equations and follow-up

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
+this script is executed, the result is +OP_TRUE+, making the transaction valid.  Although this is a valid transaction
-valid. Not only have we shown a valid transaction output script, but
+output script, note that the resulting UTXO can be spent by anyone with
-the resulting UTXO could be spent by anyone with the arithmetic skills
+the arithmetic skills
 to know that the number 2 satisfies the script.
 
 

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: