(cyrptography_chapter)=
# Cryptographic concepts and terms

```{admonition} VISUAL
:class: warning

- 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

[(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").

Hash functions are used in cryptography to produce shorthand "placeholders" for data. Two properties of cryptographic hash functions are particularly important:

- ["Pre-image resistance"](https://en.wikipedia.org/wiki/Preimage_attack): Given a hash value, it should be hard to find a message that maps to that hash value.
- ["Collision resistance"](https://en.wikipedia.org/wiki/Collision_resistance): It should be hard to find two messages that map to the same hash value.

## Symmetric-key cryptography

[Symmetric-key cryptography](https://en.wikipedia.org/wiki/Symmetric-key_algorithm) uses the same cryptographic key for both encryption and decryption. Symmetric-key cryptographic systems support *encryption/decryption* operations.

Participants in symmetric-key operations need to exchange the shared secret over a secure channel.

```{admonition} VISUAL
:class: warning

- visualization? (maybe a black key icon, following wikipedia's example?)
```

### Benefits and downsides

Symmetric-key cryptography has major benefits: it is much faster than public-key cryptography (see below). Also, most current symmetric cryptographic algorithms are considered quantum-resistant[^postquantum].

[^postquantum]: Daniel J. Bernstein (2009). ["Introduction to post-quantum cryptography" (PDF)](http://www.pqcrypto.org/www.springer.com/cda/content/document/cda_downloaddocument/9783540887010-c1.pdf) states that: "many important classes of cryptographic systems", including secret-key cryptographic mechanisms like AES "[..] are believed to resist classical computers and quantum computers." (pages 1, 2).

However, exchanging the required shared secret is a problem that needs to be solved separately.

[Hybrid cryptosystems](hybrid_cryptosystems) (see below) 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-key cryptography is used in OpenPGP in three contexts:

- most prominently, as part of a hybrid cryptosystem to encrypt and decrypt data,
- to encrypt [password-protected private key material](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#name-secret-key-encryption), and
- for [password-protected data encryption](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#name-symmetric-key-encrypted-ses) (a less commonly used feature of the standard).

Where symmetric keys are used in OpenPGP for data encryption, they are called either "message keys" or "session keys[^sessionkey]."

[^sessionkey]: In OpenPGP version 6, when using the ["Version 2 Symmetrically Encrypted Integrity Protected Data Packet Format"](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#name-version-2-symmetrically-enc), a "message key" is derived from a "session key". Previously (up to OpenPGP version 4, and in version 6 when using ["Version 1 Symmetrically Encrypted Integrity Protected Data Packet Format"](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#name-version-1-symmetrically-enc)), the "session key" was used directly as a symmetric encryption key.

### Authenticated encryption with associated data (AEAD)

[Authenticated encryption](https://en.wikipedia.org/wiki/Authenticated_encryption) is a class of cryptographic schemes that gives additional guarantees besides confidentiality.

In OpenPGP version 6, AEAD was introduced as a successor to the MDC[^MDC] mechanism. AEAD is a common mechanism to solve the problem of "malleability": In past versions of the OpenPGP protocol, some malicious changes to ciphertext were undetectable. AEAD protects against undetected changes of ciphertext.

[^MDC]: In OpenPGP version 4, a mechanism called MDC (Modification Detection Code) was introduced to serve a comparable purpose as AEAD. While MDC is a non-standard mechanism, as of this writing, there are no known attacks against the scheme.

Protecting against malleability counters a variation of the EFAIL[^efail] attack.

[^efail]: A variation of the [EFAIL](https://en.wikipedia.org/wiki/EFAIL) attack can be prevented by both the MDC and AEAD mechanisms. Also see ["No, PGP is not broken, not even with the Efail vulnerabilities"](https://proton.me/blog/pgp-vulnerability-efail), especially the section "Malleability Gadget Exfiltration Channel Attack".


## Public-key, or asymmetric cryptography

[Public-key cryptography](https://en.wikipedia.org/wiki/Public-key_cryptography) systems use asymmetric pairs of related keys. Public-key cryptographic systems support *encryption/decryption* as well as *digital signature* operations.

Unlike symmetric cryptography, public-key cryptography doesn't require participants to pre-arrange a shared secret. Instead, with public-key cryptography, the public parts of the key material can be shared openly and then used for cryptographic operations.

(asymmetric_key_pair)=
### Asymmetric cryptographic key pairs

In many places, we'll deal with asymmetric cryptographic key pairs:

```{figure} diag/cryptographic_keypair.png
---
---
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.

Note that in many contexts, only the public part is present (more on that later):

```{figure} diag/keypair_pub.png
---
---
Only the public part of an asymmetric key pair
```

### Public-key cryptography in OpenPGP

OpenPGP makes heavy use of public-key cryptography, both for encryption and signing operations.

```{admonition} Terminology
:class: note

For historical reasons, the OpenPGP RFC and other documentation often use the non-standard term "secret key" instead of the more common "private key."

So in OpenPGP, the pair of terms "public/secret key" is sometimes used instead of the more common "public/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
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- 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 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)
