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 = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111 b = 0x00000000000000009aba68ef0cf5c2bf b = x⁶³ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴³ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³³ + x³² + x²⁷ + x²⁶ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1101010111010011010001110111100001100111101011100001010111111000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 100111101101001001011111001011101101011010110111101011101000111000000000000000000000000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1000110100000110111110000011101101001000010011011000011000100000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1011110111100100100001101010001000100101110000100010010011111000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10011101011110111011100100110100101001001101111110011001000111000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 111110000011101000111011011101010000010101001011011101000110000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11000101000000001010011100110100000100110111110101101101101111100000000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1011111101110101100111111011011000111111000100010101111000000010000000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10010111001111111101110101100100110011111001001001110010111101000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1101100001011011010110001011110000110110011110110000010010110000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 100001011100001001100000101001100111010100011101100011000001111000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 111110111100000001000010010010111100111101000010011101010000100000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11000010111101000101010101001001100001110110111101101111011011100000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1011000010011100011110110100110100010111001101010101101110100010000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10101000100110000100111010001000011011110000001001100100011101000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 110010001000100010011001100111011000111111011110100110110010110000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10100100011001011110001011100101000001100101011010110011001001100000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 111110110111111000101000001010000010101010001101110001100110010000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11000011100010001000000110001110010011001111000000001001101101100000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1011001001100101110100101100001010000000000010111001011000010010000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 10100011011111101110100010110110001100111111100101010010101101000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 111001110001001000000001011001001111110000110010010000000010110000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11111011010100001101001100010111111000011000111100000101001001100000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1100001111010101011101111111000111011010111101011000111100110010000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 101100101101111000111110001111011010110000000000100110110001101000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1010000110010001010110110100101010000011110101010110011010010100000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11101100101011001100111010010110001111001000001010010000101011000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1110110000101101010011001111001001100000111011101010010000100110000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 111011010010111001001000001110101101100000110110110011010011001000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11101111001010000100000110101011101010011000011000011111000110100 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 1110101100100100010100101000100101001010111001111011101101001010 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------- | 111000110011110001110100110011001000110000100100111100111110101 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000001001100001001010000111010001100111010110111010111101011111 c_quotient = 0x000000000000000002612874675baf5f c_quotient = x⁵⁷ + x⁵⁴ + x⁵³ + x⁴⁸ + x⁴⁵ + x⁴³ + x³⁸ + x³⁷ + x³⁶ + x³⁴ + x³⁰ + x²⁹ + x²⁶ + x²⁵ + x²⁴ + x²² + x²⁰ + x¹⁹ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁶ + x⁴ + x³ + x² + x + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000111000110011110001110100110011001000110000100100111100111110101 c_remainder = 0x0000000000000000719e3a66461279f5 c_remainder = x⁶² + x⁶¹ + x⁶⁰ + x⁵⁶ + x⁵⁵ + x⁵² + x⁵¹ + x⁵⁰ + x⁴⁹ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴¹ + x³⁸ + x³⁷ + x³⁴ + x³³ + x³⁰ + x²⁶ + x²⁵ + x²⁰ + x¹⁷ + x¹⁴ + x¹³ + x¹² + x¹¹ + x⁸ + x⁷ + x⁶ + x⁵ + x⁴ + x² + 1