1. Alice generates a random sequence.
Transmits:0: or (Randomly pick H or –45)
1: or (Randomly pick V or +45)2. Bob randomly guesses filter:
Rectilinear detector: recognizes H and V photons with 100% accuracy, randomly misrecognizes diagonal photons.
Diagonal detector: recognizes -45 and +45 photons with 100% accuracy, randomly misrecognizes H and V photons.
April 22, 2023 University of Virginia CS 551 21
Detecting Photons
• Bob picks the right detector:– 100% chance of correctly recognizing bit
• Bob picks the wrong detector:– 50% chance of “guessing” bit
• Bob can’t tell the difference• But, Alice can (since she picked the
photon encoding)
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Finding Correct Guesses
3. Alice calls Bob over an insecure line, and tell him rectangular/diagonal for each bit. Bob tells Alice if he guessed right. They use the bits he guessed right on as the key.
4. Alice and Bob do some error checking (e.g., use a checksum) to make sure they have the same key.
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What about Eve?• Eve can intercept the photon stream,
and guess filters.• If she guesses right, she can resend
the same photon.• If she guesses wrong, 50% chance
she will send the wrong photon.• 50% chance Bob will guess the right
filter on this photon, so 25% chance of error
April 22, 2023 University of Virginia CS 551 24
Eve is Caught• When Alice and Bob agree on
which bits to use, Eve will have the wrong ones since she guesses different polarities.
• Eve cannot eavesdrop without Alice and Bob noticing an unusually high error rate!
April 22, 2023 University of Virginia CS 551 25
Practical Quantum Cryptography
• This may seem wacky and crazy, but it is real!
• Los Alamos LabBob’s photondetector
Alice’s photontransmitter
48 km fiber-optic wire loop
Richard Hughes, et. al.What about quantum cash?
April 22, 2023 University of Virginia CS 551 26
April 22, 2023 University of Virginia CS 551 27
Though Air• Can transmit and recognize spinning photons
through normal atmosphere!• Los Alamos group has demonstrated quantum
key distribution over 0.5km in daylight• Depends on sending laser pulse before photon
to obtain nano-second timing• Perhaps possible to send keys to satellites this
way
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What’s in the “Sneakers” Black Box?
A Quantum Computer
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Quantum Computing• Feynman, 1982• David Deustch, 1985 – design for general
purpose quantum computer• Quantum particles are in all possible states• Can try lots of possible computations at once with
the same particles• In theory, can test all possible
factorizations/keys/paths/etc. and get the right one!
• In practice, major advances required before we can build it (unless the NSA knows something we don’t…)
April 22, 2023 University of Virginia CS 551 30
Summary/Charge
• We can really use quantum physics to distribute keys with perfect secrecy!
• People with a lot of resources may (someday?) be able to use quantum physics to factor quickly
• Next time: Midterm– Don’t forget to bring you book/notes