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Edited ch04.asciidoc with Atlas code editor

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nadams 2017-05-17 09:00:28 -07:00
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@ -142,7 +142,7 @@ or
\end{equation} \end{equation}
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The _mod p_ (modulo prime number p) indicates that this curve is over a finite field of prime order _p_, also written as **F**~__p__~, where p = 2^256^ – 2^32^ – 2^9^ – 2^8^ – 2^7^ – 2^6^ – 2^4^ – 1, a very large prime number. The _mod p_ (modulo prime number p) indicates that this curve is over a finite field of prime order _p_, also written as latexmath:[\( \mathbb{F}_p \)], where p = 2^256^ – 2^32^ – 2^9^ – 2^8^ – 2^7^ – 2^6^ – 2^4^ – 1, a very large prime number.
Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical to that of an elliptic curve over real numbers. As an example, <<ecc-over-F17-math>> shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid. Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical to that of an elliptic curve over real numbers. As an example, <<ecc-over-F17-math>> shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid.