ch3: Flesh out more of the text

book/source/03-cryptography.md

@@ -1,19 +1,16 @@
 (cyrptography_chapter)=
 # Cryptographic concepts/terms
 
-```{admonition} TODO
+```{admonition} VISUAL
 :class: warning
 
-- Introduce cryptographic primitives/terms at a very superficial level
 - Introduce visualizations for cryptographic primitives
 - Show example visualizations for operations? (encrypt/decrypt and signing/verification - only if we're going to reuse the visual primitives later)
 ```
 
 ## (Cryptographic) hash functions
 
-https://en.wikipedia.org/wiki/Cryptographic_hash_function
+[(Cryptographic) hash functions](https://en.wikipedia.org/wiki/Cryptographic_hash_function) map binary data of arbitrary length to a fixed size "hash" (hashes are also sometimes called "digests").
-
-Note: hashes are sometimes called "digests".
 
 ## Symmetric-key cryptography
 
@@ -21,29 +18,29 @@ Note: hashes are sometimes called "digests".
 
 Participants in symmetric-key operations need to exchange the shared secret over a secure channel.
 
-```{admonition} TODO
+```{admonition} VISUAL
 :class: warning
 
 - visualization? (maybe a black key icon, following wikipedia's example?)
 ```
 
-Symmetric-key cryptography is much faster than public-key cryptography. Also, unlike traditional public-key mechanisms, symmetric-key cryptography is quantum-resistant.
+Symmetric-key cryptography is much faster than public-key cryptography. Also, most current symmetric cryptographic algorithms are considered quantum-resistant.
 
-So there is a trade-off: Symmetric-key has major benefits, but exchanging the shared secret is a problem that needs to be solved separately. [Hybrid cryptosystems](hybrid_cryptosystems) are one common approach.
+So symmetric-key cryptography has major benefits, but exchanging the shared secret is a problem that needs to be solved separately.
+
+[Hybrid cryptosystems](hybrid_cryptosystems) are one common approach to leverage the benefits of symmetric-key cryptography, while handling the shared secret with a separate mechanism (using public-key cryptography).
 
 ### Symmetric-key cryptography in OpenPGP
 
-Symmetric cryptography is used in OpenPGP as part of a [hybrid cryptosystem](https://en.wikipedia.org/wiki/Hybrid_cryptosystem).
+Symmetric cryptography is used in OpenPGP (as part of a hybrid cryptosystem).
 
 Where symmetric keys are used in OpenPGP, they are referred to as "session keys."
 
 ### Authenticated encryption with associated data (AEAD)
 
-```{admonition} TODO
+[Authenticated encryption](https://en.wikipedia.org/wiki/Authenticated_encryption) is a class of cryptographic schemes that gives additional guarantees besides confidentiality.
-:class: warning
 
-- AEAD solves the problem of malleability.
+In OpenPGP version 6, AEAD is used to solve the problem of "malleability": In past versions of the OpenPGP protocol, some malicious changes to ciphertext were undetectable. With AEAD undetected changes of ciphertext are not possible.
-```
 
 ## Public-key, or asymmetric cryptography
 
@@ -87,15 +84,33 @@ Note that in many contexts, only the public part is present (more on that later)
 Only the public part of an asymmetric key pair
 ```
 
-### Cryptographic digital signatures
-
 ### Public-key cryptography in OpenPGP
 
-OpenPGP makes heavy use of public-key cryptography.
+OpenPGP makes heavy use of public-key cryptography, both for encryption and signing operations.
 
-Note that, for historical reasons, OpenPGP often uses the terms "public/secret" instead of "public/private." The OpenPGP RFC and other documentation often use the non-standard term "secret key" instead of the more common "private key."
+Note that, for historical reasons, OpenPGP often uses the terms "public/secret key" instead of "public/private key." The OpenPGP RFC and other documentation often use the non-standard term "secret key" instead of the more common "private key."
+
+### Cryptographic digital signatures
+
+[Digital signatures](https://en.wikipedia.org/wiki/Digital_signature) are a mechanism that is based on asymmetric cryptography. With this mechanism, one actor can make a signature over a digital message, and another actor can check the validity of that signature.
+
+The signer uses digital signatures to make statements about the message. Third parties can then inspect these statements.
+
+```{admonition} VISUAL
+:class: warning
+
+- add visualization showing: message + private key + sign = signature -> message + signature + public key + verify = ok?
+```
+
+In OpenPGP, digital signatures are used in two different contexts:
+
+- [Certification statements](certifications_chapter)
+- [Signatures over data](signing_data)
 
 (hybrid_cryptosystems)=
 ## Hybrid cryptosystems
 
-[Hybrid cryptosystems](https://en.wikipedia.org/wiki/Hybrid_cryptosystem) combine public-key cryptosystems with symmetric-key cryptosystems in a way that makes use of their respective advantages.
+[Hybrid cryptosystems](https://en.wikipedia.org/wiki/Hybrid_cryptosystem) combine two cryptosystems and make use of their respective advantages:
+
+- A public-key cryptosystem is used to safely handle shared secrets over insecure channels (in OpenPGP: so-called "session keys")
+- A symmetric-key cryptosystem is used to efficiently encrypt and decrypt long messages (using an OpenPGP "session key" as the shared secret)