gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0040000000000000000000000000000000000000000000000000000000000000 a = x²⁴⁶
b = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 b = 0x0000000000000000000000000000000065ee6bda0b324559661859ebf3268b49 b = x¹²⁶ + x¹²⁵ + x¹²² + x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁷ + x¹¹⁵ + x¹¹⁴ + x¹¹³ + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁷ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰³ + x¹⁰² + x¹⁰⁰ + x⁹⁹ + x⁹⁷ + x⁹¹ + x⁸⁹ + x⁸⁸ + x⁸⁵ + x⁸⁴ + x⁸¹ + x⁷⁸ + x⁷⁴ + x⁷² + x⁷⁰ + x⁶⁸ + x⁶⁷ + x⁶⁴ + x⁶² + x⁶¹ + x⁵⁸ + x⁵⁷ + x⁵² + x⁵¹ + x⁴⁶ + x⁴⁴ + x⁴³ + x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³³ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁵ + x²⁴ + x²¹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹¹ + x⁹ + x⁸ + x⁶ + x³ + 1
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10111000110010101111000110111000011101010101101100111111101011101010100010100011101010001111000001010101101011100111011101101100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110011000101100010011000001100011000110011111110110101000111000110010010010011000110110010011110110011111000110110000111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10110111110000100110111010110011010000000110111110000010001010000001010001011010000101100110001000000110001011110101010110111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1111100000111101011100100000111010101100000101100001000100110101101100001101010101001011011010111100000011000100100001100101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11001111100001101001011011101010111010011100101001101110000111011111001110010111111000101111000010011010001001100100001100011000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100010110100100000101011110111111111010111011100100101011110011111110100111010100010010011101111100011010110101010110001010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10000001001010011111100011010111110001110111000000111110101010100111000110110101001011100111000011010110010011110100111110100100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001010111101010010111101100011110100010001010010110100000110001011110110000101100111011010011100110000000000100101100100110110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101111000110110100010010111001110110100010011011110001010000011101101110011101110001000100110011000011001001001101001001111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11101111011000111000101010100110111111011111111010011111011010110100010010001111010001011100100111010101101111001011111011011100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100100101111110101110100010010111010111001101000010101110110011000100010111111111101100001111000110011111100011010100001001110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10110010010000110100011111111111011100000001100110111011101010011101110110011110110101110101111001010011000101110110111101010100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1111001100111111001000001001011011001100111110100110001000110110001000110101110011001001000100110110101010110100111100111000110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11100011100011111101110010001011011010100111101110100010000100111011110110110001111010110001001000110011111001111001010001111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101000010100110000101100111111011111000001111100101000101000010111000110000001010110001100010111010101101010101000001011101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11010101001000011111011010010011110011000011000001010000011011100001010001101011101000011000000101100001110011100011101001110100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11110111111010010000100100111110110100101010011011010110111001101100001011011000100100101011010000111100000110010110011100110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111100001101011101111010001010110001001100001001011100010101000000111011101000001000010110001111011010010101000111000110100010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110110000101110101101100111110000010101101101111110111110001011110111100100000011011001011000100011110001110011010000000110100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10011111110010011000011100100000000011110100110110010100111001000100100111000001101010101101011101101000111110010101101111101000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1010100000101010101000010010100000110010010100100011110010101101000010111110001000110010000000010001110101101000100110101111010000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 110001111110110011101101001110000100100001101101011011000011111110001111101001010000001110101101111101100100101100011000110011000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11000011000000111010100011000101111000001001111001101000110101000011100101011011000001111010000100000000011000001110010111100000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1000110111110111111101110001111101101111101011100010011001101111010101101011101101000111011011100110001011011111001101110010000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1000100110010011111101001110001110111011000011100101100101000010011111001111110000001101001111000111000100111111011110101111110000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100001001001111001000110101011110101101011010101101001111110000101100001100110010111110111010111001011101110010011011000110111000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10011110100001010010001000110110100110010110001001011010101001110101101101010011100111000000000110010001010100111001110010011100000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1010101010110011111010110000010100011110000011011010000000101011001011101100011001011111101011001110111000111101000101000001110000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 110000101101111001111001011000100001000011010010010101010011001111000101111011011101100011110110000100001110000000000101000111000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10010000001010101110110101100000011010110110110111111000000100001001110111010110101100100001111101101010110100010011100011100000000000000000000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100111011110110010011100011011100111010001000010101010101111000010011110010011101001101011010000110001010011110000010011111100000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10100101010100110011000001100101100010001011101111111001010100000110001011111111110101111111000010011010011000111110110101000000000000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011011000011000110000001011100101011110110100110110101110111100100011010111001111011100110010001111000010000111000010011011000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111110111000100000101110000110101001000101101111110000100001110010000010100001101101111000111110001011011001010000111110010001000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100000101010011111001101011101000011100001011010010001010111001001110101101100110110111101001110010111101100100101000110101100000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101010001111001100010000111000001010010010011010100000001011111101101110100100000100011100001100100100101001101101011100101000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110001111101110101001101001100111101001001110110000010101110000000000110001101000111100010010111001010001000101111110111110000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10100000110010011100010010110111111111010111111000111111000010110011110010101010001111100111000111001000001000111011010111001000000000000000000000000000000 | - 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c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111011010000111110111010110010101011100010001111111100011101000011001101000110001001110001011001011101001011110000111011 c_quotient = 0x0000000000000000000000000000000001ed0fbacab88ff1d0cd189c5974bc3b c_quotient = x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁷ + x¹¹⁵ + x¹¹⁴ + x¹¹² + x¹⁰⁷ + x¹⁰⁶ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰³ + x¹⁰¹ + x¹⁰⁰ + x⁹⁹ + x⁹⁷ + x⁹⁵ + x⁹⁴ + x⁹¹ + x⁸⁹ + x⁸⁷ + x⁸⁵ + x⁸⁴ + x⁸³ + x⁷⁹ + x⁷⁵ + x⁷⁴ + x⁷³ + x⁷² + x⁷¹ + x⁷⁰ + x⁶⁹ + x⁶⁸ + x⁶⁴ + x⁶³ + x⁶² + x⁶⁰ + x⁵⁵ + x⁵⁴ + x⁵¹ + x⁵⁰ + x⁴⁸ + x⁴⁴ + x⁴³ + x³⁹ + x³⁶ + x³⁵ + x³⁴ + x³⁰ + x²⁸ + x²⁷ + x²⁴ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁵ + x¹³ + x¹² + x¹¹ + x¹⁰ + x⁵ + x⁴ + x³ + x + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111100101100010011100010010000011001001001000100001110100111100000001000010001011110100111100001111011001111000100011000100011 c_remainder = 0x000000000000000000000000000000003cb1389064910e9e02117a787b3c4623 c_remainder = x¹²⁵ + x¹²⁴ + x¹²³ + x¹²² + x¹¹⁹ + x¹¹⁷ + x¹¹⁶ + x¹¹² + x¹⁰⁹ + x¹⁰⁸ + x¹⁰⁷ + x¹⁰³ + x¹⁰⁰ + x⁹⁴ + x⁹³ + x⁹⁰ + x⁸⁷ + x⁸⁴ + x⁸⁰ + x⁷⁵ + x⁷⁴ + x⁷³ + x⁷¹ + x⁶⁸ + x⁶⁷ + x⁶⁶ + x⁶⁵ + x⁵⁷ + x⁵² + x⁴⁸ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴¹ + x³⁸ + x³⁷ + x³⁶ + x³⁵ + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁵ + x²⁴ + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁴ + x¹⁰ + x⁹ + x⁵ + x + 1