Quantum Private Comparison based on Entanglement

Swapping among EPR PairsYu-Ting Chen and Tzonelih Hwang

Quantum Information and Network Security Lab, CSIE, National Cheng Kung University

!National Computer Symposium 2013

Present: Shih-Hung Kao

Outline• Introduction

• EPR Entangled States

• EPR Entanglement Swapping

• Proposed Protocol

• Security Analysis

Introduction• Quantum Private Comparison

Alice Bob

TP (new semi-honest/active attacker)

MA MBMA = MB ? MA ≠ MB ?

help

EPR Entangled States

1 2

φ ± = 1200 ± 11( )

ψ ± = 1201 ± 10( )

EPR Entanglement Swapping

1 2

3 4

EPR Entanglement Swapping

1 2

3 4

EPR Entanglement Swapping

1 2

3 4

EPR Entanglement Swapping

1 2

3 4

Initial EPR state Swapping Result

φ+12φ+

34, φ−

12φ−

34,ψ +

12ψ +

34,ψ −

12ψ −

34φ+

13φ+

24, φ−

13φ−

24,ψ +

13ψ +

24,ψ −

13ψ −

24

φ+12φ−

34, φ−

12φ+

34,ψ +

12ψ −

34,ψ −

12ψ +

34φ+

13φ−

24, φ−

13φ+

24,ψ +

13ψ −

24,ψ −

13ψ +

24

φ+12ψ +

34, φ−

12,ψ −

34,ψ +

12φ+

34,ψ −

12φ−

34φ+

13ψ +

24, φ−

13ψ −

24,ψ +

13φ+

24,ψ −

13φ−

24

φ+12ψ −

34, φ−

12,ψ +

34,ψ +

12φ−

34,ψ −

12φ+

34φ+

13ψ −

24, φ−

13ψ +

24,ψ +

13φ−

24,ψ −

13φ+

24

Proposed Protocol1 2

Alice TP Bob

3 4ISA ∈ φ+ , φ− ,ψ + ,ψ −{ }D ∈ 0 , 1 , + , −{ }

2 D 4 D

Public Discussion Public Discussion2 4

EPR measurement

1 3

Z-base Z-baseMRA =

0 0( )1 1( )⎧⎨⎪

⎩⎪ MRB =0 0( )1 1( )⎧⎨⎪

⎩⎪RA = MA ⊕ ISA ⊕MRA RB = MB ⊕ ISB ⊕MRB

R = RA ⊕ RB ⊕ RT

RT =0 φ ±( )1 ψ ±( )⎧⎨⎪

⎩⎪

Proposed ProtocolR = RA ⊕ RB ⊕ RT R = 0 :MA = MB R = 1:MA ≠ MB

MA MB ISA ISB RT q2,q4( ) q1,q3( ) MRA MRB RA ⊕ RB ⊕ RT

0 0 φ+ φ+

φ+ ψ +

φ+ φ+

φ−

ψ +

ψ −

φ+

φ−

ψ +

ψ −

φ−

ψ +

ψ −

ψ +

ψ −

φ+

φ−

0 1( )0 1( )

0 1( )0 1( )0 1( )0 1( )0 1( )0 1( )

0 1( )0 1( )

0 1( )0 1( )

1 0( )

1 0( )1 0( )

1 0( )

0

0

0

0

0

0

0

0

Security Analysis• External Eavesdropper

• Can be detected by public discussion of decoy photons.

• Internal Attacker:

• Both and are unknown to Bob, he cannot obtain information about

• Similarly, Alice cannot obtain Bob’s

MRAISAMA

MB

Entanglement Swapping

ISA ⊕ ISB = EPRT ⊕EPRAB

RT = ISA ⊕ ISB ⊕MRA ⊕MRB

R = RA ⊕ RB ⊕ RT= ISA ⊕MRA ⊕MA( )⊕ ISB ⊕MRB ⊕MB( )⊕ ISA ⊕ ISB ⊕MRA ⊕MRB( )= MA ⊕MB

φ ± = 1200 ± 11( )

ψ ± = 1201 ± 10( )

φ+ :00, φ− :01,ψ + :10,ψ − :11

RT( ) MRA ⊕MRB( )

Conclusion• A private comparison protocol under the help of a

new semi-honest TP, in which any party does not share any key with others.

!

• The qubit efficiency can be promoted in the future work.