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 during an internship interview.

The query is from Overview topic in chapter Cryptography Overview, TCP/IP and Communication Networks of Cryptograph & Network Security

Answer 1

Correct option is (b) x^5+ x^3+ x^2+x+1

The best I can explain: 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.