gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000000010000000000000000 a = x⁶⁴
b = b00000000000000000000000000000000000000000000000000000000000000000110011001110111111000100000000101000110010100001000111110110111 b = 0x00000000000000006677e20146508fb7 b = x⁶² + x⁶¹ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴¹ + x³² + x³⁰ + x²⁶ + x²⁵ + x²² + x²⁰ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵ + x⁴ + x² + x + 1
10000000000000000000000000000000000000000000000000000000000000000 | 110011001110111111000100000000101000110010100001000111110110111 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------- | 1001100111011111100010000000010100011001010000100011111011011100 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------- | 101010100110000010011000000011110010101111000110010000110110010 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------- | 11001101000111101011100000011011010011101100111010111000000101 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111 c_quotient = 0x00000000000000000000000000000007 c_quotient = x² + x + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000011001101000111101011100000011011010011101100111010111000000101 c_remainder = 0x00000000000000003347ae06d3b3ae05 c_remainder = x⁶¹ + x⁶⁰ + x⁵⁷ + x⁵⁶ + x⁵⁴ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁵ + x⁴³ + x⁴² + x⁴¹ + x³⁴ + x³³ + x³¹ + x³⁰ + x²⁸ + x²⁵ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x² + 1