28 April 200528 April 2005CS588 Spring 2005CS588 Spring 2005

David EvansDavid Evanshttp://www.cs.virginia.edu/evanshttp://www.cs.virginia.edu/evans

Phun with Phun with PhotonsPhotons

2CS588 Lecture 22

Menu

• Visual Cryptography• Quantum Cryptography• Quantum Computing (very briefly)

• Cryptographic Hashing Attacks– Boyd and Isabelle

3CS588 Lecture 22

Visual Cryptography

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

• Yes:

0:

1:

Key Ciphertext Key Ciphertext

.5 probability .5 probability

4CS588 Lecture 22

Key + Ciphertext

Key Ciphertext Key Ciphertext

+ +

+ +

= 0

= 1

5CS588 Lecture 22

Perfect Cipher? Key Ciphertext Key Ciphertext

.5 probability .5 probability

Plaintext0

1

6CS588 Lecture 22

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!=

=

7CS588 Lecture 22

Authentication for remote voting

• Remote voting offers convenience – 69% votes cast by mail in 2001 in state of

Washington• Electronic voting is cheaper and faster

– More secure?– New problems: virus, worm, spoofing, denial

of service• Mutual authentication

– Voter authenticated to server– Server authenticated to voter

Nathanael Paul, David Evans, Avi Rubin and Dan Wallach. Workshop on Human-Computer Interaction and Security Systems. 6 April 2003 http://www.cs.virginia.edu/evans/pubs/remote-voting.html

8CS588 Lecture 22

Doing Encryption without Computers

• Can’t trust voters to have trustworthy computers– Viruses can tamper with their software

• Need to do authentication in a way that doesn’t depend on correctness of user’s software

• Lorenz cipher: use XOR to encrypt– Is there a way to do lots of XOR’s

without a computer?

9CS588 Lecture 22

Remote Voting System

Ek (k1)

Ek(kn)

Ek(k2)

… …

STEP 1 keys

ki

S

ki = “AQEGSDFASDF”

S

STEP 2STEP 3 – if ki valid… STEP 4

Key: AQEGSDFASDF

ki =

client machine client machine

Each voter is sent a key, ki

10CS588 Lecture 22

Authentication by

Transparency

11CS588 Lecture 22

Quantum Cryptography

12CS588 Lecture 22

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

13CS588 Lecture 22

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.

14CS588 Lecture 22

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)

15CS588 Lecture 22

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

16CS588 Lecture 22

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

17CS588 Lecture 22

Quantum CashUncertainty Principal BankUncertainty Principal Bank

$10000$10000

$10000$10000

$10000$10000

$10000$10000

In Dice We TrustIn Dice We Trust

Unique ID258309274917392

Spinning Photons

Richard FeynmanRichard FeynmanSafecracker, Father of Quantum ComputingSafecracker, Father of Quantum Computing

18CS588 Lecture 22

Bank Verifies Bill

Unique ID258309274917392

Spinning Photons

Uncertainty PrincipalID Amou

ntPhotons

… … …258309274917392 $10000

V-45H+45+45V

… … …

Bank aligns filters according to expected values. If photons onbill all pass through filters, the bill is valid.

19CS588 Lecture 22

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!

20CS588 Lecture 22

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.

21CS588 Lecture 22

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.

22CS588 Lecture 22

Quantum Key Distribution

23CS588 Lecture 22

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

24CS588 Lecture 22

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.

25CS588 Lecture 22

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)

26CS588 Lecture 22

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.

27CS588 Lecture 22

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

28CS588 Lecture 22

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!

29CS588 Lecture 22

Is this practical?

30CS588 Lecture 22

http://www.idquantique.com/(Geneva, Switzerland)

Movie Teaser

32CS588 Lecture 22

What’s in the “Sneakers” Black

Box?

A Quantum Computer

33CS588 Lecture 22

Quantum Computing• Feynman, 1982• 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…): 7-qubit computer– Adding another qubit is more than twice as hard

34CS588 Lecture 22

Cryptographic Hashing Attacks

35CS588 Lecture 22

Charge

• Tuesday: – Project presentations

• Order will be determined pseudorandomly

– Reports due

• Sneakers: send me email before Monday if you are coming