Quantum Cryptography

1
Quantum Cryptography

• ??????????? ?????

2
???? ???????

• ????????
• ???????? ???????
• 3 ??????? ??????
• ???????? ????????? ????????
• ??????
• ???? ????
• ?????? Quantum cryptography
• ???????? ??84

3
????????

• Quantum cryptography ???????? ?????? ???????????
  ????????? ?????????? ?? ??????????? ????
• ??????? ? ??????? ????????? ??????? ??????????? ?
  ??????? Quantum cryptography ???????????
  ???????????
• Quantum cryptography ????????!

4
????????? ?? ???????

• Classical Cryptosystems, ???????? RSA, ??????????
  ?? ???????? ?????????? ?? ?????????.
• Quantum Computers ????? ???????? ????? ?????.
• ??? ????? ????? ??????? ??????????!

5
???????? ???????

• ???????? ????? ?, ???? ?
• e(?, K)? - ??????????? ?????
• de(M, K), K ?- ??????????????

Alice
Bob
Eve
6
????????

• ?????????????? ???????????
• ??????????????
• ??????????? ??????????????

• Prob (PC) Prob (C)
• One-Time Pad (OTP)
• PP1,P2,P3 KK1,K2,K3 CC1,C2,C3
• CiPiKi mod 2 for i1,2,3
• P11 01 K01 00 CPK10
  01

7
?????????????? ????????????

• ???????????
• f ?????????? ????????????? ????????, ????
• 1) f ????? ?????????
• 2) ???????? ? ??? ??????
• 
  Ea ?? Eb
• Alice Da(Alice) CsEb(PDa(Alice)) ? Bob
• Bob Db(Cs)PDa(Alice) Ea(Da(Alice))Alice

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QC QKD OTP

• QKD Quantum Key Distribution
• ????????? ????????? ?????? ?? ????? ??????????
  ????? ? ?????????? ???????????
• ? ?????????? ??????????? ?????????????
• QC QKD OTP

9
???????? ????????? ????????

• ?????????
• ?????????? ??? ????????? QS ?????? ??. ????
  ????.
• ???????? ?????
• ??? ????????? ??? ????? ?????????? ??????? ?????,
  ?.?. 0 ? ???????????? ? ? 1 ? ???????????? b

10
??????

• ?????????? ??????
• ???????? ????? ?????????? ???????, ????????
  ????????
• ????? ????? ??????????
• ? ??????? ??????????? ???????? ????????

11
???????????

• ? ?????? ???? ???????? ???????????, ???????????,
  ? ??????? ?? ??????????.
• ?????? ??????????? ?????? ????????? ??????
  ????????? ??????

12
??????????? ? ??????

• ?????????? ??????????, ??????????? ??????
  ??????????? ??????.
• ?????? 2 ?????? ????????? ???????

??????
?????
13
????????? ???????

• ???????? ?????????, ??????? ?????????? ?????? ??
  ?????.

CaCO3 DIAGONAL axis
14
??????? ????????????????

• ??? ????? ??????? ?????????????????? ?????,
  ???? ??? ????????????? ?? ?????? ??????

??? 50 chance of getting right answer.
CaCO3 RECTILINEAR axis
15
?????? ????????? ????????????

• Quantum Key Distribution ????????? ????????
  ?????????????.
• ???? Eve ?????????? ??????????? ??????????, ??
  ????? ? ??? ?????? ?? ????.
• BB84, B92, Entanglement-Based QKD.

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BB84

• BB84-??? ?????? ?????????? ???????? ??? ????????
  ?????.
• ?? ??????? ?? ????? ??????????? ???????.
• ???? ??????? ?? ????? ,??????? ?????????? ???
  ??????.

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BB84 ??? ?????????????

• ????? ???????? ??????? ????.
• ???? ????? ?????????? ????????? ?? 2? ???????.
• ?????????? ?????? ???????? ????.

Bit 0 1 0 1 1
Basis
Photon
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BB84 ??? ????????????? (2)

• ??? ???????? ?????? ? ????????? ?? ?? ?????
  ????????? ???????.
• ????????? ?????? ?? ??????.

Photon
Basis?
Bit? 0 0 0 1 1
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BB84 ??? ????????????? (3)

• ????? ? ??? ???????? ????? ???????? ?????, ?????
  ?????? ? ??? ???????.
• ?? ????, ? ??????? ??????? ??????, ?????????
  (raw key) ????.

20
?????????
Alices Bit 0 1 0 1 1
Alices Basis
Photon
Bobs Basis
Bobs Bit 0 0 0 1 1
??????????? ???? ????????? ????? ? ???? ??????,
?????????? ????? ??? ???.
Test bits
21
????????

• ???? ??????? ???????? ????, ?? ????? ??
  ???????????.
• ???????? ???? ????????? ?? ?????, ? ??????????
  (the final key) ???????? ????!

22
????????? ????????? ?????
Alices Bit 0 1 0 1 1
Alices Basis
Photon
Bobs Basis
Bobs Bit 0 0 0 1 1
Test bits discarded
Final Key 01
23
???????? ? ??????????????

• ???? ????? ????????????, ?? ? ???????????? 25 ?
  ???????? ????? ??? ????? ??????????.
• ?????????? ??????? ???? ? ???. 0.25 ?????
  ????????.
• ?????? ?????? ???????????.

24
?????????? ??????????

• ??? ????????? ????? ?? ???????? ????????? ?????
  ????? ??????????? ?? ?????????? 23??.

?????? ???????? ?????????? quantum
cryptography. (IBM, 1989)
25
??????

• Quantum cryptography ??? ???????? ??????????
  ?????????? ? ??????? ????????????.
• ????? Q? ??????? ??????? ??????????, ??? ????????
  ? ???????????? ???????????
• ?????????? ??????????
• ????????????????? ??????????
• ???????? ???????

26
??????????

• A talk on Quantum Cryptography or how Alice
  outwits Eve Samuel J. Lomonaco, Jr.
• Quantum Cryptography Rajagopal Nagarajan, Nick
  Papanikolaou.