The AES algorithm uses the irreducible polynomial x^8+x^4+x^3+x+1 for multiplying with MDS and inverse MDS matrix for encryption and decryption, respectively.
Can we change this polynomial with another one?
Should we redesign the MDS matrix if polynomial is changed?
Yes you can. The poly must be irreducible. Any irreducible poly can be used. After changing it you have to change MDS matrix.
Yes you can. The poly must be irreducible. Any irreducible poly can be used. After changing it you have to change MDS matrix.
Dear Colleague,
Good Day,
Try and read these attached articles and see the link too, it might help you alot.
http://math.stackexchange.com/questions/1221056/greatest-common-divisor-of-polynomial-in-finite-field256-aes
Yes, technically it is possible to use any irreducible polynomial of degree 8.
(Main) Implications:
- you have to implement a change of basis or change the polynomial for the S-Box as well
- security may be significantly reduced
- will give different results for encryption - so it is no longer AES.
See this paper for a more detailed discussion:
https://www.sav.sk/journals/uploads/0728130812GMTW.ps
Yes we can change irreducible polynomial with another one irreducible polynomial and correspond we can redesign Maximum Distance Separable Matrix for encryption & decryption respectively.
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