gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000040000000000000000000 a = x⁷⁸
b = b00000000000000000000000000000000000000000000000000000000000000001101111001110000111011101111011111000001100011111011011110011011 b = 0x0000000000000000de70eef7c18fb79b b = x⁶³ + x⁶² + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³⁶ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁴ + x²³ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁴ + x³ + x + 1
1000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1101111001110000111011101111011111000001100011111011011110011011 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------- | 101111001110000111011101111011111000001100011111011011110011011000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------- | 11000101001000100110011000110000100001010010000110110001010110100000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------- | 11011010100101000100011000111010001001010111000000110110000010000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------- | 100111001001010100011001101111001001111111110000001100100110000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------- | 10000101110010111110111010010110101111001111111100001011111101100000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------- | 1011011101110110000000001100001011111010111000010111100011011010000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------- | 110100100000110111011100011010100111011011011101100111101000001000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------- | 11000111110100110010100111011011011101010010001010010001100100 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001110010000111100 c_quotient = 0x0000000000000000000000000000e43c c_quotient = x¹⁵ + x¹⁴ + x¹³ + x¹⁰ + x⁵ + x⁴ + x³ + x²
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000011000111110100110010100111011011011101010010001010010001100100 c_remainder = 0x000000000000000031f4ca76dd48a464 c_remainder = x⁶¹ + x⁶⁰ + x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁷ + x⁴⁶ + x⁴³ + x⁴¹ + x³⁸ + x³⁷ + x³⁶ + x³⁴ + x³³ + x³¹ + x³⁰ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²² + x¹⁹ + x¹⁵ + x¹³ + x¹⁰ + x⁶ + x⁵ + x²