O`ZBEKISTON RESPUBLIKASI RAQAMLI TEXNOLOGIYALAR
VAZIRLIGI
MUHAMMAD AL-XORAZMIY NOMIDAGI
TOSHKENT AXBOROT TEXNOLOGIYALARI UNIVERSITETI
KRIPTOGRAFIYA 1 FANIDAN
2-amaliy ishi
Bajardi: Xursanov Muhammadyusuf
Tekshirdi: Qozoqova To’xtajon
Mavzu: Chekli maydon va Galua maydoni
Ishdan maqsad: Chekli maydon tushunchasi va turli chekli maydonda sonalr
ustida amal bajarish bo‘yicha amaliy ko‘nikmalarga ega bo‘lish.
21-variant
21)
a=6 b=2
a=176, b=113
1) GF(2^3) a =6 a(x) = x^2+x
b=2 b(x) = x
a+b = x^2+x+x = x^2 = 100 = 5
a*b = (x^2+x)x = x^3+x^2
x3+x2
x3+x+1
x3+x+1
1
x2+x+1
Qo’shganimizda natija = 5
Ko’paytirganimizda natija = 7
m(x) = x^3+x+1
) GF(28) a=176, b=113;
m(x) = x^8+x^4+x^3+1
a = 176 = 2^7+2^5+2^4
b = 113 = 2^6+2^5+2^4+1
a(x)+b(x) = (x^7+x^5+x^4)+ (x^6+x^5+x^4+1) = x^7+x^6+1
a(x)*b(x) = (x^7+x^5+x^4) (x^6+x^5+x^4+1)
=x^13+x^12+x^11+x^7+x^11+x^10+x^9+x^5+x^10+x^9+x^8+x^4 =
x^13+x^12+x^8+x^7+x^5+x^4 =
x8+x4+x3+x+1
x13+x12+x^8+x^7+x^5+x^4
x^13+x^9+x^8+x^6+x^5
x^12+x^9+x^7+x^6+x^4
x^12+x^8+x^7+x^5+x^4
x^9+x^8+x^6+x^5
x^9+x^5+x^4+x^2+x
x^8+x^6+x^4+x^2+x
x^5+x^4+x