gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000 a = 0x000000000400000000000000 a = x⁵⁸
b = b000000000000000000000000000000000000000000000000111101111101100100100100100111111111001100111111 b = 0x000000000000f7d9249ff33f b = x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁶ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1
10000000000000000000000000000000000000000000000000000000000 | 111101111101100100100100100111111111001100111111 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------- | 1110111110110010010010010011111111100110011111100000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------- | 1100001101011011011011010000000010101010000010000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------- | 11010010000010010010011001111101011001001101110000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------- | 100101110100000000001011100010100101111110001100000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------- | 11000001001100100101111000101011010110010110011000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------- | 110110111010110111101010110100101010100101100100 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------- | 1011000111010011001110010011010101101001011011 |
c_quotient = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000110010101101 c_quotient = 0x000000000000000000000cad c_quotient = x¹¹ + x¹⁰ + x⁷ + x⁵ + x³ + x² + 1
c_remainder = b000000000000000000000000000000000000000000000000001011000111010011001110010011010101101001011011 c_remainder = 0x0000000000002c74ce4d5a5b c_remainder = x⁴⁵ + x⁴³ + x⁴² + x³⁸ + x³⁷ + x³⁶ + x³⁴ + x³¹ + x³⁰ + x²⁷ + x²⁶ + x²⁵ + x²² + x¹⁹ + x¹⁸ + x¹⁶ + x¹⁴ + x¹² + x¹¹ + x⁹ + x⁶ + x⁴ + x³ + x + 1