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Secrete sharing schemes

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????? ???? ?? ?????????? ?????, ?? ??? ??? ?? ????? ????. ... ???????? ?????? ?? Secret Sharing Scheme ???:A. Shamir ? - G. Blakley???? 1979. ... – PowerPoint PPT presentation

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Title: Secrete sharing schemes


1
Secret Sharing Schemes
2
Secret sharing schemes
  • ???? ?? ???? ??????? ?? ???? ???? ????, 4 ????? ?
    5 ??????. ????? ???? ?? ?????????? ?????, ??
    ??? ??? ?? ????? ????. ?? ????? ?? ????? ????
    ???, ??? ?? ???? ??????? ????? ???? ???? ??
    ??????????.
  • ????? ???? ???? ??????????? ???? ????? ????? ????
    ?????. ??? ???? ????? ??? ??? ????? ??
    ??????????, ?? ?????? ????? ????? ?? ????? ?????
    ??-???
  • ?? ??? ????? ???? ??????.
  • ?? ????? ?? ??? ?????? ??????.

3
  • ?? ????? ??? ???? ??? ???? ?????? ?? ????? ?????
    ?? ?????.
  • ?????? ??????? ?? ????? ???? Secret Sharing
    Schemes
  • ???????? ?????? ?? Secret Sharing Scheme ???A.
    Shamir ? - G. Blakley???? 1979.

4
??????
  • Dealer ??? ???? ????? ?? ???? ????? ????? ????
    ?????? ?????. ?? ??? ????? ??? ???? ???? share
    holder ?????? ????? ?????? ????? ???? ????
    Share.
  • Access Structure ???? ?? ??????????? ?????? ??
    ????? share holders ???????? ?? ????? ????.
  • ????? ????? Perfect ?? ?? ????? ????? Access
    Structure ?? ????? ????? ???? ?????? ?? ?????
    ????.

5
????????
  • ????????? ?????? ? Secret Sharing Schemes ????
    ????? ?????? ?? ???????.
  • ???? ????? ???? ???? ??? ????? ????? ?? ?????
    ???? ??? ????? (??????? ??????, ????? ????????
    ?????) ???? ???? ?????? ???? ?? ????? (????
    ?????? ????? ???? ????? ?? ???? ?? ????? ??????
    ?? ????? ????) ???? ??? ?? ????? ???? ?????
    ??????? ????? ?? ?? ???????????? ???? ???? ?????
    ??????.

6
????????
  • ?????? ????? ????? ??? ????? ?????? ?????? ?????
    ??? ????? ????? ?-Shares ?????? ?-n ?????, ?? ???
    k ????? ????? ????? ?? ????? (???? ??? ???? ????
    n-k ????? ?????? ????? ?? ?????).
  • ??? ???????? ??? ??? ??? ????? ?? ?????? ?? ????
    ????? m shares, ??? ???? ????.

7
????????
  • ????? ???? ??? ?????? ?????? (multi-authorization)
    .
  • ?????? ?????? ????? ??? ???? ???? ??? ??????
    ????? ?????? ????, ???? ?? ??? ???? ?????
    ????????, ?? ????? ????? ????? ??? ?????? ???
    ???? ????? ???????.
  • ????? ?-Secret Sharing Scheme ???? ??? ????? ????
    ????? ??? ???? ???? ??? ????? ?? ???? ??????? ???
    ???? ???? ?? ?????? ??? ?????? ?????.

8
(No Transcript)
9
(No Transcript)
10
  • ???? ???? ????? ???? Perfect Secret Sharing
    Schemes ???????? ?? ????? ???????.
  • ?????? ???? ???? ????????? ?? ?-Access Structure.
  • ??? ???????? ??????? ???????? ????? ??? ????? k
    ????? ???? n, ????? ?? ????? k-out-of-n Schemes.

11
k-out-of-n Schemes
  • ?? ?? k ???? n
  • n ??-?? ????????.
  • k ???? ? - Access Structure ?????? ?? ?????
    ????.
  • ????? ????? ???? ???? ?? ??????? ??? ???? ????
    ?? ???? ???? ?? ?? n ????????, ???, ???? ??????
    ?-k ?????.

12
k-out-of-n Schemes
  • ???? ?? ?????? ??? ??? Zp ???? p ??????.
  • ???? A0, ??? ???? ?????.
  • ? - Dealer ???? ????? ????? k-1 ?????? ???? Zp,
    ????A1,A2,,Ak-1 ????? ?? ????????

13
k-out-of-n Schemes
  • ???? ?? ?????, ????? ???? ???? xi ????? ???? Zp
    (??? ????) ????? ?? f(xi).
  • ????? ????? ?????? ?-i ??? ???? (xi,f(xi)).
  • ??? ?? p ?????? ?-public ????? ???.

14
?????
  • ???? k ??????? ?????? ?? ?-shares ????, ?? ??????
    ????? ??????? ?????'?
  • ????? ???????? ????? ?? ??? ???? x0.
  • ????? ???????? ???? ?? A0 ???? ??????.

15
?????
  • ?? ???? ? - k ??????? ?????? ?? ????? ???????,
    ????? ?? ????, ????? ????????? ?? ???? ?????
    ????? ??- ?? ????? ??????? ????? ??? ???? ?????
    ?? ??? ????? ?????? Zp.

16
????? 2 out of 3
  • ???? ?????? ??? ????? ???? ????. ????? ?????
    ??????? ?"? ????? ??????????? ?? ?? ??? ?????
    ???? ??????.
  • ?????
  • k2
  • n3
  • p7
  • ???? ?????? A05 (????? Zp).
  • ???? ???? ????? ???? A13

17
????? 2 out of 3
  • ????? ?? ????????
  • ???? 3 ?????? ?????? ?????? ????? Zp (??? ????
    ???????? n3)
  • x14
  • x26
  • x32

18
????? 2 out of 3
  • ???? ???? ?? x ?? y
  • y(4)53?417
  • y(6)53?623
  • y(2)53?211
  • ?? ??? ?????? ???????? ???? ??? ????? (x,y)
    ?????
  • (4,17) (6,23) (2,11)

19
????? 2 out of 3 - ?????
  • ???? ?? ?????? ?????? ??? ???? (4,17) ??????
    ???? ??? ????(6,23), ?????? ???????? ???? ????,
    ?? ?????? ?? ?????? ??????? ??????? ???????
    ?????'?

20
????? 2 out of 3 - ?????
  • ???? x0 ????? ?? ???? y5.

21
????? ????????
  • ???? ????? ?? ?? ??? ?????? ?????? ?? ??????
    ????? ??? ?? ??? ?-Y (x0) ??? ????.
  • ????? ??? ?? ????? ??? ????, ?? ???? ????? ??
    ????.

22
????? ????? ?????? ????
  • ???? ?-Alice ?-Bob ??????? ????? ????? ?????, ??
    ??? ??? ??? ??? ???? ?????? ???.?? ?????? ?????
    ??? ?? ????.
  • ???? ????? ???? ?? ?? ?????? ?-key ???011 100
    001 010
  • Alice ?-Bob ?? ?????? ?? ?-key ??"?.
  • ?? ??? ??? ???? key ????.

23
?????
  • Alice ????? key ????? ??? ???? ??? ??? ??
  • ?-key ??????.
  • Bob ???? ??-?? key ???????? ????? XOR ?? ?-key ??
    Alice ????? ?-key ????.
  • Alice 101 010 010 001
  • Bob 110 110 011 011
  • key 011 100 001 010

24
???? ???????
  • ?????? ?-k out of n ??? ???? ???? ?? ???? ?????
    ????? ???? ???? ?????? Hierarchical Schemes.
  • Hierarchical Schemes ??????? ???? ??? ??? ??????
    ?? ???? ?? ?????.
  • ?????? ??? ????? ????? ????? ?? ??? ???? ????
    ????? ?????? ??? ??? ????? ???? ???? ???? ????
    ???? ????? ????? ???

25
???? ???????
  • ??? ?? ???? ???? ?????, ?????? ??????? ????? XOR.
  • ??? ??? ???? m (management)
  • ??? ??? ???? t (technical)
  • ????? ?-k out of n ??? ???? ?? m ??? t
  • m 2 out of 3
  • t 3 out of 7
  • ??? ?? ?-Shares ???????? ??? ?????? ???????.

26
?????
  • k ???????? ????? ????? ?? ????.
  • ?????? ?-i ????? ???? ????.
  • ??? ???????? ?? ?????? ????? ?? ????.
  • ????? ???, ?????? ?-i ???? ????? ???? ?????? ??
    ????? ?? ???? ?????.
  • ???? ????? ?????? ?? ???? ????? ???? ?????? ??
    ?????? ???? ?????? ????? ?????? ?????
  • ????? ????? ????? ?????.
  • ????? ????? ????? ?? ??? ???????.
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