Elliptic Curve Cryptography Explained (2019)
I don&#x27;t know ECC at all. But a note:<p>Finite fields are of two types: &quot;Prime Fields&quot; (such as the mod 19 field discussed in this blogpost), and &quot;Extension Fields&quot; (which would be prime^n, such as 19^2 or 361. Or more commonly, the 2^x fields, such as 2, 4, 8, 16, 32, 64... 256... 65536 ... because the 2^x fields correspond very closely with binary numbers).<p>Prime fields can be taught very quickly: maybe 30 minutes of study and examples is all you really need to really get what is going on. Be it a 2, 5, or 19 field, its really cool and simple.<p>The &quot;leap&quot; from prime fields into extension fields takes a few hours of dedicated study (which probably will be done over a week to a month if you&#x27;re a busy adult like me) if you plan to do it rigorously. A lot of blogposts, textbooks, and other reference material will handwave the extension field because its... really hard math.<p>My best advice is &quot;believe in the textbooks&quot;, extension fields are possible. And this is one of those situations where you can just &quot;believe in the math&quot; and learn the details of extension fields AFTER you understand the applications of them. &quot;Extension Fields are like prime fields but way more tricky&quot;. They behave like a prime field in almost every way that&#x27;s important, but its just way harder to understand.<p>--------<p>I do recommend making the leap at some point, and truly understanding the extension fields. Once you get there, you finally understand the underlying math behind CRC32, AES, GCM mode, and ECC. Its a very worthwhile endeavor, but you really need to dedicate yourself to quiet study for some time to really get the concepts.