1. David Evans http://www.cs.virginia.edu/~evans
Lecture 14:
Blocking and Catching Photons
Background
just got here last week
finished degree at MIT week before
Philosophy of advising students
don’t come to grad school to implement someone else’s idea
can get paid more to do that in industry
learn to be a researcher
important part of that is deciding what problems and ideas are worth spending time on
grad students should have their own project
looking for students who can come up with their own ideas for research
will take good students interested in things I’m interested in – systems, programming languages & compilers, security
rest of talk – give you a flavor of the kinds of things I am interested in
meant to give you ideas (hopefully even inspiration!) but not meant to suggest what you should work on
CS551: Security and Privacy
University of Virginia
Computer Science
David Evans

2. University of Virginia CS 551
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
9 December 2018
University of Virginia CS 551

3. University of Virginia CS 551
Visual Cryptography
Can we quickly do a lot of XORs without a computer?
Yes: 0: 1:
Key Ciphertext
Key Ciphertext
.5 probability
.5 probability
9 December 2018
University of Virginia CS 551

4. University of Virginia CS 551
Key + Ciphertext
Key Ciphertext
Key Ciphertext + +
= 0 + +
= 1
9 December 2018
University of Virginia CS 551

5. University of Virginia CS 551
Perfect Cipher?
Key Ciphertext
Key Ciphertext
Plaintext 1
.5 probability
.5 probability
9 December 2018
University of Virginia CS 551

6. University of Virginia CS 551
Perfect Cipher
Key Ciphertext
Key Ciphertext
Plaintext 1
.5 probability
.5 probability
P (C = | M = 0) = .5
P (C = | M = 1) = .5 =
Yes!
P (C = | M = 0) = .5
P (C = | M = 1) = .5 =
9 December 2018
University of Virginia CS 551

7. University of Virginia CS 551
Show Demo
9 December 2018
University of Virginia CS 551

8. University of Virginia CS 551
Quantum Cryptography
9 December 2018
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
9 December 2018
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, 1920s
If you can’t know all the details about something you can’t copy it.
Bits are easy to copy; photons are impossible to copy.
9 December 2018
University of Virginia CS 551

11. University of Virginia CS 551
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)
9 December 2018
University of Virginia CS 551

12. University of Virginia CS 551
Photon Polarity
Photons have “spin”:
V H º -45º
Vertical filter:
100% of V photons
50% of +45º photons (become V photons)
50% of -45º photons (become V photons)
0% of H photons
Horizontal filter:
100% of H photons
50% of +45º photons (become H photons)
50% of -45º photons (become H photons)
0% of V photons
9 December 2018
University of Virginia CS 551

13. University of Virginia CS 551
Photon Stream
Can’t tell difference
between V and +45º
and –45º photons
Vertical filter:
100% of V photons
50% of +45º photons (become V photons)
50% of -45º photons (become V photons)
0% of H photons
9 December 2018
University of Virginia CS 551

14. University of Virginia CS 551
Quantum Cash
$10000
First Photon Bank
$10000
Spinning Photons
Unique ID
Richard Feynman, Safecracker, Father of Quantum Computing
In Light We Trust
$10000
$10000
9 December 2018
University of Virginia CS 551

15. University of Virginia CS 551
Bank Verifies Bill
First Photon Bank
Unique ID ID
Amount
Photons …
$10000
V-45H+45+45V
Spinning Photons
Bank aligns filters according to expected values. If photons on
bill all pass through filters, the bill is valid.
9 December 2018
University of Virginia CS 551

16. 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!
9 December 2018
University of Virginia CS 551

17. University of Virginia CS 551
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 = .5
If 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.
9 December 2018
University of Virginia CS 551

18. University of Virginia CS 551
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
Probability of not getting caught = .5
Forge bill with 6 photons = 1/26; use more photons for more valuable bills.
9 December 2018
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
9 December 2018
University of Virginia CS 551

20. Quantum Key Distribution
Alice generates a random sequence. Transmits:
0: or (Randomly pick H or –45)
1: or (Randomly pick V or +45)
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.
9 December 2018
University of Virginia CS 551

21. University of Virginia CS 551
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)
9 December 2018
University of Virginia CS 551

22. Finding Correct Guesses
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.
Alice and Bob do some error checking (e.g., use a checksum) to make sure they have the same key.
9 December 2018
University of Virginia CS 551

23. University of Virginia CS 551
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
9 December 2018
University of Virginia CS 551

24. University of Virginia CS 551
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!
9 December 2018
University of Virginia CS 551

25. Practical Quantum Cryptography
This may seem wacky and crazy, but it is real!
Los Alamos Lab
Bob’s photon
detector
48 km fiber-optic wire loop
Alice’s photon
transmitter
What about quantum cash?
Richard Hughes, et. al.
9 December 2018
University of Virginia CS 551

26. University of Virginia CS 551
9 December 2018
University of Virginia CS 551

27. University of Virginia CS 551
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
9 December 2018
University of Virginia CS 551

28. What’s in the “Sneakers” Black Box?
A Quantum Computer
9 December 2018
University of Virginia CS 551

29. University of Virginia CS 551
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…)
9 December 2018
University of Virginia CS 551

30. University of Virginia CS 551
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
9 December 2018
University of Virginia CS 551