Integrated Science UGS 1430
ACCESS week 2
Summer 2012

University of Utah
University of Utah map
University of Utah directory
College of Science
Math Department
Fernando Guevara Vasquez's home page

JUNE 25-29 2012

     Welcome! I'm Utah Math Professor Fernando Guevara Vasquez. My office is LCB 212, my phone number is 801-581-7467, and my email address is "fguevara at". These notes are posted at our ACCESS Math home page,

     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:
8:00-8:30 a.m.
JTB 120
Introductions; the Math Department is pleased to give each of you complimentary copies of The Code Book, by Simon Singh.
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.pdf.
10:00am-11:00am Two historical ciphers: Caesar shifts and substitution ciphers.
11:00am-12:00pm Math round table. What can you do with a Math major?
Don't forget to read the first chapter, pages 1-44, of "The Code Book" for tomorrow!

Tuesday June 26:
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 1-44) 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
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.
JTB 120
An overview of public key cryptography. Public key cryptography is a late 20th-century 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:
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!
JTB 120
"Genetic Codes," presentation by Biology Professor Jon Seger.

Friday June 29:
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 (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: to automate the encoding/decoding of a message into decimals.