From 2edb6c690a7c39fbb7459eae309192d299f1da8f Mon Sep 17 00:00:00 2001 From: "myarbrough@oreilly.com" Date: Tue, 25 Nov 2014 12:52:16 -0800 Subject: [PATCH] Made changes to ch04.asciidoc --- ch04.asciidoc | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/ch04.asciidoc b/ch04.asciidoc index fe428b86..eecc9fbb 100644 --- a/ch04.asciidoc +++ b/ch04.asciidoc @@ -107,10 +107,6 @@ $ sx newkey <> is an example of an elliptic curve, similar to that used by bitcoin. -[[ecc-curve]] -.An elliptic curve -image::images/msbt_0402.png["ecc-curve"] - Bitcoin uses a specific elliptic curve and set of mathematical constants, as defined in a standard called((("secp256k1 curve standard"))) +secp256k1+, established by the((("National Institute of Standards and Technology (NIST)"))) National Institute of Standards and Technology (NIST). The +secp256k1+ curve is defined by the following function, which produces an elliptic curve: [latexmath] @@ -129,6 +125,10 @@ or \end{equation} ++++ +[[ecc-curve]] +.An elliptic curve +image::images/msbt_0402.png["ecc-curve"] + 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 as that of an elliptic curve over the real numbers. As an example, <> 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.