The most difficult part of the section was the part about the addition law for elliptic curves. It wasn't super difficult to understand, but an example would be very helpful.
I think the most important part of the section, at least as it pertains to cryptography, is the fact that elliptic curve systems can do with 313 bit keys what certain conventional systems can only do with 4096 bit keys. The is vast improvement in efficiency, made possible by a creative cryptosystem built on powerful mathematics.
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