University of Massachusetts, Amherst
Math 471
Number Theory
Fall 2006
Click here to go the Main 471 Page
Class "Treasure Hunt"
This is an optional project for the entire class. Upon successful
completion of the treasure hunt before 11 pm Tuesday Dec. 19, 2006, I
will send to everyone in the class a copy of the final exam by e-mail.
But note that success will require cooperation among, if not all, then at
least a large percentage of the students in the class, because each
student will know only a small (encrypted) piece of the puzzle. Each
student will be sent an e-mail containing a number C which is the
encoding of a message M using the RSA encryption algorithm with
encryption key
n=1501311474263642216088455349744054707074510377730742132093950832818212164920853651140306713288071590535768003486533257194308255320295008485975893844879484549490690073538068682454982135510830059767786178366221998120693166078203841
e=1777
Below you will find a list of all 30 students in the class in a
numbered sequence.
If the decoding of the message for student 1 is M1, for student 2 is M2,
etc. then the TOTAL PLAINTEXT is simply the concatenation M1 M2 M3 etc.
which, when converted according to the ASCII Table will spell a
SECRET MESSAGE. If, by 11 pm Tuesday 12/19, a currently enrolled
Math 471 student brings this SECRET MESSAGE to me in person or by e-mail,
then I will e-mail a copy of the Final Exam
to everyone in the class.
Note: some people may be unable/unwilling to participate. Even if
only half of the students participate, you'll probably be able to
figure out the missing parts of the message easily once you decrypt
the coded messages that you know. Some students
may be more savvy about doing arithmetic with large integers on a
computer: there is no requirement that each student do their own
decoding. If you want to elect an individual or group to collect
all the information from the students and do the arithmetic, that is
perfectly legal. Please be sure to maintain a sense of collegiality
and politeness toward your fellow classmates whether they want to
participate or not. We never used it all semester but if you
log in to WEBCT, you should have a M471 page there, where you can
post messages to the bulletin board for all M471 students to see,
or you can just talk to each other by e-mail: your addresses will
all appear there.
Besides figuring out how to share all the information with each other,
the bigger problem will be that you'll have to find the decryption key
d -- Will Patrick's Program be able to factor n so you can figure out
phi(n) and then d?! (This n is a lot bigger than the n of the Mini-Me
project). What if you are unable to factor n in time using brute
force, is there any other trick you can use to find the secret
message? I have left several doors into the secret slightly ajar on
purpose -- I have a small list of hints to drop if students have
time/interest in this project and make some progress.
Once you decode your message, to convert it quickly into words from numbers
using ASCII, you can use, for example
http://www.paulschou.com/tools/xlate/
Good Luck! Don't waste too much time on this: you're better off studying.
Look to receive your coded message in your e-mail box. They have all
been sent out now (1 am, Fri Dec 15).
========================== Order of Students ================
1 Braley,Emily
2 Carlson,Stefanie
3 Cheung,Vernon
4 Chinnapongse,Vivien
5 Dasilva,Ashley
6 Dullea,Kerry
7 Grimaldi,Kevin
8 Huynh,Tin T
9 Johnsen,Kristen
10 Kelley, Robert
11 Kuksin,Maksim
12 Lacourse,Karen
13 Langlois,Timothy
14 Malloy,Michael
15 Matevossian,Ara
16 McColgan,John
17 Meehan,Matthew
18 Monahan,Elizabeth
19 Myers,Jonathan
20 Papadopulos,Patrick
21 Rich,Sarah
22 Rizki,Nicole
23 Rossolimo,Elizabeth
24 Selsov,Roger
25 Siegler,Aaron
26 Simmons,Byron
27 Somerfield,William
28 Traversi,Jaclyn
29 Wheeler,Alden
30 Widak,Christopher