Quantum Cryptography:Public key distribution

and coin tossing

Charles H.Bennett Gilles BrassardInternational Conference on Computers, Systems & Signal Processing,1984Speaker:陳君翰Quantum Information Security LabProfessor: Tzonelih Hwang

Outline

• Background

• Introduction

• BB84 Protocol

• Conclusion

Background

• Quantum Cryptography: Public key Distribution

• Charles H. Bennett, Gilles Brassard

• International Conference on Computers, Systems & Signal Processing,1984

• First Quantum key distribution protocol

Introduction

• Quantum cryptosystem:Base on property of quantum:1.The uncertainty of measurement

2.No cloning theory

BB84 Protocol• Definition

0 1

Bit:0 Bit:1

R Base

D Base

0 ° 90 °

45 ° -45 °

Quantum channel: with the property of quantum.

Classical channel: authentic channel

BB84 Protocol concept

T= 0,1

B= ,R D

T’=B’=

0,1

,R D

QB(T)

B’

B’’=Correct bases of B’

*P(B’’(1)),V(B’’(1))+………….*P(B’’(N/4)),V(B’’(N/4))+

Randomly choose half of B’’ to

discuss with Alice

ok or eavesdroppers existVerify

Case 1:No eavesdroppers

D R D R D R D R

1,3,6,8

(6,1),(8,1)

ok

1 0 1 0 1 1 1 1D D D D R R R R1 2 3 4 5 6 7 8

1 0 1 0 1 1 1 1

1 0 1 1 0 1 0 1D R D R D R D R1 2 3 4 5 6 7 8

1 0 1 1 0 1 0 1D R D R D R D R1 2 3 4 5 6 7 8

Position 1,3,6,8 are the same base

1 0 1 0 1 1 1 1D D D D R R R R1 2 3 4 5 6 7 8

Randomly choose numbers

to discuss with Alice

Case 2:Have eavesdroppers

D R D R D R D R

1,3,6,8

(6,1),(8,0)

Eavesdropper exist!

1 0 1 0 1 1 1 1D D D D R R R R1 2 3 4 5 6 7 8

1 0 1 0 1 1 1 1

1 0 1 1 1 1 1 0D R D R D R D R1 2 3 4 5 6 7 8

1 0 1 1 1 1 1 0D R D R D R D R1 2 3 4 5 6 7 8

1 0 1 0 1 1 1 1D D D D R R R R1 2 3 4 5 6 7 8

Assume use D base

1 0 1 0 1 1 1 1D D D D R R R R1 2 3 4 5 6 7 8

1 0 1 1 1 1 1 0D R D R D R D R1 2 3 4 5 6 7 8

Analysis BB84 Protocol

• Probability of eavesdropper :

1 bit:

N bit: 3

4

N

When N ↑,it’s easier to detect eavesdroppers exist or not.

1 1 1 3*

2 2 2 4

Analysis BB84 Protocol Cont.

Correct bases of B’

Qubit efficient:

(R,R) (D,D) (R,D)(D,R)

N/2 bits

N/4 bitsto discuss

N/4 bitsas key

(R,R) (D,D) (R,D)(D,R)

B’

DiscussionSecurity/Not security

N bits

• Qubit efficiency:1 1 1

*2 2 4

Utilization is only 25%!

Conclusion

• Advantages:

– Without exchanging information initially.

– Eavesdroppers can be detected.

• Disadvantages:

– Low utilization

– Photons may be lost in transmitting

Thank you