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Z/Zn groups are a better example, whether seen in RSA or Diffie-Hellman. Elliptic curves require graduate-school math to properly appreciate. Being mathematica
by ky3 12y ago
Z/Zn groups are a better example, whether seen in RSA or Diffie-Hellman.
Elliptic curves require graduate-school math to properly appreciate. Being mathematically mysterious, they are still the subject of active research.
Vanilla modular arithmetic is at least as old as Fermat, about 400 years. A breakthrough in ECC is big news. A breakthrough in the integers would flip the world upside down.
- j2kun 12y agoI think you mean the multiplicative group of units of Z/nZ, because additively Z/nZ has much more structure than a group. Still, for my example and in the article, one should be motivated to study groups because they show up in places that you don't expect to find algebraic structure. Z/nZ and its variants are the obvious places to look. Elliptic curves are surprising. Also, I wrote a series on elliptic curves which doesn't need any graduate level mathematics to appreciate [1]. Of course if you want to make breakthroughs on elliptic curves (or any serious mathematical topic) you need graduate study. [1]: http://jeremykun.com/2014/02/08/introducing-elliptic-curves/ http://jeremykun.com/2014/02/08/introducing-elliptic-curves/