Math 406, Spring 2016: Class Announcements

Welcome

Welcome to the class! Class announcements and useful documents will appear here. New material will be added at the top. Make it a habit to look here. I'm going to try keeping the lecture notes and an indication of the current assignments at the top of the page: watch for other things that might appear below.

Test II announcement

The test will be on April 15th. I feel free to cover anything on the assignments up through assignement VI, but also may indicate specific things covered next week which I may ask about. A practice test or review guide will be posted here some time next week.

Here is the review sheet for Test II.

This old Test II

is quite relevant!

Secret Message Zone

I have updated the files (the RSA file in my M406 project whose name indicates that it has been cleaned up is the right one). If you run all functions in that file, then in the last section insert your own numbers into the lines beginning

p=primehunt(your first number)

q=primehunt(your second number)

[the numbers having 100 digits or so], you can generate and test your own keys. When you have a key, send it to me and I will post it here. I may shortly set up functions for encrypting text into numbers so that we can do encoding and decoding of English text. You are welcome to write your own of course.

Randall Holmes Public Key

N = 20597352664303763308548994011836726996206151441325294535170674366084669757591362472387531537553822881253

r0 = 17095033985347620322312208998211349754784699505662663188767279924260488147466624244881066214190499158789

Stacia Orr Public Key

N = 50486888763958338533823009066235702883730243987263712430159863499611492021215614423073406357978029614997388216006698878679990184281868788441673541587637738062015325594978253535138424079004968032520626546734151477

r0 = 20209288560578417940964655171917242822775146594947442847858148938943002031537832340649136056684927964773486010213023262921698530556714674256696201775404906568320413746465738033592707256087039745249872352307599377

The Current Assignment(s)

Last assignment: 24.1, 24.2, 24.3, 24.4, 25.1, 31.1, 31.3 (hard, but do try out the formula in 31.3c). Due Wednesday by 5 pm.

Please send me your RSA key to be posted above below mine. All of you should now have access to my Math 406 project on www.sagemath.org: please copy the updated version RSAcleanedup of my RSA file to your account to work on. Please also encrypt a message for me (this can just be a number, though if you want to tell me how to decrypt it to text I will do so) and send it to me.

Assignment VI: 28.1, 28.2a (the proof in b we did in class: it would do you no harm to study it), 28.4, 28.6, 29.1, 29.2, 29.6 [all chapter 29 problems optional, but notice that 29.6 introduces another cryptosystem; I will have to have a digression about "indices" to support these three problems: read section 29 and the idea will be clear -- an index is basically a logarithm to the base of a primitive root], 20.1, 20.3 opt, 21.1, 21.3, 21.5, 22.1, 22.2, 22.7, 22.8 [the last two problems show that at least sometimes we can compute square roots]. This assignment is due on the 13th; I'll do my best to grade the papers and have them available at my door before the exam. If you complete the assignment earlier, your chances of getting it back before the exam improve.

This is the source for my recent lecture on Carmichael numbers (or parts of it). I will be adding a section to my notes about this as well. You can earn kudos (this might make it into a future homework assignment) by extending the author's table on page 4 to more pairs of primes and finding some more Carmichael numbers with three factors. My new notes section will include some discussion of his procedure but his discussion on the previous couple of pages is actually pretty clear.

The Lecture Notes from 2015 (and other tools)

Here are the lecture notes from 2015: we will transform them into "the lecture notes from 2016" as we go along. I am sure that there are some good note readers out there, who can catch typos and other slips...read, and find them (I give points if you find them before I do)!

Here is my Euclidean algorithm spreadsheet calculator.

Office Hours and Schedule

I am teaching Math 314, Real Analysis, TTh 12--1:15 MB 124 and Math 406, Advanced Number Theory, WF 10:30--11:45 MB 139. I participate in the logic seminar, which meets 3-4 PM W in MB124. I am tentatively defining my office hours as 9:15 -- 11:45 am TTh, 9:15 -- 10:15 am WF, 3 -- 5 pm TF (not WTh). I expect not to be routinely on campus at all on Mondays, though you are welcome to request an appointment if you need to meet me on a Monday. I expect to be around most of the day TWThF.

Old Assignments

Assignment V, section 14.3 in the notes, p. 43, due on the 30th (it was due on the 18th but I just now realized on the morning of the 16th that I had not posted this last week when I thought I had...).

In addition, please make certain that you have a Sage account and access to my Math 406 project. Please don't edit my project files in place -- copy them to your own account before doing anything with them! I would like each of you to use the tools in the project to generate a 200 digit RSA key for yourself. I will demonstrate soon by posting mine. Then we can send Secret Messages. Details to follow.

Test Review announcement for Test I

We do have a Test this Friday the 26th! This Test I paper is highly relevant.

So is this a Test I review sheet. I went over these in class. When I have written the test, I may telegraph some warnings about questions I ask which require you to review something unexpected on the basis of these documents. Assignment IV, section 9.4 in the notes, on p. 35 is due Friday March 3 after the test (I am extending the due date of the assignment because of malfunctions of this web page) and is test relevant. I may add a couple of problems on more recent material to this assignment.

In addition, a worksheet of RSA problems is here. You will see that this is a problem set from an ancient course, but it should serve our purposes. You can in addition do problem 18.1 in the text (low-tech) and problem 18.4 if you want to try out higher tech. Notice that the worksheet has the numerical solutions in it already, so you will get immediate feedback on whether you are doing it right.

Assignment III, section 6.4 in the notes on p. 27 is due on Friday, February 12th.

Assignment II, section 4.3 in the notes on p. 17, is due on Friday, January 29th.

Assignment I, section 2.4 in the notes on page 9, is due on Friday, January 22nd.

Everything below below this point is old stuff from the 2014 page, which I have preserved where I think it might be Useful.

Old Stuff which Might Be Useful (if it is relevant to you it will be moved upward)

a Test I

a Test II

a Test I review sheet

a Test II review sheet

a Test II review sheet

a Test III review sheet