David Evans evans

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

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• 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


Visual Cryptography

• Can we quickly do a lot of XORs without a computer?

• Yes:

0:

1:

Key Ciphertext Key Ciphertext

.5 probability .5 probability


Key + Ciphertext Key Ciphertext Key Ciphertext

+ +

+ +

= 0

= 1


Perfect Cipher? Key Ciphertext Key Ciphertext


Plaintext0

1


Perfect Cipher Key Ciphertext Key Ciphertext


Plaintext0

1

P (C = | M = 0) = .5 P (C = | M = 1) = .5

P (C = | M = 0) = .5 P (C = | M = 1) = .5

Yes!=

=


Show Demo


Quantum Cryptography


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


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.


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)


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


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


Quantum Cash

First Photon Bank

$10000

$10000

$10000

$10000

In Light We Trust

Unique ID258309274917392

Spinning Photons

Richard Feynman, Safecracker, Father of Quantum Computing


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.


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!


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.


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.


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


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.


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)


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.


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


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!


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?



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


What’s in the “Sneakers” Black Box?

A Quantum Computer


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…)


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

David Evans evans

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