In depth study of fast squaring (and multiplication) of large integers

CISC 320 Algorithms and Advanced Programming -- Spring, 2000

Goals. We will move away from the encryption context in order to focus on the algorithmic issues of squaring large integers. The goals are to
1. Create a correct squaring function, ksqr() that is faster than the benchmark classical version in csqr().
2. Calculate the asymptotic cost of your ksqr() by setting up and solving (up to big O) a recurrence relation or summation formula for the run time.
3. By timing experiments, verify or refute that the actual times experienced conform to the expectations from the a priori analysis.
Resources.
1. 320/rsaproject/main3.cc is a draft of a main() for testing ksqr(). It also contains the benchmark csqr(). Copy this as a starting point for your main().
2. 320/rsaproject/Makefile3 is a draft makefile useful for compiling and testing your code. Copy this as a starting point for your makefile.
3. 320/rsaproject/Num.h is a header containing the Num class, which now includes a random Num generator. Read and use this header, but do not change it.
4. 320/rsaproject/stopwatch.h is a header containing the timing stopwatch. Read and use this header, but do not change it. Note: it has been updated.
Deliverables.
1. Correct code: goal (1) is a team goal and the deliverable is the code for your ksqr(), together with a script showing correct computation with (a) a random number, (b) the number B^k - 1 (the number whose B-digits are each 9999) (c) the number 1, (d) the number 0.
2. There will be an optional "race". If you wish to compete, follow instructions to come later for making your ksqr() code linkable to the competition main().
3. Asymptotic analysis and experimental timing study. These goals are met with an individual deliverable, namely a short essay (3 or more pages) dealing with goals 2 and 3. A separate handout will follow itemizing points to be covered.