- To Know: I’ve put up re-do problems. I’ve added a few new ones. You can do 2 from Module 1 and 2 from Module 2. You choose. If you want one that’s not there, let me know. It’s due the Friday after Module 3.
- Use EC Factoring Tools to factor n = 290265623. You might want to increase the size of the loop! You’ll notice I modified the code so that it will catch and report on the errors it encounters. Use the result to factor n (that is, take the gcd of the non-invertible residue with n to get a non-trivial factor).
- Now do it again with a different choice of curve and point (revisit lecture for some advice on finding random curve + point pairs). Factor n.
- Now try modifying one of the middle digits of n, and see how long it takes. Factor n.
- Try modifying one of the digits a couple more times and see how long it takes. Factor n.
- Report to canvas on how long it took (what multiple of P) on different curves and points, and different n. Explain why you think it was fast sometimes and slow other times.
- That’s it for now. I’ve decided to talk about projective geometry in class, since students seem curious about it and it’s a very good topic. You can devote whatever other time you have to working on the module and re-do problems.