gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100010101000000010101010100000000 a = 0x00000000000000000000000115015500 a = x³² + x²⁸ + x²⁶ + x²⁴ + x¹⁶ + x¹⁴ + x¹² + x¹⁰ + x⁸
b = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000001000000000000000001 b = 0x00000000000000000000000010040001 b = x²⁸ + x¹⁸ + 1
100010101000000010101010100000000 | 10000000001000000000000000001 - 10000000001000000000000000001 | 1 --------------------------------- | 10101010000010101010100010000 | - 00000000000000000000000000000 | 0 - 00000000000000000000000000000 | 0 - 00000000000000000000000000000 | 0 - 10000000001000000000000000001 | 1 --------------------------------- | 101010001010101010100010001 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001 c_quotient = 0x00000000000000000000000000000011 c_quotient = x⁴ + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101010001010101010100010001 c_remainder = 0x00000000000000000000000005455511 c_remainder = x²⁶ + x²⁴ + x²² + x¹⁸ + x¹⁶ + x¹⁴ + x¹² + x¹⁰ + x⁸ + x⁴ + 1