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fix equation

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Andreas M. Antonopoulos 2013-09-06 19:51:30 -07:00
parent 3431139282
commit 34e7d37932
1 changed files with 5 additions and 4 deletions
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@ -42,20 +42,21 @@ image::images/ecc-addition.png["Addition operator on points of an elliptic curve
Bitcoin specifically uses the +secp256k1+ elliptic curve: Bitcoin specifically uses the +secp256k1+ elliptic curve:
[latexmath] [latexmath]
.The secp256k1 elliptic curve equation
++++ ++++
\begin{equation} \begin{equation}
{y^2 = (x^3 + 7)} \text(over) \mathbb{F}_p {y^2 = (x^3 + 7)} \text{over} \mathbb{F}_p
\end{equation} \end{equation}
++++
or or
[latexmath]
++++
\begin{equation} \begin{equation}
{y^2 \mod p = (x^3 + 7) \mod p} {y^2 \mod p = (x^3 + 7) \mod p}
\end{equation} \end{equation}
++++ ++++
where +p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F+, a very large prime.
where +p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F+, a very large prime.
The +mod p+ indicates that this curve is over a finite field of prime order +p+, also written as F(p). The curve 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 shown above. The +mod p+ indicates that this curve is over a finite field of prime order +p+, also written as F(p). The curve 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 shown above.