Question

Multiply the polynomials P1 = x^5 +x^2+ x) by P2 = (x^7 + x^4 +x^3+x^2 + x) in GF(28) with irreducible polynomial (x^8 + x^4 + x^3 + x + 1). The result is

(a) x^4+ x^3+ x+1

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

(c) x^5+ x^4+ x^3+x+1

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

The question was posed to me by my college director while I was bunking the class.

The question is from Polynomial and Modular Arithmetic- III in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Answer 1

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

Best explanation: On performing polynomial multiplication we get with respect to modulus (x^8 + x^4 + x^3 + x + 1) we get x^5+ x^3+x^2+x+1.