diff --git a/ch04.asciidoc b/ch04.asciidoc
index d089bd2b..1c6a1b87 100644
--- a/ch04.asciidoc
+++ b/ch04.asciidoc
@@ -182,32 +182,6 @@ large number. It is approximately 10^77^ in decimal. For comparison, the
 visible universe is estimated to contain 10^80^ atoms.
 ====
 
-[[pubkey]]
-==== Public Keys
-
-((("keys and addresses", "overview of", "public key
-calculation")))((("generator point")))The public key is calculated from
-the private key using elliptic curve multiplication, which is
-irreversible: _K_ = _k_ * _G_, where _k_ is the private key, _G_ is a
-constant point called the _generator point_, and _K_ is the resulting
-public key. The reverse operation, known as "finding the discrete
-logarithm"—calculating _k_ if you know __K__—is as difficult as trying
-all possible values of _k_, i.e., a brute-force search. Before we
-demonstrate how to generate a public key from a private key, let's look
-at elliptic curve cryptography in a bit more detail.
-
-[TIP]
-====
-Elliptic curve multiplication is a type of function that cryptographers
-call a "trap door" function: it is easy to do in one direction
-(multiplication) and impossible to do in the reverse direction
-(division). Someone with a private key can easily create the public
-key and then share it with the world knowing that no one can reverse the
-function and calculate the private key from the public key. This
-mathematical trick becomes the basis for unforgeable and secure digital
-signatures that prove control over bitcoin funds.
-====
-
 [[elliptic_curve]]
 ==== Elliptic Curve Cryptography Explained
 
@@ -339,7 +313,30 @@ that k is sometimes confusingly called an "exponent" in this case.((("",
 startref="eliptic04")))((("", startref="Celliptic04")))
 
 [[public_key_derivation]]
-==== Generating a Public Key
+==== Public Keys
+
+((("keys and addresses", "overview of", "public key
+calculation")))((("generator point")))The public key is calculated from
+the private key using elliptic curve multiplication, which is
+irreversible: _K_ = _k_ * _G_, where _k_ is the private key, _G_ is a
+constant point called the _generator point_, and _K_ is the resulting
+public key. The reverse operation, known as "finding the discrete
+logarithm"—calculating _k_ if you know __K__—is as difficult as trying
+all possible values of _k_, i.e., a brute-force search. Before we
+demonstrate how to generate a public key from a private key, let's look
+at elliptic curve cryptography in a bit more detail.
+
+[TIP]
+====
+Elliptic curve multiplication is a type of function that cryptographers
+call a "trap door" function: it is easy to do in one direction
+(multiplication) and impossible to do in the reverse direction
+(division). Someone with a private key can easily create the public
+key and then share it with the world knowing that no one can reverse the
+function and calculate the private key from the public key. This
+mathematical trick becomes the basis for unforgeable and secure digital
+signatures that prove control over bitcoin funds.
+====
 
 ((("keys and addresses", "overview of", "public key
 generation")))((("generator point")))Starting with a private key in the