Maths folks: am I right in thinking that the term "set" refers to a sequence of numbers, and that "group" refers to a set with some operator applied? e.g. [0, 1, 2, 3, 4] by itself is a set, ℤ_5 (the integers mod 5) is a group.
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I guess two other important things... groups have: - a generator (a.k.a. "base") - order (count)
I’m in my way out, but @bascule you need to brush up your group theory, soz. Groups have just one operation, you’re thinking of rings or fields. Groups do not need to have a single generator, that’s a cyclic group.
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I’m not saying this to be right on the Internet, I’m saying it because I see it a lot in people who dive right in to finite fields, it’s very easy to jumble things up, which is what I just spent half an hour trying to prevent :)
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I'm doing a lot of stuff in GF(2^n) mostly GF(2^128) lately, and elliptic curves, and yet I do feel like you're speaking to my blind spots in a way most others can't relate to...
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i'm pretty sure by "multiply" tony is referring to the action of integers on the group (aka scalar multiplication)
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Touché. All the groups I work in are cyclic groups. C'est la cryptographie.
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So I'm aware there can be multiple non-overlapping cyclic subgroups. In ECC that's the cofactor... and yeah...https://twitter.com/bascule/status/1219376049391198208 …
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