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# Introduction to TPMs
Trusted Platform Modules (TPMs) are a large and complex topic, made all
the more difficult to explain by the intricate relationships between the
relevant concepts. This is an attempt at a simple explanation -- much
simpler than reading hundreds of pages of documents, but then too, too
light on detail to be immediately useful.
So what is a TPM? Well, it's a cryptographic co-processor with special
features to enable "root of trust measurement" (RTM), remote attestation
of system state, unlocking of local resources that are kept encrypted
(e.g., filesystems), and more. A TPM can do those things, and it can do
it with rich authentication and authorization policies.
> The standards development organization that publishes TPM specifications
> is the [Trusted Computing Group (TCG)](https://trustedcomputinggroup.org).
Typically a TPM is a hardware module, a chip, though there are firmware,
virtual, and simulated TPMs as well, all implemented in software.
To simplify things we'll consider only TPM 2.0.
Other parts of this [tutorial](README.md) may cover specific concepts in
much more detail.
# Goals
The goal of this introductory material is to help readers new to TPMs to
understand them well enough to approach the subjects of:
- [attestation](/Attestation/README.md)
- [secure boot](/Boot-with-TPM/README.md)
and to think about the sorts of things that one can do with TPMs in
general, which include:
- device on-boarding
- ascertaining the state of a device (e.g., has it executed only
trusted code)
- unlocking of devices using TPM-based authentication and authorization
policies (e.g., unlocking a laptop on boot multiple factors such as
biometrics, smartcards, passwords, time of day, even interaction with
remote services)
- using a TPM as a source of entropy for a running OS
> NOTE: At this time this introduction is very much a layman's
> introduction, and only an introduction. Readers seeking to do
> software development using TPMs will want to make use of [TCG
> specifications and other resources](#Other-Resources).
## Glossary
> For a glossary, see section 4 of [TCG TPM 2.0 Library part 1:
> Architecture](https://trustedcomputinggroup.org/wp-content/uploads/TCG_TPM2_r1p59_Part1_Architecture_pub.pdf).
# Core Concepts
Some core concepts in the world of TPMs:
> NOTE: We will not cover all of these here.
- cryptography
- hash extension
- cryptographic object naming
- platform configuration registers (PCRs)
- immutability of object public areas
- key hierarchies
- key wrapping
- restricted cryptographic keys
- limited resources
- sessions and authorization
- other object types, mainly non-volatile (NV) indexes
- attestation
We'll assume reader familiarity with the basics of cryptography -- the
basics of cryptographic primitives as interfaces, but not their
internals. E.g., hash functions, symmetric encryption, asymmetric
encryption, and digital signatures.
Authorization is the most important aspect of a TPM, since that's
ultimately what it exists for: to authorize a system or application to
perform certain duties when all the desired conditions allow for it.
TPMs have a very rich set of options for authorization. It's not just
[policies](#Policies), but also cryptographic object names used with
restricted keys to allow access only to applications that also have
other access.
Where to start? Let's start with hash extension.
## Hash Extension
Hash extension is just appending some data to a current digest-sized
value, hashing that, and then calling the output the new current value:
```
v_0 = 0 # size-of-digest-output zero bits
v_1 = Extend(v_0, e_0)
= H(v_0 || e_0)
v_2 = Extend(v_1, e_1)
= H(v_1 || e_1)
= H(H(v_0 || e_0) || e_1)
v_3 = Extend(v_2, e_2)
= H(v_2 || e_2)
= H(H(v_1 || e_1) || e_2)
= H(H(H(v_0 || e_0) || e_1) || e_2)
..
v_n = Extend(v_n-1, e_n-1)
= H(v_n-1 || e_n-1)
= H(H(v_n-2 || e_n-2) || e_n-1)
= H(H(...) || e_n-1)
```
where `H()` is a cryptographic hash function.
Each extension value can be arbitrarily large, and the TPM will use the
traditional `Init`/`Update`/`Final` approach to making digest
computation online.
Note that `H(e0 || e1 || e2) != Extend(Extend(Extend(0, e0), e1), e2)`.
Hash extension makes "message" boundaries strong.
Hash extension is most of what a PCR is, but hash extension is used in
other TPM concepts besides PCRs, such as policy naming.
## Coping with Severe Resource Limits Using Digests and Hash Extension
Hardware TPMs are extremely limited in memory and non-volatile memory
capacity. As a result they cannot hold large entities.
A common theme in TPMs is the use of digests, and hash extension digests
in particular, as a stand-in for large entities that might not fit at
once on the TPM.
TPMs use digests as stand-ins for large entities of various types:
- eventlogs
- policies
- auditing
We'll discuss at least two of those: event logs, and policies.
## Platform Configuration Registers (PCRs)
A PCR, then, is just a hash extension output. The only operations on
PCRs are: read, extend, and reset. All richness of semantics of PCRs
come from how they are used:
- what the governing TCG platform specification says about them
- what they are extended with and by what code (in what locality)
- what purposes they are read for
- attestation
- authorization
Note that a PCR value by itself is devoid of meaning. To add meaning
one must have access to the list of discrete values extended into the
PCR, as well as the order in which they were extended into the PCR. And
one must know the meaning of each such value.
### Eventlogs
Any TPM-using platform has to provide a way to keep a log of PCR hash
extension values. Such a log is known as the "eventlog".
The TPM itself cannot hold this log -- the TPM is too
resource-constrained.
## Root of Trust Measurements (RTM)
When a computer and its TPM start up, most PCRs are set to all-zeros,
and then the computer's boot firmware performs a core root of trust
measurement (CRTM) to "measure" (i.e., hash) the the next boot stage and
extend it into an agreed-upon PCR. The entire boot process should,
ideally, perform RTMs. At the end of the boot process some set of PCRs
should reflect the totality of the code path taken to complete booting.
Some PCRs are used to measure the BIOS, others to measure option ROMs,
and others to measure the operating system. Each platform has a
specification for which PCRs are used or reserved for what purposes. In
principle one could measure the entirety of an operating system and all
the code that is installed on the system.
RTM can be used to ensure that only known-trusted code is executed, and
that important resources are not unlocked unless the state of the system
when they are needed is "has only executed trusted code to get here".
Note that some PCRs are left to be used by "applications".
Some terms:
- core RTM (CRTM) -- initial measurements performed upon power-on
- static RTM (SRTM) -- subsequent-to-CRTM measurements of next boot
stages
- dynamic RTM (DRTM) -- measurements involved in rebooting
Resource unlocking can be done by creating objects tied to a set of PCRs
such that they must each have specific values for the TPM to be willing
to unlock (unseal) the object.
### The PCR Extension Eventlog
On the "PC platform" (which includes x64 servers) the BIOS keeps a log
of all the PCR extensions it has performed. The OS should keep its own
log of extensions it performs of PCRs reserved to the OS. Each
application has to keep a log of the extensions of the PCRs allocated to
it. Again, the TPM itself cannot do this.
The eventlog documents how each PCR evolved to their current state,
whatever it might be. Since PCR extension values are typically digests,
the eventlog is very dry, but it can still be used to evaluate whether
the current PCR values represent a trusted state. For example, one
might have a database of known-good and known-bad firmware/ROM digests,
then one can check that only known-good ones appear in the eventlog and
that reproducing the hash extensions described by the eventlog produces
the same PCR values as one can read, and if so it follows that the
system has only executed trusted code to arrive at the state identified
by the PCRs.
Note though that PCRs and RTM are not enough on their own to keep a
system from executing untrusted code. A system can be configured to
allow execution of arbitrary code at some point (e.g., download and
execute) and to not extend PCRs accordingly, in which case the execution
of untrusted code will not be reflected in any RTM.
## Tickets
> Tickets are yet another device for coping with TPMs having limited
> resources. Interaction with TPMs is via request/response
> commands, and tickets are largely about making TPMs stateless between
> related commands.
To avoid having to re-perform various operations -or remember having
performed them- between command invocations, a TPM can produce a
"ticket" that consists of an HMAC over a TPM-generated assertion, keyed
by a key known only to the TPM, and return it to the caller who can then
present it in a subsequent command related to the first.
For example, when signing data the TPM will first digest the data to
sign over several commands and generate a ticket saying it did produce
that digest, then later it can sign the digest after validating the
ticket that it produced.
Another example is a policy ticket, which allows one to avoid having to
re-authenticate (e.g., with smartcard, biometrics, passwords) on every
command for small window of time.
> When would a user be authenticated? Well, typically at boot time, or
> maybe at wake from sleep/hibernate time. A laptop could be configured
> to require a user to authenticate with biometrics and possibly a
> password or a smartcard. Note that such policies are not required by
> the specifications, but rather something that one can choose to use.
> There are five types of tickets. We won't cover them here. Readers
> who end up needing to know about them can look at section 11.4.6.3 of
> `TCG TPM 2.0 Library, part 1: Architecture`.
## Cryptographic Object Naming
TPMs support a variety of types of objects. Objects generally have
pointer-like "handles" that they are often used in the TPM APIs. But
more importantly, objects have cryptographically-secure names that are
used in many cases.
The cryptographically-secure name of an object is the hash of the
object's "public area".
The public area of, say, an asymmetric key is a data structure that
includes the public key (corresponding to the private key), and various
attributes of the key (e.g., its algorithm, but also whether it is bound
to the TPM where it resides, or to its key hierarchy), unseal policy,
and access policy.
This concept is extremely important. Because object names are the
outputs of cryptographically strong digest (hash) functions, they are
resistant to collision attacks, first pre-image attacks, and second
pre-image attacks -- as strong as the hash algorithm used anyways.
Which means that object names cannot be forged easily, which means that
they can be used in context where a peer needs certain guarantees, or
to defeat active attacks.
### Immutability of Object Public Areas
Because the name of an object is a digest of its public area, the public
area cannot be changed after creating it. One can delete and then
recreate an object in order to "change" its public area, but this
necessarily yields a new name.
### Cryptographic Object Naming as a Binding
> This section comes too soon, since it relates to attestation and
> restricted keys. Still, it may be useful to illustrate cryptographic
> object naming with one particularly important use of it.
A pair of functions, `TPM2_MakeCredential()` and
`TPM2_ActivateCredential()`, illustrate the use of cryptographic object
naming as a binding or a sort of authorization function.
`TPM2_MakeCredential()` can be used to encrypt a datum (a "credential")
to a target TPM such that the target will _only be willing to decrypt
it_ if *and only if* the application calling `TPM2_ActivateCredential()`
to decrypt that credential has access to some key named by the sender,
and that name is a cryptographic name that the sender can and must
compute for itself.
The semantics of these two functions can be used to defeat a
cut-and-paste attack in attestation protocols.
## Key Hierarchies
TPMs have multiple key hierarchies, each with zero, one or more primary
keys, each with zero, one, or more children keys:
```
seed
|
|
v
primary key (asymmetric encryption)
|
|
v
secondary keys (of any kind)
|
|
v
...
```
Note that every key has a parent or is a primary key.
There are four built-in hierarchies:
- platform hierarchy
- endorsement hierarchy
- storage hierarchy
- null hierarchy
of which only the endorsement and storage hierarchies will be of
interest to most readers.
The endorsement hierarchy is used to authenticate (when needed) that a
TPM is a legitimate TPM. The primary endorsement key is known as the EK
(endorsement key). Hardware TPMs come with a certificate for the EK
issued by the TPM's manufacturer. This EK certificate ("EKcert") can be
used to authenticate the TPM's legitimacy. The EK's public key
("EKpub") can be used to uniquely identify a TPM, and possibly link to
the platform's, and even the platform's user(s)' identities.
The `TPM2_CreatePrimary()` and `TPM2_CreateLoaded()` commands create key
objects deterministically from the hierarchy's seed and the "template"
used to create the key (which includes a "unique" area that provides
"entropy" to the key derivation function).
## Key Wrapping and Resource Management
Key wrapping is encrypting a secret or private key (key encryotion key,
or KEK) such that a specific entity may recover the plain key.
A decrypt-only asymmetric private key can be used to encrypt secrets to
the TPM on which that private key resides.
As well as wrapping secrets by encryption to public keys, TPMs also use
wrapping in a symmetric key known only to the TPM for the purpose of
saving keys off the TPM.
This is used for resource management: since hardware TPMs have very
limited resources, objects need to created or loaded, used, then saved
off-TPM to make room for other objects to be loaded (unless they are not
to be used again, then saving them is pointless). Only a TPM that saved
an object can load it again, but some objects can be exported to other
TPMs by encrypting them to their destination TPMs' EKpubs.
With a resource manager and access broker, a TPM can appear to have
infinite resources.
### Controlling Exportability of Keys
A key that is `fixedTPM` cannot leave the TPM in cleartext. It can be
saved off the TPM it resides in, but only that TPM can load it again.
A key that is `fixedParent` cannot be moved from one part of a key
hierarchy to another -- it cannot be "re-parented". Though if its
parent is neither `fixedParent` nor `fixedTPM` then the parent and its
descendants can be moved as a group to some other TPM.
> Key hierarchies are an important TPM topic that we're not really
> addresing in this intro.
## Persistence
In a TPM, key objects are, by default, transient, meaning the TPM will
forget them if restarted. Still, they can be saved (encrypted in a
secret key only the TPM knows) and later reloaded.
Transient objects can be made persistent, but because hardware TPMs have
very little non-volatile memory, few keys should be made persistent.
Instead you can save them (wrapped to a TPM-only KEK) and reload them as
needed.
Because primary keys (for any hierarchy other than the null hierarchy)
are derived deterministically from a built-in and protected seed, and
from a template, they are persistent even when not moved to NV storage
and even when not saved as long as the hierarchy's seed is not reset.
(Resetting the endorsement hierarchy seed is a very dramatic action, as
it changes the EK/EKpub and renders any provisioned EKcert useless.
Resetting the storage hierarchy seed is much less dramatic. The NULL
hierarchy is reset every time the TPM resets.)
PCRs always persist, but they get reset on restart.
NV indexes always persist. (But in disorderly resets/shutdowns a
hybrid NV index may not be sync'ed to NV.)
## Non-Volatile (NV) Indexes
TPMs also have a special kind of non-volatile object: NV indexes.
> NOTE: NV indexes are not "objects" in the sense that the TCG's
> specifications mean. TCG's definition of "object" is
>
> > key or data that has a public portion and, optionally, a
> > sensitive portion; and which is a member of a hierarchy
NV indexes come in multiple flavors for various uses:
- store public data (e.g., an NV index is used to store the EKcert)
- emulate PCRs
- monotonic counters
- fields of write-once bits (bitfields) (for, e.g., revocation)
- ...
NV indexes can be used standalone, and/or in connection with policies,
to enrich application TPM semantics.
## Authentication and Authorization
TPMs have multiple ways to authenticate users/entities:
- plain passwords (legacy)
- HMAC based on secret keys or passwords
- public key signed attestations of identification by biometric
authentication devices
TPMs have two ways to authorize access to various objects:
- plain passwords (legacy)
- HMAC proof of possession of a secret key or password
- arbitrarily complex policies that can make reference to:
- PCR state
- NV index state
- time of day
- authentication state
- etc.
### Policies
A policy consists of a sequence of "commands" that each asserts
something of interest.
Policies are particularly interesting because they are cryptographically
named using hash extension with the sequence of "commands" that make up
a policy. Therefore no matter how complex and large a policy is, it is
always "compressed" to a hash digest.
It is the responsibility of the application that will attempt to use a
policy-protected resource to know what the policy's definition is and
restate it to the TPM when it goes to make use of that resource. The
TPM will evaluate the policy and, at the end, check that its digest
matches that of the policy-protected resource. Thus, and because policy
digests are small and fixed-sized, they can be arbitrarily more complex
than a TPM's limited resources would otherwise allow.
All the policy commands that are to be evaluated successfully to grant
access have to be known to the entity that wants that access. Of
course, that entity will have to satisfy -at access time- the conditions
expressed by the relevant policy. And that entity has to know the
policy because the TPM knows only a digest of it.
### Policy Construction
Construction of a policy consists of computing it by hash extending an
initial all-zeroes value with the commands that make up the policy.
### Policy Evaluation
Evaluation of a policy consists of issuing those same commands to the
TPM in a session, with those commands either evaluated immediately or
deferred to the time of execution of the to-be-authorized command, but
the TPM computes the same hash extension as it goes. Once all policy
commands being evaluated have succeeded, the resulting hash extension
value is compared to the policy that protects the resource(s) being used
by the to-be-authorized command, and if it matches, then the command is
allowed, otherwise it is not.
### Indirect Policies
Because an object's policy is part of its name, that policy cannot be
changed after creation. An indirect policy command allows for a policy
to change over time without having to recreate the authorized object.
### Compound Policies
Policies consist of a conjunction (logical-AND) of assertions that must
be true at evaluation time.
However, there is a special policy command that allows for alternation
(logical-OR). This policy command has a number of alternative policy
digests. At evaluation time, one of the alternation digests must match
the extension value for the policy commands up to (but excluding) the
logical-OR policy command. At evaluation time the caller must have
picked one of the alternatives and executed the commands that make it
up.
(Recall that the application has to know the definition of the policy
because the TPM knows only the policy's digest.)
### Rich Policy Semantics
With all these features, and with all the flexibility allowed by NV
indexes, policies can be used to:
- require that N-of-M users authenticate
- require multi-factor authentication (password, biometric, smartcard)
- enforce bank vault-like time of day restrictions
- check revocation (using NV index bit-field objects)
- check system RTM state (PCRs)
- distinguish user roles
## Sessions
A session is an object (meaning, among other things, that it can be
loaded and unloaded as needed) that represents the current policy
construction or evaluation hash extension digest (the `policyDigest`),
and the objects that have been granted access.
## Restricted Cryptographic Keys
Cryptographic keys can either be unrestricted or restricted.
An unrestricted signing key can be used to sign arbitrary content.
A restricted signing key can be used to sign only TPM-generated content
as part of specific TPM restricted signing commands. Such content
always begins with a magic byte sequence. Conversely, the TPM refuses
to sign externally generated content that starts with that magic byte
sequence.
A restricted decryption key can only be used to decrypt ciphertexts
whose plaintexts have a certain structure. In particular these are used
for `TPM2_MakeCredential()`/`TPM2_ActivateCredential()` to allow the
TPM-using application to get the plaintext if and only if (IFF) the
plaintext cryptographically names an object that the application has
access to. This is used to communicate secrets ("credentials") to TPMs.
There is also a notion of signing keys that can only be used to sign
PKIX certificates.
## Attestation
Attestation is the process of demonstrating that a system's current
state is "trusted", or the truthfulness of some set of assertions.
Often a system gets something in exchange for attesting to its current
state. E.g., keys for unlocking filesystems, or device credentials.
As you can see in our [tutorial on attestation](/Attestation/README.md),
many TPM concepts can be used to great effect:
- using PCRs to attest to system state
- using policies and sealed-to-PCRs objects to attest to authentication
events on the system
- using restricted keys and cryptographic object naming to authenticate
a TPM and bind it to its host
- delivering key material to authenticated systems via their TPMs
- unlocking resources following successful attestation
- authorization of devices onto a network
- etc.
# Other Resources
[A Practical Guide to TPM 2.0](https://trustedcomputinggroup.org/resource/a-practical-guide-to-tpm-2-0/)
is an excellent book that informed much of this tutorial.
Nokia has a [TPM course](https://github.com/nokia/TPMCourse/tree/master/docs).
The TCG has a number of members-only tutorials, but it seems that it is
possible to be invited to be a non-fee paying member.
Core TCG TPM specs:
- [TCG TPM 2.0 Library part 1: Architecture](https://trustedcomputinggroup.org/wp-content/uploads/TCG_TPM2_r1p59_Part1_Architecture_pub.pdf).
- [TCG TPM 2.0 Library part 2: Structures](https://trustedcomputinggroup.org/wp-content/uploads/TCG_TPM2_r1p59_Part2_Structures_pub.pdf).
- [TCG TPM 2.0 Library part 3: Commands, section 12](https://trustedcomputinggroup.org/wp-content/uploads/TCG_TPM2_r1p59_Part3_Commands_pub.pdf).
- [TCG TPM 2.0 Library part 3: Commands Code, section 12](https://trustedcomputinggroup.org/wp-content/uploads/TCG_TPM2_r1p59_Part3_Commands_code_pub.pdf).

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## Current list of tutorials from [TPM.dev] members
1. Attestation, MakeCredential, ActivateCredential
1. Boot with TPM: Secure vs Measured vs Trusted
1. Random Number Generator
1. TPM Introduction (Work in progress - PR #8)
1. [Boot with TPM: Secure vs Measured vs Trusted](Boot-with-TPM/tpmboot.md)
1. [Random Number Generator](Random_Number_Generator/article.md)
1. [Attestation, MakeCredential, ActivateCredential](Attestation/README.md)
1. Introduction to TPM Concepts (Work in progress - PR #8)
## List of tutorials that will be transfered to GitHub from [TPM.dev]