They act as the syntax that allows forming and interpreting complex statements about data and identities.
Without signatures there would only be loose keys, impossible to associate with their owner.
Signatures are the glue that allows for keys, subkeys and identities to be assembled into hierarchical certificates and for messages to gain authenticity.
So far we've looked at the components in an OpenPGP certificate, but certificates actually contain another set of elements, which bind the components together, and add metadata to them.
Internally, an OpenPGP certificate consists of a sequence of OpenPGP packets. These packets are just stringed together, one after the other. When a certificate is stored in a file[^tpk], it's easy to remove some of these packets, or add new ones.
[^tpk]: When stored in a file, OpenPGP certificates are in a format called [transferable public key](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#name-transferable-public-keys).
However, the owner of a certificate doesn't want a third party to add subkeys (or add [identity components](identity_components)) to their certificate, pretending that the certificate owner put those components there.
To prevent malicious addition of components, OpenPGP uses cryptographic signatures. These signatures show that components have been added by the owner of the OpenPGP certificate (these linking signatures are issued by the primary key of the certificate).
So while anyone can still unilaterally store unrelated subkeys and [identity components](identity_components) in an OpenPGP certificate dataset, OpenPGP implementations that read this certificate should discard components that don't have a valid cryptographic connection with the certificate.
(Conversely, it's easy for a third party to leave out packets when passing on an OpenPGP certificate. An attacker can, for example, choose to omit revocation packets. The recipient of such a partial copy has no way to notice the omission, without access to a different source for the certificate that contains the revocation packet.)
Note, though, that there are some cases where third parties legitimately add "unbound" packets to certificates (that is: packets that are not signed by the certificate's owner):
- [Third-party certifications](third_party_cert) are traditionally added to the certificate that they make a statement about (this can cause problems in systems that unconditionally accept and include such certifications[^flooding]),
- OpenPGP software may add [unbound identity data](unbound_user_ids), locally.
[^flooding]: Storing third-party identity certifications in the target OpenPGP certificate is convenient for consumers: it is easy to find all relevant certifications in one central location. However, when third parties can unilaterally add certifications, this opens an avenue for denial-of-service attacks by flooding. The SKS network of OpenPGP key servers [allowed and experienced this problem](https://dkg.fifthhorseman.net/blog/openpgp-certificate-flooding.html).
The term *signature* can have multiple meanings in the context of the OpenPGP specification.
Cryptographic keys create raw signatures which are byte sequences calculated according to some signature scheme.
OpenPGP packs these raw signatures up into OpenPGP signature packets, which carry additional information in the form of signature subpackets.
For the purpose of this document, the term signature will refer to an OpenPGP signature packet (tag 2).
OpenPGP signatures can be separated into *data signatures* and *certifications*.
A data signature serves the purpose to cryptographically guarantee the authenticity (and implicitly also the integrity) of a message, e.g. an email or a file, while a certification is used to attach metadata or subkeys to a certificate.
Different types of signatures are distinguished by a signature type code and are calculated in different ways.
Signatures can either be distributed standalone as *detached* signatures, or can be inlined with OpenPGP data, such as an OpenPGP message or a key or certificate.
Data signatures (type 0x00 and 0x01) are created by hashing the message content and calculating a cryptographic signature over the hash.
The result is packed up into an OpenPGP signature packet, which can either be included in the OpenPGP message (TODO: See section about forming messages, cleartext signature framework), or distributed separately as a so called *detached* signature.
Data signatures are always calculated using a **S**igning key.
A typical use-case for a self-certification is to attach a User ID, such as a name and email address to a certificate.
This is done by calculating the signature over the User ID and the public primary key.
The resulting User ID certification (typically type 0x13, potentially type 0x10-0x12) can then be inserted into the certificate, right after the User ID packet.
Other examples for self-signatures are binding signatures for subkeys.
In order to add an OpenPGP subkey to a certificate, a subkey binding signature is calculated over the public primary key, followed by the public subkey.
The resulting subkey binding signature (type 0x18) can then be inserted into the certificate right after the subkey.
If the subkey itself is intended to be used as a **S**igning key, an extra step is required.
To prevent an attacker from being able to "adopt" a victims signing subkey and then being able to claim to be the origin of signatures in fact made by victim, subkey binding signatures for signing subkeys need to include an embedded "back signature" (formally known as primary key binding signature) made by the signing key itself.
Certifications over User IDs can also be used to certify certificates of third-parties.
If Alice is certain that `Bob Baker <bob@example.com>` controls the key `0xB0B`, she can create a User ID certification signature for that identity and send it to Bob.
A revocation signature can either be hard or soft. A soft revocation of a certificate invalidates it from the revocation signature's creation time onwards, meaning signatures that were issued before the revocation remain intact, while a hard revocation invalidates the certificate retroactively, rendering all issued signatures invalid, regardless of creation time. Soft revocations are typically used whenever a key or User ID is retired or superseded gracefully, while hard revocations can for example signal compromise of secret key material.
There is a number of different Signature Types in the form of numerical IDs.
These give guidance on what the intent of a signature is and how it needs to be interpreted, however, the meaning of a signature also depends on who issued it.
A self-signature has a different meaning from a signature issued by a third party.
A `DirectKeySignature` issued as a self-signature can be used to set preferences and advertise features that apply to the whole certificate.
A third-party `DirectKeySignature` carrying a `TrustSignature` subpacket on the other hand can be interpreted as a statement by the issuer that it delegates trust to the signed certificate (WoT).
Self-certifications of types `0x10` - `0x13` can be used to bind a User ID to a certificate, while the same types issued by a third-party are statements by the issuer that they have checked the authenticity of the signed User ID to some degree.
There are further signature types for signatures on data, as well as designated types to bind and revoke subkeys.
For this reason, the OpenPGP protocol introduced signature subpackets with rfc4880.
These are well-defined data structures that can be placed as subelements into signature packets, which give additional context and meaning to a signature.
Typical examples are the issuer fingerprint subpacket, which contains the fingerprint of the issuer key, or the key flags subpacket which states, what purpose a component key is intended for.
Signature subpackets can reside in two different areas of a signature packet.
Subpackets in the *hashed area* are incorporated in the digest calculation that is done during signature calculation and are therefore covered by the cryptographic signature.
In other words; hashed subpackets are *authenticated*.
If a subpacket is placed in the *unhashed area* instead, it is not included in the signature calculation procedure and is therefore not protected against tampering.
Due to the fact that the unhashed area doesn't provide any cryptographic guarantees, it is only intended for advisory packets, or packets that self-authenticate (e.g. the issuer fingerprint subpacket, whose "correctness" can be proven by successfully verifying the signature using the referenced issuer key).
Each signature subpacket has a flag that indicates whether or not the subpacket is *critical*.
Since different OpenPGP implementations might support subsets of the standard, it would be fatal, if for example an implementation did not understand the concept of signature expiration.
Such an implementation would potentially accept an already expired signature.
By marking the expiration date subpacket as critical, the user can indicate, that implementations that do not understand this type of subpacket are supposed to reject the signature as invalid.
Sections 5.2.3.11 - 5.2.3.36 give guidance on which subpackets are usually marked as critical.
As mentioned above, different signatures are used for different purposes.
In this section, we will try to give guidance on how to create certain signatures by example.
#### Change Algorithm Preferences
In order to change what symmetric, compression, hash or AEAD algorithms are preferred by the key owner, they can issue a direct-key signature (type 0x1F) on the primary key.
This signature should have the following structure:
The recommended way to change the expiration time of a certificate is by issuing a new `DirectKey` signature (type 0x1F) with an adjusted Key Expiration Time subpacket.
The structure of such a signature is the same as in the section above.
It is also possible to change the expiration date of individual User IDs (see section below) or separate subkeys (see [section X](#add_subkey)).
"User ID" identity components are bound to an OpenPGP certificate by issuing a self-signature ("User Attributes" work analogously).
For example, the User ID `Alice Adams <alice@example.org>` may be associated with Alice's certificate `AAA1 8CBB 2546 85C5 8358 3205 63FD 37B6 7F33 00F9 FB0E C457 378C D29F 1026 98B3`.
Alice can link a User ID to her OpenPGP certificate with a cryptographic signature. To link a User ID, a self-signature is created (usually with the signature type [PositiveCertification](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#sigtype-positive-cert)). This signature is issued by the primary key.
```{figure} diag/user_id_certification.png
---
---
Linking a User ID to an OpenPGP certificate
```
This signature is calculated over the primary key and User ID.
Self-certifications over User IDs can optionally carry the same subpackets as listed in the previous table (key flags, features, algorithm preferences).
This way, separate capabilities can be assigned to different identities.
Since OpenPGP certificates are often distributed by the means of key servers, new signatures on a certificate are often "merged" into existing copies of the certificate locally by the recipient.
This means, that it is not really possible to remove signatures / User IDs from a certificate, as there is no way to communicate the intention of packet deletion to the recipient.
So in order to mark a User ID as invalid, the user can publish a copy of their certificate with a `CertificationRevocation` (signature type 0x30) attached to the invalidated User ID.
This signature signals that the holder of the certificate no longer wants to be associated with that User ID.
The structure of a certification revocation is as follows:
| Signature Creation Time | Hashed | True | True | Current time |
| Issuer Fingerprint | Hashed | True or false | Strongly Recommended | The primary key is the issuer |
| Reason for Revocation | Hashed | True | False | Decides over soft / hard revocation |
For User ID revocations, the value of the reason subpacket can either be `0` (no reason specified) or `32`, signaling that the User ID is no longer valid.
The latter would result in a soft revocation, while a reason code of `0` is considered a hard revocation.
Omitting the reason packet altogether is also equivalent to a hard revocation.
It is recommended to issue User ID certifications using a reason code `32` and to do certificate revocations using a direct-key signature.
Linking a subkey to an OpenPGP certificate is done with a ["Subkey Binding Signature"](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#sigtype-subkey-binding). Such a signature signals that the "primary key wants to be associated with the subkey".
The subkey binding signature also adds metadata.
```{figure} diag/subkey_binding.png
Linking an OpenPGP subkey to the primary key with a binding signature
```
The [Signature packet](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#name-signature-packet-tag-2) that binds the subkey to the primary key has the signature type [SubkeyBinding](https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-10.html#name-subkey-binding-signature-si).
Optional algorithm preference subpackets can be used to signal per-subkey preferences that deviate from those set in the certificates `DirectKey` signature.
In order to specify an expiration time for the subkey, a key expiration time subpacket can be included. Note, that the validity of the subkey is bounded by that of the primary key, meaning an expired primary key causes the subkey to be invalidated, no matter the subkey expiration time.
Binding subkeys with the "signing" key flag is a special case:
When binding a signing subkey to a primary key, it is not sufficient that the "primary key wants to be associated with the subkey." In addition, the subkey must signal that it "wants to be associated with that primary key."
Otherwise, Alice could "adopt" Bob's signing subkey and convincingly claim that she made signatures that were in fact issued by Bob.
This is to prevent an attack where the attacker "adopts" the victims signing subkey as their own in order to claim ownership over documents which were in fact signed by the victim.
Contrary to the `SubkeyBinding` signature, which is issued by the certificates primary key, the `PrimaryKeyBinding` signature is instead created by the subkey.
Linking an OpenPGP signing subkey to the primary key with a binding signature, and an embedded primary key binding signature
```
This additional "Primary Key Binding" Signature is informally called a "back signature" (because the subkey uses the signature to point "back" to the primary key) is an embedded `PrimaryKeyBinding` "back signature" (type 0x19).
| Signature Creation Time | Hashed | True | True | Current time |
| Issuer Fingerprint | Hashed | True or false | Strongly Recommended | The primary key is the issuer |
| Reason for Revocation | Hashed | True | False | Decides over soft / hard revocation |
In `SubkeyRevocation` signatures, the reason subpacket cannot have value `32`, but instead may be from the range of `0-3`.
Values `1` (key superseded) and `3` (key retired and no longer used) are soft reasons, while `0` (no reason) and `2` (key compromised) are considered hard.
A user might want to revoke their whole certificate, rendering it unusable.
Depending on the circumstances, they might either want to revoke it softly, e.g. in case of migration to a new certificate, or they want to issue a hard revocation, e.g. in case of secret key material compromise. A soft-revoked certificate can be re-validated at a later point in time, by issuing a new certification, while a hard revocation is typically permanent.
There are some subpackets that are expected to be included in any type of signature.
* **Signature Creation Time**: Every OpenPGP signature MUST contain a Signature Creation Time subpacket (2) containing the timestamp at which the signature was made. This packet MUST be present in the hashed area of the signature and SHOULD be marked as critical.
* **Issuer Fingerprint**: In order to be able to verify a signature, the verifier needs to know, which (sub-)key was used to issue the signature in the first place. Therefore, every OpenPGP v6 signature SHOULD contain an Issuer Fingerprint subpacket (33) containing the 32 byte fingerprint of the particular component key that was used to create the signature.
:::{note}
The issuer key might be a subkey.
:::
Since the issuer fingerprint subpacket is self-authenticating, it can either be included as a hashed or unhashed subpacket, but the authors of this book recommend to place it in the hashed area of the signature.
Since the hashed and unhashed areas of a signature are just lists of subpackets, in principle they allow duplicates of the same subpacket, which might lead to conflicts.
Therefore, packets in the hashed area take precendence over the unhashed area.
However, there may still be conflicts between packets in the same area, e.g. two conflicting expiration dates, etc.
In some cases, duplicate packets with conflicting content even make sense, e.g. if a signature was made by a version 4 issuer key whose key material was migrated from an older OpenPGP version such as v3.
In this case, either the v3 or v4 key could be used to validate the v4 signature, but since the key ID calculation scheme was changed between v3 and v4, these identifiers would differ.
Therefore, the signature could contain two isuer key ID subpackets with conflicting, but correct values.
