I want a deep understanding of elliptic curve cryptography. This led me to study algebraic geometry, which led me to study category theory. I think I’m ready to go back to algebraic geometry now.
I am not sure how comfortable you are with mathematics (and algebra in particular), but my courses in algebraic geometry were among the hardest I have taken so far (and the study of elliptic curves is a specialisation of the study of algebraic geometry). After studying algebra for 4 years I can now finally understand most of the introductory chapter of my book on elliptic curves, though not all of it. Since you want to learn about a specific algorithm rather than all of elliptic curves I think it shouldn’t take you the 4⁄5 years that it is taking me, but be warned that acquiring a deep understanding might prove to be very hard.
This sounds like an interesting project. I’ve studied quite some category theory myself, though mostly from the “oh pretty!” point of view, and dipped my feet into algebraic geometry because it sounded cool. I think that reading algebraic geometry with the sight set on cryptography would be more giving than the general swimming around in its sea that I’ve done before. So if you want a reading buddy, do tell. A fair warning though: I’m quite time limited these coming months, so will not be able to keep a particularly rapid pace.
I want a deep understanding of elliptic curve cryptography. This led me to study algebraic geometry, which led me to study category theory. I think I’m ready to go back to algebraic geometry now.
I am not sure how comfortable you are with mathematics (and algebra in particular), but my courses in algebraic geometry were among the hardest I have taken so far (and the study of elliptic curves is a specialisation of the study of algebraic geometry). After studying algebra for 4 years I can now finally understand most of the introductory chapter of my book on elliptic curves, though not all of it. Since you want to learn about a specific algorithm rather than all of elliptic curves I think it shouldn’t take you the 4⁄5 years that it is taking me, but be warned that acquiring a deep understanding might prove to be very hard.
This sounds like an interesting project. I’ve studied quite some category theory myself, though mostly from the “oh pretty!” point of view, and dipped my feet into algebraic geometry because it sounded cool. I think that reading algebraic geometry with the sight set on cryptography would be more giving than the general swimming around in its sea that I’ve done before. So if you want a reading buddy, do tell. A fair warning though: I’m quite time limited these coming months, so will not be able to keep a particularly rapid pace.