Today, we’re going to try a little Quadratic Sieve factoring. Let n = 539873. Use the Quadratic Sieve Tools to show how the Quadratic Sieve would factor this. That is, write up a description of your factor base, what numbers you will B-factor and where they come from, what results (“facts”) you get, and how you use that to factor. Hand this in on the dropbox. Note: it’s up to you how many primes to keep in the factor base, and how big a list of numbers to B-factor. Just try to guess how much you’ll need to get facts, and expand your net if you need to. Comment: I say “would factor this” because I’m going to allow you a little shortcut. I’ve built in a “B-factor” function that will factor out small divisors of a number. You set the factor base and then it will factor powers of those numbers out. In the real quadratic sieve, you would use “sieving” to find the B-factorizations, not do them one-by-one (for runtime reasons). Instead, here, the tools will simply print out the B-factorizations and you can proceed from there.

Also To Do: Please finish the RSA ciphertext chain (including decrypting the message sent to you) because it’s important practice.

Announcement: There’s a Math Club at CU that hosts talks. Here’s the website (I’m speaking Tue morning) http://math.colorado.edu/mathclub/.

Module “corrections” (repeating because it’s important). I’d like to allow you to do corrections for the module assessments. For Module 1, I’d like you to email me / direct message me a maximum of two problems (individual problems/parts, not problems with multiple parts, e.g. 4d) from the assessment that you would like to re-do, to replace your current grade on those problems, up to a maximum of 80% credit. I will then look at the problems people are asking for and make “replacement” problems for you to attempt. This cannot lower your grade, it can only improve it. It is optional.