Shifrlash.
Berilgan xabar M harfi bilan belgilanadi. Shifrtekst esa, C bilan belgilanadi. Xabar bit ko‗rinishida yozib olinadi (m1, m2, …, mn):
⎛ n ⎞
⎜∑bi mi ⎟mod q = ci
⎝ i=1 ⎠
formula yordamida shifrlanadi. Shifrtekst C = {c1, c2, …} ko‗rinishida hosil bo‗ladi.
Shifrni ochish.
C = {c1, c2, …} ko‗rinishidagi shifrtekstni
(r−1c ) mod q = m
i i
formula yordamida ochiladi. Ochilgan mi larni yig‗ib chiqib, M hosil qilinadi.
R.Merkl tizimni buzib ocha olgan odamga 100 AQSh dollari mukofoti berishini e‘lon qildi. 1982 yilda Adi Shamir bu mukofotga sazovor bo‗ldi. U mahfiy kalitga teng bo‗lmagan kalit yasab shifrlarni ocha oldi.
Misol.
O‗suvchi ketma-ketlik w = {2, 3, 7, 15}, modul son q=28, q modul bilan o‗zaro tub bo‗lgan r=11, shifrlanadigan matn M=HA so‗zi bo‗lsin.
Shifrlash:
HA so‗zini ASCII jadvali yordamida bit ko‗rinishga o‗tkazamiz: 0100100001000001.
bi = (wi * r) mod q formula orqali normal ketma-ketlik hosil qilamiz:
b1=(w1 ⋅ r) mod q= b2 =(w2 ⋅ r) mod q= b3 =(w3 ⋅ r) mod q= b4 =(w4 ⋅ r) mod q=
(2 ⋅11)mod 28=22
(3⋅11)mod 28=5
(7 ⋅11)mod 28=21
(15 ⋅11)mod 28=25
Ketma-ketlik hadlari 4 ta bo‗lgani uchun matnni 4 bitdan bloklarga
M1 = {m1, m2 , m3 , m4 } = 0100, M 2 = {m1, m2 , m3 , m4 } = 1000,
ajratamiz: M
= {m , m , m , m } = 0100, M = {m , m , m , m } = 0001.
3 1 2 3 4 4 1 2 3 4
⎛ 4 ⎞
⎜∑bi mi ⎟mod q = ci
formula yordamida shifrlaymiz:
⎝ i=1 ⎠
c = ⎛ 4 ⎞
1 ⎜ ∑bi mi ⎟ mod q = (22 ⋅ 0 + 5 ⋅1+ 21⋅ 0 + 25 ⋅ 0)mod 28 = 5
⎝ i=1 ⎠
c = ⎛ 4 ⎞
2 ⎜ ∑bi mi ⎟ mod q = (22 ⋅1+ 5 ⋅ 0 + 21⋅ 0 + 25⋅ 0)mod 28 = 22
⎝ i=1 ⎠
⎛ 4 ⎞
c3 = ⎜ ∑bi mi ⎟ mod q = (22 ⋅ 0 + 5 ⋅1+ 21⋅ 0 + 25 ⋅ 0)mod 28 = 5
⎝ i=1 ⎠
⎛ 4 ⎞
c4 = ⎜ ∑bi mi ⎟ mod q = (22 ⋅ 0 + 5 ⋅ 0 + 21⋅ 0 + 25⋅1)mod 28 = 25
⎝ i=1 ⎠
Shifrtekst hosil bo‗ladi:
Shifrni ochish:
C = {c1, c2 , c3 , c4 } = {5, 22,5, 25 }.
O‗suvchi ketma-ketlik w = {2, 3, 7, 15}, modul son q=28, q modul bilan o‗zaro tub bo‗lgan r=11, C={5, 22, 5, 25} bizga ma‘lum.
r sonining q modul bo‗yicha teskarisini topamiz: 11-1mod28= 1111mod28=(11(112 mod 28)5 )mod 28 = (11*95 )mod 28 = (11*9(92 mod
28)2 )mod 28 = (11 * 9 * 252 )mod 28 = 23
(r−1c ) mod q = m
formuladan matnni topamiz:
i
M1 = (23
i
⋅ 5) mod 28 = 3=2 ⋅ 0 +3⋅1 + 7 ⋅ 0 + 15 ⋅ 0 , bundan M1 = 0100
ekanligini aniqlaymiz.
M2
= (23
⋅ 22) mod 28 = 2=2 ⋅1 +3⋅ 0 + 7 ⋅ 0 + 15⋅ 0 , bundan M2=1000
ekanligini aniqlaymiz.
M3 = (23 ⋅ 5) mod 28 = 3=2 ⋅ 0 +3⋅1 + 7 ⋅ 0 + 15 ⋅ 0 , bundan M3 = 0100
ekanligini aniqlaymiz.
M4=(23 · 25) mod 28 = 15 = 2·0+3·0+7·0+15·1, bundan M4=0001
ekanligini aniqlaymiz.
Barcha Mi larni ketma-ket yozib harflarga o‗tiladi: M=0100100001000001
0100 1000 2 = 48 16 = H
0100 0001 2 = 41 16 = A
M = ―HA‖
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={163, 314, 591, 62}, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={437, 101, 294, 286}, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={275, 213, 90, 490 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={ 90, 286, 325, 275 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={398, 518, 163, 275 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={163, 275, 398, 518 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={479, 437, 367, 286 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={367, 437, 325, 275 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={101, 286, 437, 213 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={398, 437, 367, 294 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={426, 437, 591, 294 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={591, 437, 367, 294 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={518, 314, 202, 275 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={426, 437, 101, 202 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={90, 437, 266, 275 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={101, 286, 325, 275 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={294, 286, 367, 314 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={591, 62, 314, 367 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={591, 275, 90, 437 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={398, 437, 101, 275 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={163, 314, 591, 62}, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={437, 101, 294, 286}, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={275, 213, 90, 490 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={90, 286, 325, 275 }, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={398, 518, 163, 275 }, M=?
m=727, n=111, a={2,3,6,12,24,49,100,200}, C={540,662,378,662,
296}, M=?
m=727, n=111, a={2,3,6,12,24,49,100,200}, C={613,285,378,
418,573}, M=?
m=727, n=111, a={2,3,6,12,24,49,100,200}, C={8,662,378,236,41}, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={296,142,30,296,
377}, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={378,377,72, 223,
367}, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={82,40, 101, 142,
184}, M=?
m=397, n=17, a={2,3,6,12,24,49,100,200}, C={ 30, 19, 396, 367,
40}, M=?
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