math equations

ch08_signatures.adoc

@@ -875,7 +875,7 @@ integers are modulus p:
 [latexmath]
 ++++
 \begin{equation}
-s = k^-1^ (Hash(m) + x × R)
+s = k^{-1} (Hash(m) + x \times R)
 \end{equation}
 ++++
 _s_ = __k__^-1^ (__Hash__(__m__) + __x__ × __R__)
@@ -893,6 +893,12 @@ the _R_, _s_ values and the public key to calculate a value _K_, which
 is a point on the elliptic curve (the public nonce used in
 signature creation):
 
+[latexmath]
+++++
+\begin{equation}
+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:

ch14_applications.adoc

@@ -926,16 +926,19 @@ time. This feature is called a _hash time lock contract_, or _HTLC_, and
 is used in both bidirectional and routed payment channels.
 
 Let's first explain the "hash" part of the HTLC. To create an HTLC, the
-intended recipient of the payment will first create a secret +R+. They
-then calculate the hash of this secret +H+:
+intended recipient of the payment will first create a secret _R_. They
+then calculate the hash of this secret _H_:
 
-----
+[latexmath]
+++++
+\begin{equation}
 H = Hash(R)
-----
+\end{equation}
+++++
 
-This produces a hash +H+ that can be included in an output's
+This produces a hash _H_ that can be included in an output's
 script. Whoever knows the secret can use it to redeem the output. The
-secret +R+ is also referred to as a _preimage_ to the hash function. The
+secret _R_ is also referred to as a _preimage_ to the hash function. The
 preimage is just the data that is used as input to a hash function.
 
 [role="less_space pagebreak-before"]
@@ -958,7 +961,7 @@ ELSE
 ENDIF
 ----
 
-Anyone who knows the secret +R+, which when hashed equals to +H+, can
+Anyone who knows the secret _R_, which when hashed equals to _H_, can
 redeem this output by exercising the first clause of the +IF+ flow.
 
 If the secret is not revealed and the HTLC claimed after a certain
@@ -966,11 +969,11 @@ number of blocks, the payer can claim a refund using the second clause in
 the +IF+ flow.
 
 This is a basic implementation of an HTLC. This type of HTLC can be
-redeemed by _anyone_ who has the secret +R+. An HTLC can take many
+redeemed by _anyone_ who has the secret _R_. An HTLC can take many
 different forms with slight variations to the script. For example,
 adding a +CHECKSIG+ operator and a public key in the first clause
 restricts redemption of the hash to a particular recipient, who must also
-know the((("Bitcoin", "as application platform", "payment channels", secondary-sortas="application platform", startref="bitcoin-app-platform-payment")))((("application platform, Bitcoin as", "payment channels", startref="app-platform-payment")))((("payment channels", startref="payment-channel")))((("payment channels", "HTLC (Hash Time Lock Contract)", startref="payment-channel-htlc")))((("HTLC (Hash Time Lock Contract)", startref="htlc")))((("Hash Time Lock Contract (HTLC)", startref="hash-time-lock-contract"))) secret +R+.
+know the((("Bitcoin", "as application platform", "payment channels", secondary-sortas="application platform", startref="bitcoin-app-platform-payment")))((("application platform, Bitcoin as", "payment channels", startref="app-platform-payment")))((("payment channels", startref="payment-channel")))((("payment channels", "HTLC (Hash Time Lock Contract)", startref="payment-channel-htlc")))((("HTLC (Hash Time Lock Contract)", startref="htlc")))((("Hash Time Lock Contract (HTLC)", startref="hash-time-lock-contract"))) secret _R_.
 
 [[lightning_network]]
 === Routed Payment Channels (Lightning Network)