Question

Find the inverse of (x^5) modulo (x^8+x^4 +x^3+ x + 1).

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

(b) x^5+ x^4+ x^3

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

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

I had been asked this question in my homework.

The above asked question is from Polynomial and Modular Arithmetic topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Answer 1

Right choice is (c) x^5+ x^4+ x^3+1

The best explanation: Finding the inverse with respect to (x^8+x^4 +x^3+ x + 1) we get x^5+ x^4+ x^3+1 as the inverse.