Transcript Lecture

Lecture 14:
Blocking and Catching
Photons
CS551: Security and Privacy
University of Virginia
Computer Science
David Evans
http://www.cs.virginia.edu/~evans
Menu
• Visual Cryptography
– Identify your pictures
– Work in groups to think about problem on manifest
•
•
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Quantum Cryptography
Quantum Computing
Midterm Wednesday
Office Hours: Tuesday 3-4:30
– Will not answer questions about anything except
the Dumpster Document
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Visual Cryptography
• Can we quickly do a lot of XORs without
a computer?
• Yes:
Key Ciphertext
Key Ciphertext
0:
1:
.5 probability
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.5 probability
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Key + Ciphertext
Key Ciphertext
Key Ciphertext
+
+
+
+
=0
=1
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Perfect Cipher?
Plaintext
0
Key Ciphertext
Key Ciphertext
1
.5 probability
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.5 probability
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Perfect Cipher
Plaintext
0
Key Ciphertext
Key Ciphertext
1
.5 probability
.5 probability
P (C =
P (C =
| M = 0) = .5
=
| M = 1) = .5
P (C =
P (C =
| M = 0) = .5
=
| M = 1) = .5
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Yes!
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Show Demo
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Quantum Cryptography
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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
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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.
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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)
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Photon Polarity
Photons have “spin”:
V
H
+45º -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
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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
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Quantum Cash
$10000
First Photon Bank
$10000
Spinning Photons
Unique ID
258309274917392
Richard Feynman, Safecracker, Father of Quantum Computing
$10000
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In Light We Trust
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$10000
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Bank Verifies Bill
Unique ID
258309274917392
Spinning Photons
First Photon Bank
ID
…
Amount Photons
…
…
$10000
258309274917392
…
…
V-45H+45+45V
…
Bank aligns filters according to expected values. If photons on
bill 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 = .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.
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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.
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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
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Quantum Key Distribution
1. 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.
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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
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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!
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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?
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Richard Hughes, et. al.
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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…)
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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
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