gf(2) mod

c = a % b

Calculate c = a/b, result is cremainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000010101010100010100010001010100010101000101000000000000000101000101010001010101000000000101010101
a = 0x00000000554511515140005151540155
a = x94 + x92 + x90 + x88 + x86 + x82 + x80 + x76 + x72 + x70 + x68 + x64 + x62 + x60 + x56 + x54 + x38 + x36 + x32 + x30 + x28 + x24 + x22 + x20 + x18 + x8 + x6 + x4 + x2 + 1

b = b00000000000000000000000000000000000001000000000001000101000000000100010101000100000000010001000101010000010001010000010001000101
b = 0x00000000040045004544011150450445
b = x90 + x78 + x74 + x72 + x62 + x58 + x56 + x54 + x50 + x40 + x36 + x32 + x30 + x28 + x22 + x18 + x16 + x10 + x6 + x2 + 1

  10101010100010100010001010100010101000101000000000000000101000101010001010101000000000101010101 | 1000000000001000101000000000100010101000100000000010001000101010000010001010000010001000101
- 1000000000001000101000000000100010101000100000000010001000101010000010001010000010001000101     | 1
  ----------------------------------------------------------------------------------------------- |
    101010100000101000001010101010000010100000000000100010100010001010101000001000100010100000101 |
-  0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000    | 0
-   1000000000001000101000000000100010101000100000000010001000101010000010001010000010001000101   | 1
  ----------------------------------------------------------------------------------------------- |
      1010100000001010101010101000001000000010000000101010000000100010100000100000101010000010001 |
-    0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000  | 0
-     1000000000001000101000000000100010101000100000000010001000101010000010001010000010001000101 | 1
  ----------------------------------------------------------------------------------------------- |
        10100000000010000010101000101010101010100000101000001000001000100010101010101000001010100 |

cquotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010101
cquotient = 0x00000000000000000000000000000015
cquotient = x4 + x2 + 1

cremainder = b00000000000000000000000000000000000000010100000000010000010101000101010101010100000101000001000001000100010101010101000001010100
cremainder = 0x00000000014010545554141044555054
cremainder = x88 + x86 + x76 + x70 + x68 + x66 + x62 + x60 + x58 + x56 + x54 + x52 + x50 + x44 + x42 + x36 + x30 + x26 + x22 + x20 + x18 + x16 + x14 + x12 + x6 + x4 + x2