Account security on the modern web is a bit of a nightmare. Everyone understands the need for strong passwords which are different for each account, but managing them is problematic because the human mind just can’t remember hundreds of complete gibberish words so everyone uses a password manager (which, lets admit it, for a lot of people is to write it down). A solution to this problem has long been something called two factor authentication (2FA) which authenticates you by something you know (like a password) and something you posses (like a TPM or a USB token). The problem has always been that you ideally need a different 2FA for each website, so that a compromise of one website doesn’t lead to the compromise of all your accounts.

Enter webauthn. This is designed as a 2FA protocol that uses public key cryptography instead of shared secrets and also uses a different public/private key pair for each website. Thus aspiring to be a passwordless secure scalable 2FA system for the web. However, the webauthn standard only specifies how the protocol works when the browser communicates with the remote website, there’s a different standard called FIDO or U2F that specifies how the browser communicates with the second factor (called an authenticator in FIDO speak) and how that second factor works.

It turns out that the FIDO standards do specify a TPM as one possible backend, so what, you might ask does this have to do with the Linux Gadget subsystem? The answer, it turns out, is that although the standards do recommend a TPM as the second factor, they don’t specify how to connect to one. The only connection protocols in the Client To Authenticator Protocol (CTAP) specifications are USB, BLE and NFC. And, in fact, the only one that’s really widely implemented in browsers is USB, so if you want to connect your laptop’s TPM to a browser it’s going to have to go over USB meaning you need a Linux USB gadget. Conspiracy theorists will obviously notice that if the main current connector is USB and FIDO requires new USB tokens because it’s a new standard then webauthn is a boon to token manufacturers.

How does Webauthn Work?

The protocol comes in two flavours, version 1 and version 2. Version 1 is fixed cryptography and version 2 is agile cryptography. However, version1 is simpler so that’s the one I’ll explain.

Webauthn essentially consists of two phases: a registration phase where the authenticator is tied to the account, which often happens when the remote account is created, and authentication where the authenticator is used to log in again to the website after registration. Obviously accounts often outlive the second factor, especially if it’s tied to a machine like the TPM, so the standard contemplates a single account having multiple registered authenticators.

The registration request consists of a random challenge supplied by the remote website to prevent replay and an application id which is constructed by the browser from the website supplied ID and the web origin of the site. The design is that the application ID should be unique for each remote account and not subject to being faked by the remote site to trick you into giving up some other application’s credentials.

The authenticator’s response consists of a unique public key, an opaque key handle, an attestation X.509 certificate containing a public key and a signature over the challenge, the application ID, the public key and the key handle using the private key of the certificate. The remote website can verify this signature against the certificate to verify registration. Additionally, Google recommends that the website also verifies the attestation certificate against a list of know device master certificates to prove it is talking to a genuine U2F authenticator. Since no-one is currently maintaining a database of “genuine” second factor master certificates, this last step mostly isn’t done today.

In version 1, the only key scheme allowed is Elliptic Curve over the NIST P-256 curve. This means that the public key is always 65 bytes long and an encrypted (or wrapped) form of the private key can be stashed inside the opaque key handle, which may be a maximum of 255 bytes. Since the key handle must be presented for each authentication attempt, it relieves the second factor from having to remember an ever increasing list of public/private key pairs because all it needs to do is unwrap the private key from the opaque handle and perform the signature and then forget the unwrapped private key. Note that this means per user account authenticator, the remote website must store the public key and the key handle, meaning about 300 bytes extra, but that’s peanuts compared to the amount of information remote websites usually store per registered account.

To perform an authentication the remote website presents a unique challenge, the raw ID from which the browser should construct the same application ID and the key handle. Ideally the authenticator should verify that the application ID matches the one used for registration (so it should be part of the wrapped key handle) and then perform a signature over the application ID, the challenge and a unique monotonically increasing counter number which is sent back in the response. To validly authenticate, the remote website verifies the signature is genuine and that the count has increased from the last time authentication has done (so it has to store the per authenticator 4 byte count as well). Any increase is fine, so each second factor only needs to maintain a single monotonically increasing counter to use for every registered site.

Problems with Webauthn and the TPM

The primary problem is the attestation certificate, which is actually an issue for the whole protocol. TPMs are actually designed to do attestation correctly, which means providing proof of being a genuine TPM without compromising the user’s privacy. The way they do this is via a somewhat complex attestation protocol involving a privacy CA. The problem they’re seeking to avoid is that if you present the same certificate every time you use the device for registration you can be tracked via that certificate and your privacy is compromised. The way the TPM gets around this is that you can use a privacy CA to produce an arbitrary number of different certificates for the same TPM and you could present a new one every time, thus leaving nothing to be tracked by.

The ability to track users by certificate has been a criticism levelled at FIDO and the best the alliance can come up with is the idea that perhaps you batch the attestation certificates, so the same certificate is used in hundreds of new keys.

The problem for TPMs though is that until FIDO devices use proper privacy CA based attestation, the best you can do is generate a separate self signed attestation certificate. The reason is that the TPM does contain its own certificate, but it’s encryption only, not signing because of the way the TPM privacy CA based attestation works. Thus, even if you were willing to give up your privacy you can’t use the TPM EK certificate as the FIDO attestation certificate. Plus, if Google carries out its threat to verify attestation certificates, this scheme is no longer going to work.

Aside about Browsers and CTAP

The crypto aware among you will recognise that there is already a library based standard that can be used to talk to a variety of USB tokens and even the TPM called PKCS#11. Mozilla Firefox, for instance, already supports using this as I demonstrated in a previous blog post. One might think, based on what I said about the one token per key problem in the introduction, that PKCS#11 can’t support the new key wrapping based aspect of FIDO but, in fact, it can via the C_WrapKey/C_UnwrapKey API. The only thing PKCS#11 can’t do is the new monotonic counter.

Even if PKCS#11 can’t perform all the necessary functions, what about a new or extended library based protocol? This is a good question to which I’ve been unable to get a satisfactory answer. Certainly doing CTAP correctly requires that your browser be able to speak directly to the USB, Bluetooth and NFC subsystems. Perhaps not too hard for a single platform browser like Internet Explorer, but fraught with platform complexity for generic browsers like FireFox where the only solution is to have a rust based accessor for every supported platform.

Certainly the lack of a library interface are where the TPM issues come from, because without that we have to plug the TPM based FIDO layer into a browser over an existing CTAP protocol it supports, i.e. USB. Fortunately Linux has the USB Gadget subsystem which fits the bill precisely.

Building Synthetic HID Devices with USB Gadget

Before you try this at home, I should point out that the Linux HID Gadget has a longstanding bug that will cause your machine to hang unless you have this patch applied. You have been warned!

The HID subsystem is for driving Human Interaction Devices meaning keyboard and mice. However, it has a simple packet (called report in USB speak) based protocol which is easy for most things to use. In order to facilitate this, Linux actually provides hidraw devices which allow you to send and receive these reports using read and write system calls (which, in fact, is how Firefox on Linux speaks CTAP). What the hid gadget does when set up is provide all the static emulation of HID device protocols (like discovery pages) while allowing you to send and receive the hidraw packets over the /dev/hidgX device tap, also via read and write (essentially operating like a tty/pty pair²). To get the whole thing running, the final piece of the puzzle is that the browser (most likely running as you) needs to be able to speak to the hidraw device, so you need a udev rule to make it accessible because by default they’re 0600. Since the same goes for every other USB security token, you’ll find the template in the same rpm that installs the PKCS#11 library for the token.

The way CTAP works is that every transaction is split into 64 byte reports and sent over the hidraw interface. All you need to do to get this setup is initialise a report descriptor for this type of device. Since it’s somewhat cumbersome to do, I’ve created this script to do it (run it as root). Once you have this, the hidraw and hidg devices will appear (make them both user accessible with chmod 666) and then all you need is a programme to drive the hidg device and you’re done.

A TPM Based Hid Gadget Driver

Note: this section is written describing TPM 2.0.

The first thing we need out of the TPM is a monotonic counter, but all TPMs have NV counter indexes which can be created (all TPM counters are 8 byte, whereas the CTAP protocol requires 4 bytes, but we simply chop off the top 4 bytes). By convention I create the counter at NV index 01000101. Once created, this counter will be persistent and monotonic for the lifetime of the TPM.

The next thing you need is an attestation certificate and key. These must be NIST P-256 based, but it’s easy to get openssl to create them

openssl genpkey -algorithm EC -pkeyopt ec_paramgen_curve:prime256v1 -pkeyopt ec_param_enc:named_curve -out reg_key.key

openssl req -new -x509 -subj '/CN=My Fido Token/' -key reg_key.key -out reg_key.der -outform DER

This creates a self signed certificate, but you could also create a certificate chain this way.

Finally, we need the TPM to generate one NIST P-256 key pair per registration. Here we use the TPM2_Create() call which gets the TPM to create a random asymmetric key pair and return the public and wrapped private pieces. We can simply bundle these up and return them as the key handle (fortunately, what the TPM spits back for a NIST P-256 key is about 190 bytes when properly marshalled). When the remote end requests an authentication, we extract the TPM key from the key handle and use a TPM2_Load to place it in the TPM and sign the hash and then unload it from the TPM. Putting this all together this project (which is highly experimental) provides the script to create the devices and a hidg driver that interfaces to the TPM. All you need to do is run it as

hidgd /dev/hidg0 reg_key.der reg_key.key

And you’re good to go. If you want to test it there are plenty of public domain webauthn test sites, webauthn.org and webauthn.io³ are two I’ve tested as working.

TODO Items

The webauthn standard specifies the USB authenticator should ask for permission before performing either registration or authentication. Currently the TPM hid gadget doesn’t have any external verification, but in future I’ll add a configurable pinentry to add confirmation and possibly also a single password for verification.

The current code also does nothing to verify the application ID on a per authorization basis. This is a security problem because you are currently vulnerable to being spoofed by malicious websites who could hand you a snooped key handle and then use the signature to fake your login to a different site. To avoid this, I’m planning to use the policy area of the TPM key to hold the application ID. This should work because the generated keys have no authorization, either policy or password, so the policy area is effectively redundant. It is in the unwrapped public key, but if any part of the public key is tampered with the TPM will detect this via a hash in the wrapped private error and give a binding error on load.

The current code really only does version 1 of the FIDO protocol. Ideally it needs upgrading to version 2. However, there’s not really much point because for all the crypto agility, most TPMs on the market today can only do NIST P-256 curves, so you wouldn’t gain that much.

Conclusions

Using this scheme you’re ready to play with FIDO/U2F as long as you have a laptop with a functional TPM 2.0 and a working USB gadget subsystem. If you want to play, please remember to make sure you have the gadget patch applied.

One of the useful features of Apache (or indeed any competent web server) is the ability to use client side certificates. All this means is that a certificate from each end of the TLS transaction is verified: the browser verifies the website certificate, but the website requires the client also to present one and verifies it. Using client certificates, when linked to your own client certificate CA gives web transactions the strength of two factor authentication if you do it on the login page. I use this feature quite a lot for all the admin features my own website does. With apache it’s really simple to turn on with the

SSLCACertificateFile

Directive which allows you to specify the CA for the accepted certificates. In my own setup I have my own self signed certificate as CA and then all the authority certificates use it as the issuer. You can turn Client Certificate verification on per location basis simply by doing

<Location /some/web/location>
      SSLVerifyClient require
</Location

And Apache will take care of requesting the client certificate and verifying it against the CA. The only caveat here is that TLSv1.3 currently fails to work for this, so you have to disable it with

SSLProtocol -TLSv1.3

Client Certificates in Firefox

Firefox is somewhat hard to handle for SSL because it includes its own hand written mozilla secure sockets code, which has a toolkit quite unlike any other ssl toolkit⁴. In order to import a client certificate and key into firefox, you need to create a pkcs12 file containing them and import that into the “Your Certificates” box which is under Preferences > Privacy & Security > View Certificates

Obviously, simply supplying a key file to firefox presents security issues because you’d like to prevent a clever hacker from gaining access to it and thus running off with your client certificate. Firefox achieves a modicum of security by doing all key operations over the PKCS#11 API via a software token, which should mean that even malicious javascript cannot gain access to your key but merely the signing API

However, assuming you don’t quite trust this software separation, you need to store your client signing key in a secure vault like a TPM to make sure no web hacker can gain access to it. Various crypto system connectors, like the OpenSSL TPM⁵ and TPM2 engine, already exist but because Firefox uses its own crytographic code it can’t take advantage of them. In fact, the only external object the Firefox crypto code can use is a PKCS#11 module.

Aside about TPM2 and PKCS#11

The design of PKCS#11 is that it is a loadable library which can find and enumerate keys and certificates in some type of hardware device like a USB Key or a PCI attached HSM. However, since the connector is simply a library, nothing requires it connect to something physical and the OpenDNSSEC project actually produces a purely software based cryptographic token. In theory, then, it should be easy

The problems come with the PKCS#11 expectation of key residency: The library allows the consuming program to enumerate a list of slots each of which may, or may not, be occupied by a single token. Each token may contain one or more keys and certificates. Now the TPM does have a concept of a key resident in NV memory, which is directly analagous to the PKCS#11 concept of a token based key. The problems start with the TPM2 PC Client Profile which recommends this NV area be about 512 bytes, which is big enough for all of one key and thus not very scalable. In fact, the imagined use case of the TPM is with volatile keys which are demand loaded.

Demand loaded keys map very nicely to the OpenSSL idea of a key file, which is why OpenSSL TPM engines are very easy to understand and use, but they don’t map at all into the concept of token resident keys. The closest interface PKCS#11 has for handling key files is the provisioning calls, but even there they’re designed for placing keys inside tokens and, once provisioned, the keys are expected to be non-volatile. Worse still, very few PKCS#11 module consumers actually do provisioning, they mostly leave it up to a separate binary they expect the token producer to supply.

Even if the demand loading problem could be solved, the PKCS#11 API requires quite a bit of additional information about keys, like ids, serial numbers and labels that aren’t present in the standard OpenSSL key files and have to be supplied somehow.

Solving the Key File to PKCS#11 Mismatch

The solution seems reasonably simple: build a standard PKCS#11 library that is driven by a known configuration file. This configuration file can map keys to slots, as required by PKCS#11, and also supply all the missing information. the C_Login() operation is expected to supply a passphrase (or PIN in PKCS#11 speak) so that would be the point at which the private key could be loaded.

One of the interesting features of the above is that, while it could be implemented for the TPM engine only, it can also be implemented as a generic OpenSSL key exporter to PKCS#11 that happens also to take engine keys. That would mean it would work for non-engine keys as well as any engine that exists for OpenSSL … a nice little win.

Building an OpenSSL PKCS#11 Key Exporter

A Token can be built from a very simple ini like configuration file, with the global section setting global properties, like manufacurer id and library description and each individual section being used to instantiate a slot containing one key. We can make the slot name, the id and the label the same if not overridden and use key file directives to load the public and private keys. The serial number seems best constructed from a hash of the public key parameters (again, if not overridden). In order to support engine keys, the token library needs to know which engine to invoke, so I added an engine keyword to tell it.

With that, the mechanics of making the token library work with any OpenSSL key are set, the only thing is to plumb in the PKCS#11 glue API. At this point, I should add that the goal is simply to get keys and tokens working, not to replicate a full featured PKCS#11 API, so you shouldn’t use this as something to test against for a reference implementation (the softhsm2 token is much better for that). However, it should be functional enough to use for storing keys in Firefox (as well as other things, see below).

The current reasonably full featured source code is here, with a reference build using the OpenSUSE Build Service here. I should add that some of the build failures are due to problems with p11-kit and others due to the way Debian gets the wrong engine path for libp11.

At Last: Getting TPM Keys working with Firefox

A final problem with Firefox is that there seems to be no way to import a certificate file for which the private key is located on a token. The only way Firefox seems to support this is if the token contains both the private key and the certificate. At least this is my own project, so some coding later, the token now supports certificates as well.

The next problem is more mundane: generating the certificate and key. Obviously, the safest key is one which has never left the TPM, which means the certificate request needs to be built from it. I chose a CSR type that also includes my name and my machine name for later easy discrimination (and revocation if I ever lose my laptop). This is the sequence of commands for my machine called jarvis.

create_tpm2_key -a key.tpm
openssl req -subj "/CN=James Bottomley/UID=jarivs/" -new -engine tpm2 -keyform engine -key key.tpm -nodes -out jarvis.csr
openssl x509 -in jarvis.csr -req -CA  my-ca.crt -engine tpm2 -CAkeyform engine -CAkey my-ca.key -days 3650 -out jarvis.crt

As you can see from the above, the key is first created by the TPM, then that key is used to create a certificate request where the common name is my name and the UID is the machine name (this is just my convention, feel free to use your own) and then finally it’s signed by my own CA, which you’ll notice is also based on a TPM key. Once I have this, I’m free to create an ini file to export it as a token to Firefox

manufacturer id = Firefox Client Cert
library description = Cert for hansen partnership
[mozilla-key]
certificate = /home/jejb/jarvis.crt
private key = /home/jejb/key.tpm
engine = tpm2

All I now need to do is load the PKCS#11 shared object library into Firefox using Settings > Privacy & Security > Security Devices > Load and I have a TPM based client certificate ready for use.

Additional Uses

It turns out once you have a generic PKCS#11 exporter for engine keys, there’s no end of uses for them. One of the most convenient has been using TPM2 keys with gnutls. Although gnutls was quick to adopt TPM 1.2 based keys, it’s been much slower with TPM2 but because gnutls already has a PKCS#11 interface using the p11 kit URI format, you can easily build a config file of all the TPM2 keys you want it to use and simply use them by URI in gnutls.

Unfortunately, this has also lead to some problems, the biggest one being Firefox: Firefox assumes, once you load a PKCS#11 module library, that you want it to use every single key it can find, which is fine until it pops up 10 dialogue boxes each time you start it, one for each key password, particularly if there’s only one key you actually care about it using. This problem doesn’t seem solvable in the Firefox token interface, so the eventual way I did it was to add the ability to specify the config file in the environment (variable OPENSSL_PKCS11_CONF) and modify my xfce Firefox action to set this in the environment pointing at a special configuration file with only Firefox’s key in it.

Conclusions and Future Work

Hopefully I’ve demonstrated this simple PKCS#11 converter can be useful both to keeping Firefox keys safe as well as uses in other things like gnutls. Unfortunately, it turns out that the world wide web is turning against PKCS#11 tokens as having usability problems and is moving on to something called FIDO2 tokens which have the web browser talking directly to the USB token. In my next technical post I hope to explain how you can use the Linux Kernel USB gadget system to connect a TPM up easily as a FIDO2 token so you can use the new passwordless webauthn protocol seamlessly.

One of the most significant advances going from TPM1.2 to TPM2 was the addition of algorithm agility: The ability of TPM2 to work with arbitrary symmetric and asymmetric encryption schemes.  In practice, in spite of this much vaunted agile encryption capability, most actual TPM2 chips I’ve seen only support a small number of asymmetric encryption schemes, usually RSA2048 and a couple of Elliptic Curves.  However, the ability to support any Elliptic Curve at all is a step up from TPM1.2.  This blog post will detail how elliptic curve schemes can be integrated into existing cryptographic systems using TPM2.  However, before we start on the practice, we need at least a tiny swing through the theory of Elliptic Curves.

What is an Elliptic Curve?

An Elliptic Curve (EC) is simply the set of points that lie on the curve in the two dimensional plane (x,y) defined by the equation

y² = x³ + ax + b

which means that every elliptic curve can be parametrised by two constants a and b.  The set of all points lying on the curve plus a point at infinity is combined with an addition operation to produce an abelian (commutative) group.  The addition property is defined by drawing straight lines between two points and seeing where they intersect the curve (or picking the infinity point if they don’t intersect).  Wikipedia has a nice diagrammatic description of this here.  The infinity point acts as the identity of the addition rule and the whole group is denoted E.

The utility for cryptography is that you can define an integer multiplier operation which is simply the element added to itself n times, so for P ∈ E, you can always find Q ∈ E such that

Q = P + P + P … = n × P

And, since it’s a simple multiplication like operation, it’s very easy to compute Q.  However, given P and Q it is computationally very difficult to get back to n.  In fact, it can be demonstrated mathematically that trying to compute n is equivalent to the discrete logarithm problem which is the mathematical basis for the cryptographic security of RSA.  This also means that EC keys suffer the same (actually more so) problems as RSA keys: they’re not Quantum Computing secure (vulnerable to the Quantum Shor’s algorithm) and they would be instantly compromised if the discrete logarithm problem were ever solved.

Therefore, for any elliptic curve, E, you can choose a known point G ∈ E, select a large integer d and you can compute a point P = d × G.  You can then publish (P, G, E) as your public key knowing it’s computationally infeasible for anyone to derive your private key d.

For instance, Diffie-Hellman key exchange can be done by agreeing (E, G) and getting Alice and Bob to select private keys d_A, d_B.  Then knowing Bob’s public key P_B, Alice can select a random integer r, which she publishes, and compute a key agreement as a secret point on the Elliptic Curve (r d_A) × P_B.  Bob can derive the same Elliptic Curve point because

(r d_A) × P_B = (r d_A)d_B × G = (r d_B) d_A × G = (r d_B) × P_A

The agreement is a point on the curve, but you can use an agreed hashing or other mechanism to get from the point to a symmetric key.

Seems simple, but the problem for computing is that we really want to use integers and right at the moment the elliptic curve is defined over all the real numbers, meaning E is of infinite size and involves floating point computations (of rather large precision).

Elliptic Curves over Finite Fields

Fortunately there is a mathematical theory of finite fields, called Galois Theory, which allows us to take the Galois Field over prime number p, which is denoted GF(p), and compute Elliptic Curve points over this field.  This derivation, which is mathematically rather complicated, is denoted E(GF(p)), where every point (x,y) is represented by a pair of integers between 0 and p-1.  There is another theory that says the number of elements in E(GF(p))

n = |E(GF(p))|

is roughly the same size as p, meaning if you choose a 32 bit prime p, you likely have a field over roughly 2^32 elements.  For every point P in E(GF(p)) it is also mathematically proveable that n × P = 0. where 0 is the zero point (which was the infinity point in the real elliptic curve).

This means that you can take any point, G,  in E(GF(p)) and compute a subgroup based on it:

E_G = { ∀m ∈ Z_n : m × G }

If you’re lucky |E_G| = |E(GF(p))| and G is the generator of the entire group.  However, G may only generate a subgroup and you will find |E_G| = h|E(GF(p))| where integer h is called the cofactor.  In general you want the cofactor to be small (preferably less than four) for E_G to be cryptographically useful.

For a computer’s purposes, E_G is the elliptic curve group used for integer arithmetic in the cryptographic algorithms.  The Curve and Generator is then defined by (p, a, b, Gx, Gy, n, h) which are the published parameters of the key (Gx, Gy represent the x and y elements of point G).  You select a random number d as your private key and your public key P = d × G exactly as above, except now P is easy to compute with integer operations.

Problems with Elliptic Curves

Although I stated above that solving P = d × G is equivalent in difficulty to the discrete logarithm problem, that’s not generally true.  If the discrete logarithm problem were solved, then we’d easily be able to compute d for every generator and curve, but it is possible to pick curves for which d can be easily computed without solving the discrete logarithm problem. This is the reason why you should never pick your own curve parameters (even if you think you know what you’re doing) because it’s very easy to choose a compromised curve.  As a demonstration of the difficulty of the problem: each of the major nation state actors, Russia, China and the US, publishes their own curve parameters for use in their own cryptographic EC implementations and each of them thinks the parameters published by the others is compromised in a way that allows the respective national security agencies to derive private keys.  So if nation state actors can’t tell if a curve is compromised or not, you surely won’t be able to either.

Therefore, to be secure in EC cryptography, you pick and existing curve which has been vetted and select some random Generator Point on it.  Of course, if you’re paranoid, that means you won’t be using any of the nation state supplied curves …

Using the TPM2 with Elliptic Curves in Cryptosystems

The initial target for this work was the openssl cryptosystem whose libraries are widely used for deriving other uses (like https in apache or openssh). Originally, when I did the initial TPM2 enabling of openssl as described in this blog post, I added TPM2 as a patch to the existing TPM 1.2 openssl_tpm_engine.  Unfortunately, openssl_tpm_engine seems to be pretty much defunct at this point, so I started my own openssl_tpm2_engine as a separate git tree to begin experimenting with Elliptic Curve keys (if you don’t use git, you can download the tar file here). One of the benefits to running my own source tree is that I can now add a testing infrastructure that makes use of the IBM TPM emulator to make sure that the basic cryptographic operations all work which means that make check functions even when a TPM2 isn’t available.  The current key creation and import algorithms use secured connections to the TPM (to avoid eavesdropping) which means it’s only really possible to construct them using the IBM TSS. To make all of this easier, I’ve set up an openSUSE Build Service repository which is building for all major architectures and the openSUSE and Fedora distributions (ignore the failures, they’re currently induced because the TPM emulator only currently works on 64 bit little endian systems, so make check is failing, but the TPM people at IBM are working on this, so eventually the builds should be complete).

TPM2 itself also has some annoying restrictions.  The biggest of which is that it doesn’t allow you to pass in arbitrary elliptic curve parameters; you may only use elliptic curves which the TPM itself knows.  This will be annoying if you have an existing EC key you’re trying to import because the TPM may reject it as an unknown algorithm.  For instance, openssl can actually compute with arbitrary EC parameters, but has 39 current elliptic curves parametrised by name. By contrast, my Nuvoton TPM2 inside my Dell XPS 13 knows precisely two curves:

jejb@jarvis:~> create_tpm2_key --list-curves
prime256v1
bnp256

However, assuming you’ve picked a compatible curve for your EC private key (and you’ve defined a parent key for the storage hierarchy) you can simply import it to a TPM bound key:

create_tpm2_key -p 81000001 -w key.priv key.tpm

The tool will report an error if it can’t convert the curve parameters to a named elliptic curve known to the TPM

jejb@jarvis:~> openssl genpkey -algorithm EC -pkeyopt ec_paramgen_curve:brainpoolP256r1 > key.priv
jejb@jarvis:~> create_tpm2_key -p 81000001 -w key.priv key.tpm
TPM does not support the curve in this EC key
openssl_to_tpm_public failed with 166
TPM_RC_CURVE - curve not supported Handle number unspecified

You can also create TPM resident private keys simply by specifying the algorithm

create_tpm2_key -p 81000001 --ecc bnp256 key.tpm

Once you have your TPM based EC keys, you can use them to create public keys and certificates.  For instance, you create a self-signed X509 certificate based on the tpm key by

openssl req -new -x509 -sha256  -key key.tpm -engine tpm2 -keyform engine -out my.crt

Why you should use EC keys with the TPM

The initial attraction is the same as for RSA keys: making it impossible to extract your private key from the system.  However, the mathematical calculations for EC keys are much simpler than for RSA keys and don’t involve finding strong primes, so it’s much simpler for the TPM (being a fairly weak calculation machine) to derive private and public EC keys.  For instance the times taken to derive a RSA key from the primary seed and an EC key differ dramatically

jejb@jarvis:~> time tsscreateprimary -hi o -ecc bnp256 -st
Handle 80ffffff

real 0m0.111s
user 0m0.000s
sys 0m0.014s

jejb@jarvis:~> time tsscreateprimary -hi o -rsa -st
Handle 80ffffff

real 0m20.473s
user 0m0.015s
sys 0m0.084s

so for a slow system like the TPM, using EC keys is a significant speed advantage.  Additionally, there are other advantages.  The standard EC Key signature algorithm is a modification of the NIST Digital Signature Algorithm called ECDSA.  However DSA and ECDSA require a cryptographically strong (and secret) random number as Sony found out to their cost in the EC Key compromise of Playstation 3.  The TPM is a good source of cryptographically strong random numbers and if it generates the signature internally, you can be absolutely sure of keeping the input random number secret.

Why you might want to avoid EC keys altogether

In spite of the many advantages described above, EC keys suffer one additional disadvantage over RSA keys in that Elliptic Curves in general are very hot fields of mathematical research so even if the curve you use today is genuinely not compromised, it’s not impossible that a mathematical advance tomorrow will make the curve you chose (and thus all the private keys you generated) vulnerable.  Of course, the same goes for RSA if anyone ever cracks the discrete logarithm problem, but solving that problem would likely be fully published to world acclaim and recognition as a significant contribution to the advancement of number theory.  Discovering an attack on a currently used elliptic curve on the other hand might be better remunerated by offering to sell it privately to one of the national security agencies …