diff --git a/ch04_keys.adoc b/ch04_keys.adoc
index a107763e..4d36bdab 100644
--- a/ch04_keys.adoc
+++ b/ch04_keys.adoc
@@ -479,7 +479,7 @@ program has supported IP address payments for almost((("public key cryptography"
 [[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")))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")))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
@@ -603,7 +603,7 @@ 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")))((("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")))((("commitments", startref="commitment")))checksums.
 
 [[base58]]
 === Base58Check Encoding