diff --git a/ch04_keys.adoc b/ch04_keys.adoc
index c0deecd8..a31215be 100644
--- a/ch04_keys.adoc
+++ b/ch04_keys.adoc
@@ -411,7 +411,7 @@ authorized by an input script that acts like a ((("public key cryptography", "in
 [[p2pk]]
 === IP Addresses: The Original Address for Bitcoin (P2PK)
 
-We've ((("public key cryptography", "IP address payments and", id="pub-key-ipaddress")))((("IP addresses for Bitcoin payments", id="ipaddress-payment")))((("payments", "via IP addresses", id="payment-ipaddress")))((("P2PK (pay to public key)", id="p2pk-ch4")))established that Alice can pay Bob by assigning some of her
+We've ((("public key cryptography", "IP address payments and", id="pub-key-ipaddress")))((("IP addresses for Bitcoin payments", id="ipaddress-payment")))((("payments", "via IP addresses", id="payment-ipaddress")))((("P2PK (pay to public key)", id="p2pk-ch4")))((("addresses", "P2PK (pay to public key)", id="address-p2pk-ch4")))established that Alice can pay Bob by assigning some of her
 bitcoins to one of Bob's public keys.  But how does Alice get one of
 Bob's public keys?  Bob could just give her a copy, but let's look again
 at the public key we worked with in <<public_key_derivation>>.  Notice
@@ -487,12 +487,12 @@ to see the benefits when we look at the following section.
 
 This type of output is known today as _pay to public key_, or _P2PK_ for
 short.  It was never widely used for payments, and no widely used
-program has supported IP address payments for almost((("public key cryptography", "IP address payments and", startref="pub-key-ipaddress")))((("IP addresses for Bitcoin payments", startref="ipaddress-payment")))((("payments", "via IP addresses", startref="payment-ipaddress")))((("P2PK (pay to public key)", startref="p2pk-ch4"))) a decade.
+program has supported IP address payments for almost((("public key cryptography", "IP address payments and", startref="pub-key-ipaddress")))((("IP addresses for Bitcoin payments", startref="ipaddress-payment")))((("payments", "via IP addresses", startref="payment-ipaddress")))((("P2PK (pay to public key)", startref="p2pk-ch4")))((("addresses", "P2PK (pay to public key)", startref="address-p2pk-ch4"))) a decade.
 
 [[addresses_for_p2pkh]]
 === Legacy Addresses for P2PKH
 
-Entering ((("public key cryptography", "hash functions and", id="pub-key-hash")))((("hash functions", "Bitcoin payments and", id="hash-payment")))((("payments", "with hash functions", secondary-sortas="hash functions", id="payment-hash")))((("P2PKH (pay to public key hash)", id="p2pkh-legacy")))the IP address of the person you want to pay has a number of
+Entering ((("public key cryptography", "hash functions and", id="pub-key-hash")))((("hash functions", "Bitcoin payments and", id="hash-payment")))((("payments", "with hash functions", secondary-sortas="hash functions", id="payment-hash")))((("P2PKH (pay to public key hash)", id="p2pkh-legacy")))((("addresses", "P2PKH (pay to public key hash)", id="address-p2pkh-legacy")))the IP address of the person you want to pay has a number of
 advantages, but it also has a number of downsides.  One particular
 downside is that the receiver needs their wallet to be online at their
 IP address, and it needs to be accessible from the outside world.  For
@@ -617,7 +617,7 @@ Bitcoin wallet to Alice's wallet.  There are commonly used encodings for
 byte values, such as hexadecimal, but any mistake made in copying a
 commitment would result in the bitcoins being sent to an unspendable
 output, causing them to be lost forever.  In the next section, we'll
-look at compact encoding and reliable ((("public key cryptography", "hash functions and", startref="pub-key-hash")))((("hash functions", "Bitcoin payments and", startref="hash-payment")))((("payments", "with hash functions", secondary-sortas="hash functions", startref="payment-hash")))((("P2PKH (pay to public key hash)", startref="p2pkh-legacy")))((("commitments", startref="commitment")))checksums.
+look at compact encoding and reliable ((("public key cryptography", "hash functions and", startref="pub-key-hash")))((("hash functions", "Bitcoin payments and", startref="hash-payment")))((("payments", "with hash functions", secondary-sortas="hash functions", startref="payment-hash")))((("P2PKH (pay to public key hash)", startref="p2pkh-legacy")))((("addresses", "P2PKH (pay to public key hash)", startref="address-p2pkh-legacy")))((("commitments", startref="commitment")))checksums.
 
 [[base58]]
 === Base58Check Encoding