From 27b324da744863b61515c586846269976ab0fda9 Mon Sep 17 00:00:00 2001
From: Clare Laylock <claylock@oreilly.com>
Date: Wed, 1 Nov 2023 13:26:24 -0400
Subject: [PATCH] equations and follow-up

---
 ch07_authorization-authentication.adoc | 6 +++---
 ch08_signatures.adoc                   | 4 +---
 2 files changed, 4 insertions(+), 6 deletions(-)

diff --git a/ch07_authorization-authentication.adoc b/ch07_authorization-authentication.adoc
index 4909896e..4280a66d 100644
--- a/ch07_authorization-authentication.adoc
+++ b/ch07_authorization-authentication.adoc
@@ -194,9 +194,9 @@ The validation software combines the scripts:
 ----
 
 As we see in <<simplemath_script>>, when
-this script is executed, the result is +OP_TRUE+, making the transaction
-valid. Not only have we shown a valid transaction output script, but
-the resulting UTXO could be spent by anyone with the arithmetic skills
+this script is executed, the result is +OP_TRUE+, making the transaction valid.  Although this is a valid transaction
+output script, note that the resulting UTXO can be spent by anyone with
+the arithmetic skills
 to know that the number 2 satisfies the script.
 
 
diff --git a/ch08_signatures.adoc b/ch08_signatures.adoc
index 46d1648d..6bf15e3d 100644
--- a/ch08_signatures.adoc
+++ b/ch08_signatures.adoc
@@ -56,7 +56,7 @@ signing key is the user's private key. The result is the signature:
 [latexmath]
 ++++
 \begin{equation}
-\(Sig = F_{sig}(F_{hash}(m), x)\)
+(Sig = F_{sig}(F_{hash}(m), x))
 \end{equation}
 ++++
 
@@ -878,7 +878,6 @@ integers are modulus p:
 s = k^{-1} (Hash(m) + x \times R)
 \end{equation}
 ++++
-_s_ = __k__^-1^ (__Hash__(__m__) + __x__ × __R__)
 
 
 where:
@@ -899,7 +898,6 @@ signature creation):
 K = s^{-1} \times Hash(m) \times G + s^{-1} \times R \times X
 \end{equation}
 ++++
-_K_ = __s__^-1^ × __Hash__(__m__) × _G_ + __s__^-1^ × _R_ × _X_
 
 where: