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