70 karma · joined September 27, 2019
It seems that elliptic curves are used quite shrewdly in public key exchanges, used as a sort of off-the-shelf arithmetic system that renders some benefits (harder to solve the elliptic curve discrete log problem) and drawbacks (more expensive to compute, because of these point ops) compared to key exchanges relying on the integer discrete log problem. There is generally much energy spent on explaining the point operations but not much on explaining this context: this is an alternate arithmetic inserted into the Diffie Helman scheme that is secure and not so hard to work with.
The finite fields in application (e.g. in X25519) are so large compared to the toy examples that the technical details matter more for understanding the performance of the algorithms than the actual cryptographic method. Understanding (and convincing yourself of) the core behavior of the key exchange itself is perhaps best done with the number theory and group theory lens. There was a discussion here on HN a couple days ago which largely bashed the theoretical approach in favor of simply cargo culting the tools, which was appalling. I hope they all enjoy this link!
Anyhow, the application of elliptic curves to cryptography is clever and I would recommend everyone with an interest (and a little background in algebra) read Koblitz's paper[1] and Miller's earlier description [2] if they are looking for more context for OP's wonderful presentation.
1: Koblitz: Elliptic Curve Cryptosystems https://www.ams.org/journals/mcom/1987-48-177/S0025-5718-198...
2: Miller: Use of Elliptic Curves in Cryptography https://link.springer.com/chapter/10.1007/3-540-39799-X_31
Any political wins made by groups exploiting and dominating mainstream media (Trump) are explained by the fact that the barrier to entry in political action is so low—just getting a few people to vote is politically effective because almost everyone is just watching the news instead of doing anything real. Meanwhile Trump's team meets with money and accrues powerful stakeholders by annexing their agenda, building support in institutions and markets.
So ignoring political news and pursuing interfaces with actual nexuses of power is far more politically effective than the hundreds of people with twenty tabs of The Atlantic open and the WSJ draped across their lap like a religious shawl every morning. Go out, meet politically active people in your city, email representative staff, make friends with people with money and vested interests that are vulnerable to political changes.
I think we, as software people, are susceptible to 2—software is successful in some cases because of this kind of cross contamination where it replaces the tools and methods of a separate field with its own, sometimes with great success (art, finance).