gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000 a = 0x000000000040000000000000 a = x⁵⁴
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
1000000000000000000000000000000000000000000000000000000 | 111101111101100100100100100111111111001100111111 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------- | 111011111011001001001001001111111110011001111110000000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------- | 110000110101101101101101000000001010101000001000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------- | 1101001000001001001001100111110101100100110111000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------- | 10010111010000000000101110001010010111111000110 | - 000000000000000000000000000000000000000000000000 | 0
c_quotient = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011001010 c_quotient = 0x0000000000000000000000ca c_quotient = x⁷ + x⁶ + x³ + x
c_remainder = b000000000000000000000000000000000000000000000000010010111010000000000101110001010010111111000110 c_remainder = 0x0000000000004ba005c52fc6 c_remainder = x⁴⁶ + x⁴³ + x⁴¹ + x⁴⁰ + x³⁹ + x³⁷ + x²⁶ + x²⁴ + x²³ + x²² + x¹⁸ + x¹⁶ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁶ + x² + x