diff --git a/book/source/03-cryptography.md b/book/source/03-cryptography.md
index 843751b..bf4de3d 100644
--- a/book/source/03-cryptography.md
+++ b/book/source/03-cryptography.md
@@ -79,7 +79,7 @@ Unlike symmetric cryptography, participants are not required to pre-arrange a sh
 (asymmetric_key_pair)=
 ### Asymmetric cryptographic key pairs
 
-In many places, we'll deal with asymmetric cryptographic key pairs:
+Throughout this document, we will frequently reference asymmetric cryptographic key pairs:
 
 ```{figure} diag/cryptographic_keypair.png
 ---
@@ -87,14 +87,14 @@ In many places, we'll deal with asymmetric cryptographic key pairs:
 An asymmetric cryptographic key pair
 ```
 
-An asymmetric cryptographic key pair consists of a public and a private part. In this document, we'll show the public part of a key pair in green, and the private part in red.
+Each key pair comprises two components: the public key and the private key. For ease of identification, we will depict the public key in green and the private key in red throughout this document.
 
-Note that in many contexts, only the public part is present (more on that later):
+It's important to note that in many scenarios, only the public key is exposed or used (we will expand on these situations in subsequent sections):
 
 ```{figure} diag/keypair_pub.png
 ---
 ---
-Only the public part of an asymmetric key pair
+The public component of an asymmetric key pair
 ```
 
 ### Public-key cryptography in OpenPGP