Week 7

Question 1

Find the order of an element of 𝑍_𝑝 for 𝑝 prime

Question 2

Prove that the order of an element of 𝑍_𝑝 for 𝑝 prime is a divisor of 𝑝−1

Question 3

Define the term primitive element of 𝑍_𝑝 for 𝑝 prime

Question 4

Appreciate that all elements of 𝑍_𝑝 for 𝑝 prime can be expressed as powers of a primitive element

Question 5

Determine whether an element of 𝑍_𝑝 with 𝑝 prime is primitive

Question 6

Appreciate that the Discrete Logarithm Problem in 𝑍_𝑝 for 𝑝 prime is believed to be computationally difficult for suitably chosen 𝑝