gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x01000000000000000000000000000000 a = x¹²⁰
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
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1101111001110000111011101111011111000001100011111011011110011011 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 101111001110000111011101111011111000001100011111011011110011011000000000000000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11000101001000100110011000110000100001010010000110110001010110100000000000000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11011010100101000100011000111010001001010111000000110110000010000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 100111001001010100011001101111001001111111110000001100100110000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10000101110010111110111010010110101111001111111100001011111101100000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1011011101110110000000001100001011111010111000010111100011011010000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 110100100000110111011100011010100111011011011101100111101000001000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11000111110100110010100111011011011101010010001010010001100100000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11001101000111100011100101100101101001010110100100110000010110000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10011011011101101011110010010011001001110011010000111110000110000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1000101000001100101001001100100111001101011101110001001100000110000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 101010001111100010010100011111000001100111110001010010010011101000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11101101000100001111010100010111101100001111110111111101010000100000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 110011011000000001101111100000011100010111001001001010110110010000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 100111111000010000001011101100000010001000110100111001111111100000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10000011111010011100101010001111110001110111011010100000110001100000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1011101100110010010010001111000000001101111100100010111010111010000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 110010101000010101001100000011111001100011111011001100100100001000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 101001111010110100010111110000101100101110100100001011101100100000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11110011101110111111001001101010000101000101011100110010101001100000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 101101110010110001110010011101110101011101100010000101001111010000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11010010101110010011100100000001001011011101101101000110110111100000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1100110010011101011111110110111011000101010011110001010001010000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1001011101101100100011001100100000100110000001010001111001011000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 100100100011100011000100011111111100111100010101010100111000011000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10011000100100000101010100010000000111010011010111001000001110100000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1000110111000001011101111100111110111001011101001111111101000010000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 101001110110001100110010011100001111000111110110100100011011001000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11110010001001111011100100001110011000001111001001001100010100100000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 101100010101110101011111111001101000010111110111111011110010010000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11011110010110110110001000100010100010001111000010110001011111100 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1010111000110011010101010010010111111100000110111001010 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000001110010000111100010010011110100111100110110001001111110110 c_quotient = 0x00000000000000000390f127a79b13f6 c_quotient = x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵² + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴⁰ + x³⁷ + x³⁴ + x³³ + x³² + x³¹ + x²⁹ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²⁰ + x¹⁹ + x¹⁷ + x¹⁶ + x¹² + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x⁴ + x² + x
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000000000001010111000110011010101010010010111111100000110111001010 c_remainder = 0x0000000000000000005719aa92fe0dca c_remainder = x⁵⁴ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁴ + x⁴³ + x⁴⁰ + x³⁹ + x³⁷ + x³⁵ + x³³ + x³¹ + x²⁸ + x²⁵ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹¹ + x¹⁰ + x⁸ + x⁷ + x⁶ + x³ + x