I need help with part b. I couldn't come up with a formula for doubling the speed every 18 months. Here is the question:

Suppose we have an enhanced version of DES that uses 128 bit keys instead of 56 bit keys.

a. If a DES chip can do three decryptions in five clock cycles and it is clocked

at 4 GHz, compute the average and worst case time (in years) required to

do a brute force attack with a known plaintext. How does this compare

with the age of the earth which is estimated to be 4.55 billion years?

b. If the chip speed doubles every 18 months (Moores Law), how many

years do we have to wait before this enhanced version can be broken by

brute force in 24 hours? How do the results change if 10000 chips run in

parallel in each case? Compare the times and comment on the results.