Question

On multiplying (x^5 + x^2 + x) by (x^7 + x^4 + x^3 + x^2 + x) in GF(28) with irreducible polynomial (x^8 + x^4 + x^3 + x + 1) we get

(a) x^12+x^7+x^2

(b) x^5+x^3+x^3

(c) x^5+x^3+x^2+x

(d) x^5+x^3+x^2+x+1

I had been asked this question in examination.

I'm obligated to ask this question of Polynomial and Modular Arithmetic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Answer 1

The correct answer is (d) x^5+x^3+x^2+x+1

Explanation: Multiplication gives us (x^12 + x^7 + x^2) mod (x^8 + x^4 + x^3 + x + 1).

Reducing this via modular division gives us, (x^5+x^3+x^2+x+1)