Question

On multiplying (x^6+x^4+x^2+x+1) by (x^7+x+1) in GF(2^8) with irreducible polynomial (x^8 + x^4 + x^3 + x + 1) we get

(a) x^7+x^6+ x^3+x^2+1

(b) x^6+x^5+ x^2+x+1

(c) x^7+x^6+1

(d) x^7+x^6+x+1

This question was addressed to me in an internship interview.

Query is from Polynomial and Modular Arithmetic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Answer 1

Right answer is (c) x^7+x^6+1

For explanation I would say: Multiply and Obtain the modulus we get the polynomial product as x^7+x^6+1.