MultiPhoton Quantum Cryptography

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Multi-Photon Quantum Cryptography

• George Khoury
• Dirk Bouwmeester
• UC Santa Barbara

2
Outline

• Review of classical cryptography
• Multi-photon QC proposal
• Protocol
• Advantages
• Challenges

3
The Players
Alice
Bob
Eve
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Vernam Cipher

• Alice and Bob share secret key k
• Unconditionally secure if k is secret
• Message m 101010101
• Key k 001001111
• Ciphertext C m?k 100011010
• Decrypt m C?k 101010101

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Vernam Cipher

• Inconvenient k m
• Really inconvenient k used only once
• C1 m1?k
• C2 m2?k
• C1?C2 m1?k?m2?k m1?m2

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Public Key Cryptography

• Bob distributes public key, keeps secret key
• No shared secret necessary
• Maybe computationally secure

Alice encrypts with public key
Only Bobs secret key decrypts
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Quantum Cryptography

• Bits encoded in quantum states
• Security from quantum mechanics
• Eves tampering disturbs quantum state
• Cant prevent, only detect, Eve

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Multi-photon pulses

• Security risk in single-photon protocols
• Hard to avoid

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Multi-photon QC Protocol
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Singlet States
Form preserved in any basis (nh)Bob
(nv)Alice (nhnv)Bob (nvnh)Alice
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nah
nbh
EOM
EOM
nav
nbv
PBS
PBS
Basis
Result
Basis
Result

• Alice and Bob randomly measure in non-orthogonal
  bases
• Alice (Bob) records nh(nv), nhnv
• Correlated results if they use the same basis

L C C C L C L L C L
L C L L L C L C C L
2 1 1 3 3 1 2 1 1 0
2 1 0 1 3 1 2 2 1 0
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Key sifting
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Error estimation

• Alice and Bob announce random subset of sifted
  key
• Ideally, no errors
• QBER error rate in sifted key
• Assume all errors due to Eve

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Error correction Privacy Amplification

• Classical error correction eliminates Bobs
  errors
• Privacy amplification reduces Eves information
  to zero. Possible if

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What about losses?

• Linear losses (independent of intensity) modeled
  by beamsplitter in front of detectors

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Simple Eavesdropping Strategy

• Assume Eve controls the source
• Eve replaces with
• Constrained to mimic expected probabilities

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Secrecy Capacity

• For losses lt 35, using two photon pulses
  increases capacity

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Technical Challenges

• Bright source of entangled photons
• Efficient photon counters
• Low loss transmission links

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Entangled Photon Source
a
BBO
?/2
UV pump
b
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Visible Light Photon Counter

• Developed by Boeing for Fermilab
• High quantum efficiency photon counter

Courtesy Don Lincoln, Fermilab
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VLPC Operation
VB
As atoms form impurity band 50 meV below
conduction band Photon absorbed in Si creates
electron-hole pair
Si
As-doped
n
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VLPC Operation
VB
Hole accelerates, ionizes As e- into CB
Si
As-doped
These electrons accelerate, ionize As As charge
limits avalanche
n
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Conclusion

• Single photon pulses are not necessary if you
  have photon counters
• Multi-photon pulses can increase bit rate
• Efficiency necessary currently unobtainable over
  long distance

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No information without disturbance
Eve would like U such that
But U is unitary
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Entropy, Mutual Information
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RSA details

• Choose two large primes p, q
• Compute n pq, f(n) (p-1)(q-1)
• Choose e rel. prime to f
• Compute d, s.t. ed 1 (mod f)
• Public key (e, n) Secret key (d,n)
• E(M)Me (mod n)
• M(E) Ed (mod n)

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Error Correction

• Shannon limit
• e.g. Hamming code
• Check bits compute parity of different
  subsections of message
• 1 means error in that subset
• Intersection of all subsets w/ error is the error
  location

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Privacy Amplification

• Replace sets of bits with their XOR
• If Eve knows only one of the bits, she has no
  idea about the XOR

1 ? ? ? 0 ? ? ?
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Message Authentication

• Alice and Bob agree on a set of functions F M ?
  T
• Also share secret key, which chooses an f from F
• Alice sends m, t f(m)
• Bob computes f(m), compares to t

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Message Authentication

• Eve knows f is in F f(m1) t1
• F has M / T members
• M / T2 also satisfy f(m2) t2
• Eve can only guess which function in F is being
  used, but only 1 / T will be correct
• Trick is to find a small set F (so that key is
  small)

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Electronics
clock
counter
write
RAM
addr
disc.
x4
data
VLPC
-Vb