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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 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( )