Here is the review sheet for Test II.
This old Test II
is quite relevant!
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.
r0 = 17095033985347620322312208998211349754784699505662663188767279924260488147466624244881066214190499158789
r0 = 20209288560578417940964655171917242822775146594947442847858148938943002031537832340649136056684927964773486010213023262921698530556714674256696201775404906568320413746465738033592707256087039745249872352307599377
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.
Here is my Euclidean algorithm spreadsheet calculator.
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.
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.
a Test II
a Test I review sheet
a Test II review sheet
a Test II review sheet
a Test III review sheet