CS216: Problem Set 5: 0101 0000 0101 0011 0000 0101
1 of 4 3/22/2006 10:21 AM
University of Virginia Computer Science
CS216: Program and Data Representation, Spring 2006
http://www.cs.virginia.edu/cs216/ps/ps5/
22 March 2006
[PDF version for printing]
Problem Set 5
Representing Numbers
Out: 22 March
Due: Wednesday (beginning of class), 29 March
Collaboration Policy - Read Carefully (similar to PS4)
For this assignment, you may work on your own or with any one other person of your choice except for
anyone you worked with on PS3 or PS4. If you work with a partner, you should turn in one assignment
with both of your names on it. If you would prefer to be assigned a partner, send email to
[email protected] before 5pm on Friday, 24 March (include any constraints or preferences you have
on your assigned partner). If a suitable match requests a partner, you will receive a partner assignment.
Partners will be assigned using a greedy algorithm based on when requests arrive, so you are more likely to
receive a suitable partner assignment if you send in your request early.
You may consult any outside resources including books, papers, web sites and people you wish, except you
may not copy code from other big number representation implementations. There are many implementations
of big numbers in C available on the web (for example, there is one in the Python interpreter and GMP), and
it would certainly defeat the purpose of this assignment if you copied one of them instead of thinking on
your own. You may look at design documents for big integer implementations is you wish, but we
recommend thinking about your own design first, and only looking for other designs if you are really stuck.
You are also encouraged to discuss these problems with students in the class. You must acknowledge any
people and outside resources you work with on your assignment. If you discuss the assignment with people
other than your partner, you may not take any written materials out of your discussion. It is fine to bounce
ideas off other people, but the answers you turn in must be your own.
You are strongly encouraged to take advantage of the staffed lab hours posted on the CS216 web site.
Purpose
Learn how numbers are represented.
Discover experimentally properties of your C implementation
Implement a variable-length integer encoding in C that is better than Microsoft's (Excel)
Submission: For this assignment, you should submit all your answers
(including code) on paper in class on March 29. In addition, you should
submit your code for your bignum implementation (questions 7-9)
electronically using the form at
http://www.cs.virginia.edu/cs216/ps/ps5/submit.html
Power Analysis
Differential Power Analysis is a technique for analyzing the power consumption a device uses to determine
something about the cryptographic keys is contains. The amount of current a processor uses depends on
what operations it is performing. In particular, flipping the value of a bit uses more current than when the
same value is maintained. Although the current differences is small, they can be measured (especially if the
processor is repeatedly performing operations).
Here, we will consider a simple hypothetical smart card with one 8-bit register using little-endian encoding.
The current used for each operation scales linearly with the number of bits in the register that flip (either a 0
becomes a 1, or a 1 becomes a 0). The card implements a simple counter: the value in the register increases
