(i) Explain the idea of public key cryptography. Give an example of a public key system, explaining how it works.

(ii) What is a general feedback register of length $d$ with initial fill $\left(X_{0}, \ldots, X_{d-1}\right)$ ? What is the maximal period of such a register, and why? What does it mean for such a register to be linear?

Describe and justify the Berlekamp-Massey algorithm for breaking a cypher stream arising from a general linear feedback register of unknown length.

Use the Berlekamp-Massey algorithm to find a linear recurrence in $\mathbb{F}_{2}$ with first eight terms $1,1,0,0,1,0,1,1$.