gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000000040000000000000000 a = x⁶⁶
b = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111 b = 0x00000000000000009aba68ef0cf5c2bf b = x⁶³ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴³ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³³ + x³² + x²⁷ + x²⁶ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1
1000000000000000000000000000000000000000000000000000000000000000000 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------- | 1101010111010011010001110111100001100111101011100001010111111000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------- | 100111101101001001011111001011101101011010110111101011101000111 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001001 c_quotient = 0x00000000000000000000000000000009 c_quotient = x³ + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000100111101101001001011111001011101101011010110111101011101000111 c_remainder = 0x00000000000000004f692f976b5bd747 c_remainder = x⁶² + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁴ + x⁵³ + x⁵¹ + x⁴⁸ + x⁴⁵ + x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁶ + x³⁴ + x³³ + x³² + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²² + x²⁰ + x¹⁹ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁶ + x² + x + 1