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Thomas H. Ptacek @tqbf
, 4 tweets, 1 min read Read on Twitter
I don’t believe you can get much insight about how elliptic curves work from pictures. The lines and tangents in the group law are not really the point.
Curves are straightforward equations. To understand what’s happening in an invalid curve attack, define a small curve with pencil/paper-manageable coefficients and then play with points.
What you want is Sean’s Cryptopals #57, which explains the actual mechanics of subgroup confinement, and #59, which maps them to curves.

toadstyle.org/cryptopals/57.…
toadstyle.org/cryptopals/59.…
I’ve tried a couple times just now to summarize the two challenges but: that makes me part of the problem. Don’t just read summaries. Play with the math! If you finished 10th grade, I promise it’s accessible to you.
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