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ets tee

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?atas?e?? S??a?t?se?? ap??s ??t?? s?s?et?s ?? (Resilient and Correlation Immune ... Ciphers (AES, DES) ?at????? ?et?????a. ?at????? ?et?????? e??a? ??a? p??a?a? ... – PowerPoint PPT presentation

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Title: ets tee

1
?????? ?ets?ß?? ????te??e??

S???? ?fa?µ?sµ???? ?a??µat???? ?a? F?s????
?p?st?µ??
??p??µat??? ???as?a
S?????S????? S?????S??? ??? ?F????G?S S???
??????G??F??
?a???? Ge????a
???µe??? ep?t??p? ??????ß???? ???st??(ep?ß??p??
?a????t??)
?apa???????
????a?d???
Sp????t?? ???????

2
?at????? ?et?????a ?a? S??d?ast???? S?ed?asµ??

?at????? ?et?????a
?e????? a???µ?? ?????????? ?at?????? ?et?a?????
??? S?ed?asµ??
???s? se
Stat?st??? s?ed?asµ? pe??aµ?t??
Te???a d?????s?? ?a???
?pt??? ???pt???af?a (Visual Cryptography)
?????????? p??a?e? (Orthogonal Arrays)
??st?p???s? ??d???? (Authentication Codes)
?atas?e?? S??a?t?se?? ap??sß??t?? s?s?et?sµ??
(Resilient and Correlation Immune Functions)
?atas?e?? ??e?d??? S??ed????

3
???pt???af?a

???pt?s?st?µa (P, C, K, E, D)
P s????? a?????? ?e?µ????
C s????? ???pt??e?µ????
K s????? p??a??? ??e?d???
E s????? ?a????? ???pt????f?s??
D s????? ?a????? ap????pt????f?s??

4
??d? ???pt?s?st?µ?t??
5
?at????? ?et?????a

?at????? ?et?????? e??a? ??a? p??a?a?
ap? n d?af??et??? st???e?a ?ste ???e ??aµµ?
?a? ???e st??? ?a pe??????? d?af??et??? st???e?a.
??? ?at????? ?et?????a ?????ta? aµ??ßa?a
????????a (MOLS), a? ?pe???t??t?? ta se ??a
t??t?, a?t? ??e? st???e?a ta a?t?st???a
d?ateta?µ??a ?e??? ?? e??a? ??a d?af??et???
µeta?? t???.

6
?atas?e???

?at?????? ?et?a????? 1? ??aµµ? se ?a??????
µ??f?, ?? ?p????pe? µe µeta??se??
S?????? MOLS
????? n pa1pa2pak
?p? (k2, k2 k, k 1, k, 1) BIB s?ed?asµ?
?atas?e?????ta? k 1 MOLS

7
?????????? S?ed?asµ?? (orthogonal arrays)

??(s, n) p??a?a? s x n2 ?ste d?? ?p??esd?p?te
??aµµ?? d????? sta ?ata????fa ?e?????a t??? ???e
d?ateta?µ??? ?e????? s?????? a???ß?? µ?a f???
S?????? ?pa????

8
?atas?e?? ??

?p? t? MOLS 123 123
312 231
231 312
?????pte? ? s?ed?asµ??
111 222 333
123 123 123
123 312 231
123 231 312

9
???s? ?at?????? ?et?a????? st?? ???pt???af?a

?a???a? ???pt????f?s??
?? µ???µa (i, j) ???pt???afe?ta? sa? t? ??s? (i,
j) d??
ep??e?µ???? MOLS.
?.?
?p??????µe t? 2? ?a? t? 3? ?at????? ?et??????.
???pt????f?s? G?a t? (2, 4) µetad?deta? t? (1,
2).
?p????pt????f?s? ?pe???t??t?? ta ß??s???µe se
p??a ??s? ß??s?eta? t? (1, 2).

10
???s?et? ?sf??e?a

??t?µet??es? ??aµµ?? ?a? st???? sta MOLS t??
??e?d???.
??t?µet??es? st???e??? t?? MOLS t?? ??e?d???.
?? ??e?d? ?a a????e? ta MOLS p?? ???s?µ?p?????ta?
??a t?? ap????pt????f?s? µet? ap?
???e ?e???? st???e???
s???e???µ??? µ???? µ???µat??
se ?p???d?p?te st?d??

11
???s? F ?et?a????? st?? ???pt???af?a

???pt????f?s? ?pe???t??ta? ta tet?????a
st?????µe t? ??s? p?? ß??s?eta? t? µ???µa p???
???pt????f?s?.
?p????pt????f?s? ???s???µe ta st???e?a p??
ß??s???ta? st? ??s? p?? ?aµß????µe

12
???s?et? asf??e?a

?? ??e?d? ep????e? ?p???d?p?te ?p?s????? p??????.
?p????? ?a a?t?µetate????
??aµµ?? ?a? st??e?
st???e?a p??????
?? ??e?d? ep????e? d?af??et??? s????? p?????? ??a
t?? ???pt????f?s? se d?af??et??? st?d?a.

13
S?µpe??sµata

?e?????t?µa ?a ?t?µa p?? ?????? ?a
ep????????s??? p??pe? ?a ????? s??a?t??e? ??a ?a
a?ta??????? ??e?d? ep????????a?.
??e??e?t?µata
?d?a?te?a d?s???? ? ap????pt????f?s?, ??????
?ta? ? a???µ?? MOLS e??a? µe?????.
?????? ?????? ???pt????f?s?? ?a?
ap????pt????f?s??
S?µp?es? µ???µ?t??
???te???µe?? µ???d?? ??ta??a?? ??e?d??? µ?s?
???pt?pa??t?? d?µ?s??? ??e?d???, a?ta??a??
µ???µ?t?? µ?s? ???pt????f?s?? µe ????????a
?at????? ?et?????a.

14
??? s?ed?asµ??

?s????p?µ????, µ? p????? s?ed?asµ?? ?at?
blocks (u, b, r, k, ?), ?p??
u t? p????? t?? d?a???t?? st???e???
b t? p????? t?? blocks
r p????? blocks sta ?p??a ???e st???e?? a???e?
k p????? st???e??? p?? pe????e? ???e block
? p????? blocks sta ?p??a ???e ?e???? st???e???
a???e?
???a?a? a?t?st????s?? ? (aij) aij 1 a? ti
a???e?
st? block Bi.
S?µµet????? ??? s?ed?asµ??, ?ta? b u ?a? r k.

15
SBIB s?ed?asµ??

???t?a ????? s?µf???s?
?pt??? ???pt???af?a
S?st?µata ??a??µ?? ??e?d??? S??ed????
S?st?µata ??a??µ??

16
??a??a?e?, µ? ??a??? s?????e? ?pa???? ???
s?ed?asµ??

bk ur
?(u - 1) r(k - 1)
b u ?a? r k
AAT (r - ?)?u ?Ju ?a? JuA kJub

17
?atas?e??? ??? S?ed?asµ??

?p? k 1 MOLS ?atas?e???eta? ? (k2, k2 k, k
1, k, 1) ??? s?ed?asµ??.
?p? s????? d?af???? (u, k, ?) ?atas?e???eta?
s?µµet????? ??? s?ed?asµ??.
?atas?e?????ta? ?? BIB s?ed?asµ?? µe pa?aµ?t????
(4t 1, 8t 2, 4t, 2t, 2t - 1), ?ta? 4t 1
p??t?? (? d??aµ? p??t??).
?atas?e?????ta? ?? SBIB s?ed?asµ?? µe pa?aµ?t????
(4t 3, 2t 1, t), ?ta? 4t 3 p??t?? (? d??aµ?
p??t??).
?p? p??ß????? ep?ped? t???? q2 q 1,
?atas?e???eta? SBIB s?ed?asµ?? µe pa?aµ?t????
(q2 q 1, q 1, 1)

18
?atas?e??? s?ed?asµ?? ap? ?d? ?p?????te?
s?ed?asµ???

?????? s?ed?asµ?? (??? a?? b u)
?e??a??t?? s?ed?asµ?? (??? p??ta BIBD)
S?µp????µat???? s?ed?asµ??, ??e? pa?aµ?t???? (u,
b, b r, u k, b 2r, ?)
d ????ap??s???, ??e? pa?aµ?t???? (u, db, dr, k,
d?)
?a?a??µe??? ?? p??? t? block Bu µe pa?aµ?t????
(k, u 1, k 1, ?, ? - 1), ??1
?p??e?p?µe??? ?? p??? t? block Bu µe pa?aµ?t????
(u k, u 1, k, k ?, ?) ??k - 1

19
???????µ?? ?atas?e??? ???a?a ??t?st????s??

?f??? ?atas?e??? p??a?a a?t?st????s?? SBIB
s?ed?asµ?? µe pa?aµ?t???? (q2 q 1, q 1, 1)
??????ta? p?s?t?te?
IJ(i, j) ij mod u, 1 i, j q 1
???a?a? ??s??
PA(i, IJ(i, j)) j, 1 i q 1, 0 j
q 1
???a?a? ???????? ep??tas??

20
?a??de??µa epe????s?? a??????µ??

???a?a? a?t?st????s?? (7, 3, 1) SBIB s?ed?asµ??

21
????p????t?ta ???????µ??

St?? a??????µ? ?????ta? µ??? ??
apa?a?t?t?? ?p?????sµ??, ?p?te ?
p???p????t?ta µe???eta? ?at? p???.
????p????t?ta ?(u) O(q2)
?a?a??te??? a??????µ?? ????? ep?t??e?
p???p????t?ta O(q4) ? st?? ?a??te??
pe??pt?s? O(q3).

22
???s? ??? S?ed?asµ?? st?? ???pt???af?a

?? s?µµet????? ??? s?ed?asµ?? µp????? ?a
???s?µ?p??????? se ??a S?st?µa ??a??µ??
??e?d??? S??ed???? (conference key
distribution system)
µ? d??at?t?ta ap????pt????f?s?? µ???µat?? ap? µ?
e???s??d?t?µ??? ?t?µ?
p?st?p???s? ta?t?t?ta? ap?st???a

23
?e????af? d?ad??as?a? a?ta??a??? ??e?d???

u s??ed??? ????? ??a p??s?p??? ??e?d?, ?st? rj
??a t?? s??ed?? j
1? ß?µa ? s??ed??? j st???e? t? p??s?p??? t??
??e?d? rj st? s??ed?? i a? st?? p??a?a
a?t?st????s?? ?s??e? ?t? aij 1 ?a? o s??ed??? i
?p??????e? t?? p?s?t?ta
2? ß?µa ? s??ed??? j st???e? st? s??ed?? i t?
kij p?? ??e? ?p?????se? a? aji 1 ?a? ? s??ed???
i ?p??????e? t? ??e?d? µe ß?s? t?? t?p?

24
?p?de???

St? 1? ß?µa ? s??ed??? i ?aµß??e? k 1
d?af??et??? ??e?d?? ?a? ?p??????e? k d?af??et???
????µe?a ap? k 1 d?af??et??? ??e?d??.
St? 2? ß?µa ? s??ed??? i pa?a?aµß??e? k 1
d?af??et??? ????µe?a kij, ta ?p??a ?a
ap?te????ta?
ap? k(k - 1) d?af??et??? p??s?p??? ??e?d??. ?p?
t? s??s? k(k - 1) ?(u - 1), p????pte? ?t? t?
k(k - 1) ?a pe????e? ? f???? ta p??s?p??? ??e?d??
rj, e?t?? ap? t? d??? t?? ??e?d?, ?p?te p???a-
p?as???e? µe t? ri? ??a ?a p??e? t? s?st? ??e?d?.

25
?a??de??µa ??a (11, 5, 2) SBIBD
26
?e???e?t?µata

????? st? µet?d?s? t?? µ???µat?? ???? sfa?µ?t??
t?? s?st?µat??
???a?? pa??µßas? ap? e?sß???a

?e?????f??ta?
???p?? ?p?????sµ?? ??e?d??? ap? t? s?st?µa
???t?????? ep????????a? µeta?? t?? s???d???

28
?p?????sµ?? ??e?d??? ap? t? s?st?µa

n p x q , ?p?? p, q p??? µe????? p??t??
G?a ???e s??ed?? ep????eta? ??a? a??et? µe?????
p??t?? a???µ?? ei ?ste ?a e??a? p??t?? ?? p???
t?? a???µ? (p - 1)x(q - 1) ?a? ? a???µ?? di ap?
t? ??s? t?? d??fa?t???? e??s?s?? ei x di 1 mod
(p - 1)x(q - 1)
g a???e? st? GF(p) ?a? GF(q)
??st??? p????f???a SI IDid
??µ?s?? ??e?d? (ei, g, n)
?d??t??? ??e?d? (di, SI)

29
?a??de??µa