gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0001000000000000000000000000000000000000000000000000000000000000 a = 0x1000000000000000 a = x⁶⁰
b = b0000000000000000000000000000000010110000110000010101001011111001 b = 0x00000000b0c152f9 b = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
1000000000000000000000000000000000000000000000000000000000000 | 10110000110000010101001011111001 - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 11000011000001010100101111100100000000000000000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 1110011110001000001100100011101000000000000000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 101011101001001011000001100001100000000000000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 111100101001110010011011111110000000000000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 10000100101110111001001000000010000000000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 110100011110101100000011111011000000000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 11000010010101001010001000101010000000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 1110010100101011111000011010011000000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 101010111101010101100110101111100000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 110110001010000110100010001110000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 11010000110000011110000110000010000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 1100000000000001011001101111011000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 111000011000000001101000000111100000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 10100010100000100111010111001110000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 10010010000110010011100110111000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 100010110110000110101101000001000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 1110111010000011111111111111010000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 101111001000010101011010000110100 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------------- | 11000100010000001000111000110 | - 00000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000101110011011110011111001010110 c_quotient = 0x000000002e6f3e56 c_quotient = x²⁹ + x²⁷ + x²⁶ + x²⁵ + x²² + x²¹ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹³ + x¹² + x¹¹ + x¹⁰ + x⁹ + x⁶ + x⁴ + x² + x
c_remainder = b0000000000000000000000000000000000011000100010000001000111000110 c_remainder = 0x00000000188811c6 c_remainder = x²⁸ + x²⁷ + x²³ + x¹⁹ + x¹² + x⁸ + x⁷ + x⁶ + x² + x