Quantum Position Verification in the Plane Serge Fehr and Dominique - - PowerPoint PPT Presentation

Dominique Unruh

Quantum Position Verification in the Plane

Serge Fehr and Dominique Unruh

CWI University of Tartu

Dominique Unruh

Position Verification

Speed of light  Position verified

2 Quantum Position Verification in 2D

Dominique Unruh

A generic protocol

time space

x y f (x,y) g(x,y)

prover verifier 1 verifier 2

3 Quantum Position Verification in 2D

Dominique Unruh

A generic attack

time space

x y f (x,y) g(x,y)

adv 1 verifier 1 verifier 2 adv 2

x y

4 Quantum Position Verification in 2D

[CGMO09] Chandran, Goyal, Moriarty, Ostrovsky, Position Based Cryptography, Crypto 2009

Dominique Unruh

Way out: quantum crypto

• In attack: adversary copies x,y
• If x or y quantum: No cloning!
• Attack does not work
• Other attacks?

– Without extra assumptions: Generic attack (exponential entanglement)

[BCF+11] Buhrman, Chandran, Fehr, Gelles, Goyal, Ostrovsky, Schaffner: Position-Based Quantum Crypto, Crypto 2011

x y

5 Quantum Position Verification in 2D

Dominique Unruh

Quantum crypto: A secure protocol

time

𝒚 𝑪 Basis B

prover verifier 1 verifier 2 [TFKW13] Tomamichel, Fehr, Kaniewski, Wehner: One-Sided Device- Independent QKD and Position-Based Cryptography from Monogamy Games, Eurocrypt 2013 (and [BCF+11])

Assumption: No entangled photons in

6 Quantum Position Verification in 2D

Dominique Unruh

2D/3D case

time space verifier 0 verifier 1

7 Quantum Position Verification in 2D

Measure Ψ in basis 𝜄1 ⊕ 𝜄2

space verifier 2 verifier 0 verifier 1

𝜄1 𝜄2

verifier 2

(There is a secure 3D protocol in the random oracle model, though [Unr14])

Dominique Unruh

Our result

• Security proof in 2D-case
• Sufficient for position verification “on earth”
• 3D-case: open problem

Quantum Position Verification in 2D 8

Dominique Unruh

Why is 2D/3D tricky?

• Events (like getting all three

messages) along complicated space-time surfaces

• In some space-time areas,

some but not all messages known

• Complicated mix

geometry + quantum

Quantum Position Verification in 2D 9

Dominique Unruh

Proof technique: Space-time circuits

• Tool: Space-time circuits

– Gates have positions in space-time – No wire leaves light cone

• Derive connectivity

from geometry

• Then forget about geometry,
• nly use connectivity

– Normal game-based proof

AND OR OR AND OR AND OR

10 Quantum Position Verification in 2D

[Unruh, Quantum Pos. Verif. in the RO model, Crypto 14]

Dominique Unruh

Proof – analyzing space-time regions

Quantum Position Verification in 2D 11

before protocol reachable by

• ne verifier

reachable by two verifiers reaches two verifiers reaches

• ne verifier

many copies many copies many copies many copies

𝜄1𝜄2 𝜄1𝜄2 𝜄1𝜄2

Analyzed in [TFKW13]: Pr[both verifiers guess 𝒚] exponentially small.

Dominique Unruh

Conclusion

• 2D case solved
• Lesson learned:

Relativistic protocols complicated in 2D/3D

– [BCF+11] got it wrong.

• Use space-time circuits!

(Also for relativistic commitments)

• 3D case: open problem

Quantum Position Verification in 2D 12

Dominique Unruh

Thank you for your attention

13

Dominique Unruh

Postdoc Positions (also phd) Verification of Quantum Crypto

Formal verification of quantum crypto protocols (“QuEasyCrypt” tool) http://tinyurl.com/postdoc-vqc