
WEEK 2, A.M. SCHEDULE JUNE 2529 2012
Welcome! I'm
Utah Math Professor
Fernando Guevara Vasquez.
My office is
LCB 212,
my phone number is
8015817467, and my email address is
"fguevara at math.utah.edu". These notes are posted at our
ACCESS Math home page,
http://www.math.utah.edu/~fguevara/ACCESS2012
Sara Sanders (sciencechick316 at gmail dot com)
is our ACCESS TA for the entire Summer session, and
Heather Brooks (h.brooks11 at gmail dot com)
is our math TA. Heather is an undergraduate Math major.
Our theme for the first math week will be codes and cryptography. Our
planned schedule is below, although
it could change as the week
progresses. This class is based on previous ACCESS classes by Nick Korevaar.
Monday June 25:
8:008:30 a.m.
JTB 120

Introductions; the Math Department is pleased to
give each of you complimentary copies of
The Code Book, by Simon Singh. 
8:30am10:00am
Marriott Library 1008

I'll hand out copies of these notes: computers.pdf, computers.doc. Introduction to the lab: your accounts,
email, internet, software; emailing
Fernando your formula for the group assignment function that produces the group assignment: group_assignment.pdf using Maple's mod and trunc functions. Fernando's problem is here:
groups.mw, groups.pdf.

10:00am11:00am

Two historical ciphers: Caesar shifts and substitution ciphers.

11:00am12:00pm

Math round table. What can you do with a Math major?


Don't forget to read the first chapter, pages 144, of "The Code Book" for
tomorrow!

Tuesday June 26:
8:30am10:30am.
Marriott Library 1745

An introduction to historical cryptography: Caesar Shifts and other
substitution ciphers, as described
in "The Code Book". Please read chapter 1 (pages 144) before class.
Simon Singh tells the story of how Mary Queen of Scots lost her head,
not understanding how easy it is to break substitution
ciphers with frequency analysis. There is a cipher for us to solve,
and MAPLE 13 will help us. Everything we need to know is in
Tuesdaydocs

10:45am11:15am
JTB 120

After solving the substitution cipher problem above via frequency analysis,
we'd like you to exercise your thinking abilities in different ways by
considering one of the most fundamental historical code breaking successes
ever: we'd like each group to use experimental data and logic to deduce the
"genetic code" most of you learned as a "fact" in biology. Here's the
background for the problem,
Cracking_the_Code.pdf, and your precise group assignment,
bio.pdf.
Utah evolutionary biology Professor
Jon Seger, who will be presenting on Thursday, created
the Cracking_the_Code document. We're hoping each group is ready to
contribute to a discussion of
solutions on Thursday, before Jon's presentation! Heather's presentation is here: dna.pdf.

11:15am12pm
JTB 120

An overview of public key cryptography.
Public key cryptography is a late 20thcentury
conceptual
breakthrough that has allowed the internet to be used for
secure transactions. We'll be working for most of the rest of
week 2 to understand the
number theory behind the most widely
used public key system:
RSA cryptography. Here are our notes for this discussion:
overview.pdf.

Wednesday June 27:
8:30am12pm
JTB 120

We'll discuss and work with the modular arithmetic (also sometimes called "clock" or "remainder" or "residue" arithmetic) which underlies RSA cryptography; we'll
get comfortable with the
operations of addition, subtraction, multiplication, and using the
multiplicative inverse (don't say "dividing"!) in
modular number systems.
Remember prime numbers, greatest common divisors, and
all the arithmetic surrounding these
ideas that you thought you'd never see again? Well, surprise!
Here
are the notes: modulararithmetic.pdf.
Next, we'll
learn about the amazing (and confusing at first)
Euclidean algorithm for finding gcd's and multiplicative
inverses in modular arithmetic.
Here are the notes:
Euclid.pdf.

Thursday June 28:
8:30am  9:40am
JTB 120

Continuing discussion of the number theory behind RSA cryptography.
We'll begin with a few volunteers showing some of
yesterday's homework problems on multiplicative inverses
via the Euclidean algorithm. Then we'll move on to power functions
in modular arithmetic, with these class notes:
modularpowers.pdf. We'll also use
the
Tom Davis notes on cryptography, which are a nice distillation of
historical cryptography ideas, culminating in RSA public key
cryptography.
Other good references are the latter chapters of "The Codebook", Wikipedia,
and the original breakthrough
paper by
Rivest, Shamir, Adleman.

9:50am  10:20am
JTB 120

Problem session on the genetic code problem: Each group should be
prepared to contribute!

10:30am12:00pm
JTB 120

"Genetic Codes," presentation by Biology Professor
Jon Seger.

Friday June 29:
8:30am12pm
Marriott Library 1745 
We'll finish the number theory behind RSA cryptography and then
work through the Davis notes
example of RSA encryption together, letting MAPLE do
the math steps. The Maple document you need to open is
RSA.mw. (To see what this looks like with the commands filled in,
see RSAverbose.pdf)
We'll also use the
Alice and Bob diagram from last year (so the date is wrong
on the document). After we understand RSA,
groups will begin their week 1 project work in the
MARRIOTT computer lab  Here is the precise project assignment
for week 1:
project1.pdf.
It may be easier for you to use these procedures: Davisconversion.mw to automate the encoding/decoding of a message into decimals.


