Coefficient matrix in AES in Decryption stage

Question

I know that in AES, in encryption stage, in MixColumns, we use [4x4] coefficient matrix with values having only (00,01,02,03). Does anyone know what values are used for coefficient matrix in InvMixColumns at decryption stage? I know those coefficients occur by taking inverse of 00,01,02,03 in rajindel field. I calculated those as

00---------->00  
01---------->01
02---------->141
03---------->246  

The association shown above is coefficient--------->Its inverse in Rajindel field represented in decimal. Are the values correct? I need some confirmation. Thanks in advance!!

Answer 1

The polynomial coefficients of AES are actually:

03, 01, 01, 02

Which can be inverted to:

0B, 0D, 09, 0E

See also section 4.3 of FIPS 197, particular equations (4.14), (4.15), (5.5), and (5.9).

Note that it is not as simple as inverting each coefficient in the field GF(2⁸). Instead, you invert the polynomial in the whole ring of polynomials modulo x⁴+1.