9. Determine how long (years, days, hours, seconds) it will take one million computers, each capable of processing one million operations per second, to: (a) multiply two 1000-bit numbers together; (b) perform a complete exhaustive search for a 128-bit key; (c) find the correct key (on average) while performing an exhaustive search for a 128-bit key.

10. Suppose we want a cover time of 10 years for a particular plaintext. You see an advert for a encryption product from Cqure Systems that claims: Our encryption product is so strong that even taking into account future improvements in computer power, a complete exhaustive search of the key space will take 40 years! Do you think you should buy it?

14. Suppose that you have been asked at work to recommend the strength of encryption needed to protect the contents of a database. Draw up a list of some of the questions that you think you will need to answer before you can meaningfully attempt to establish a notion of practical security for this application.