Hey! I'm David, the author of the Real-World Cryptography book. I'm a crypto engineer at O(1) Labs on the Mina cryptocurrency, previously I was the security lead for Diem (formerly Libra) at Novi (Facebook), and a security consultant for the Cryptography Services of NCC Group. This is my blog about cryptography and security and other related topics that I find interesting.

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# User authentication with passwords, What’s SRP? posted May 2020

The Secure Remote Password (SRP) protocol is first and foremost a Password Authenticated Key Exchange (PAKE). Specifically, SRP is an asymmetric or augmented PAKE: it’s a key exchange where only one side is authenticated thanks to a password. This is usually useful for user authentication protocols. Theoretically any client-server protocol that relies on passwords (like SSH) could be doing it, but instead such protocols often have the password directly sent to the server (hopefully on a secure connection). As such, asymmetric PAKEs offer an interesting way to augment user authentication protocols to avoid the server learning about the user’s password.

Note that the other type of PAKE is called a symmetric or balanced PAKE. In a symmetric PAKE two sides are authenticated thanks to the same password. This is usually useful in user-aided authentication protocols where a user attempts to pair two physical devices together, for example a mobile phone or laptop to a WiFi router. (Note that the recent WiFi protocol WPA3 uses the DragonFly symmetric PAKE for this.)

In this blog post I will answer the following questions:

• What is SRP?
• How does SRP work?
• Should I use SRP today?

## What is SRP?

The stanford SRP homepage puts it in these words:

The Secure Remote Password protocol performs secure remote authentication of short human-memorizable passwords and resists both passive and active network attacks. Because SRP offers this unique combination of password security, user convenience, and freedom from restrictive licenses, it is the most widely standardized protocol of its type, and as a result is being used by organizations both large and small, commercial and open-source, to secure nearly every type of human-authenticated network traffic on a variety of computing platforms.

and goes on to say:

The SRP ciphersuites have become established as the solution for secure mutual password authentication in SSL/TLS, solving the common problem of establishing a secure communications session based on a human-memorized password in a way that is crytographically sound, standardized, peer-reviewed, and has multiple interoperating implementations. As with any crypto primitive, it is almost always better to reuse an existing well-tested package than to start from scratch.

But the Stanford SRP homepage seems to date from the late 90s.

SRP was standardized for the first time in 2000 in RFC 2944 - Telnet Authentication: SRP. Nowadays, most people refer to SRP as the implementation used in TLS. This one was specified in 2007 in RFC 5054 - Using the Secure Remote Password (SRP) Protocol for TLS Authentication.

## How does SRP work?

The Stanford SRP homage lists 4 different versions of SRP, with the last one being SRP 6. Not sure where version 4 and 5 are, but version 6 is the version that is standardized and implemented in TLS. There is also the revision SRP 6a, but I’m also not sure if it’s in use anywhere today.

To register, Alice sends her identity, a random $salt$, and a salted hash $x$ of her password. Right from the start, you can see that a hash function is used (instead of a password hash function like Argon2) and thus anyone who sees this message can efficiently brute-force the hashed password. Not great. The use of the user-generated salt though, manage to prevent brute-force attacks that would impact all users.

The server can then register Alice by exponentiating a generator of a pre-determined ring (an additive group with a multiplicative operation) with the hashed password. This is an important step as you will see that anyone with the knowledge of $x$ can impersonate Alice.

What follows is the login protocol:

You can now see why this is called a password authenticated key exchange, the login flow includes the standard ephemeral key exchange with a twist: the server’s public key $B’$ is blinded or hidden with $v$, a random value derived from Alice’s password. (Note here $k$ is a constant fixed by the protocol so we will just ignore it.)

Alice can only unblinds the server’s ephemeral key by deriving $v$ herself. To do this, she needs the $salt$ she registered with (and this is why the server sends it back to Alice as part of the flow).  For Alice, the SRP login flow goes like this:

• Alice re-computes $x = H(salt, password)$ using her password and the salt received from the server.
• Alice unblinds the server’s ephemeral key by doing $B=B’- kg^x = g^b$
• Alice then computes the shared secret $S$ by multiplying the results of two key exchanges:
• $B^a$, the ephemeral key exchange
• $B^{ux}$, a key exchange between the server’s public key and a value combining the hashed password and the two ephemeral public keys

Interestingly, the second key exchange makes sure that the hashed password and the transcript gets involved in the computation of the shared secret. But strangely, only the public keys and not the full transcript are used.

The server can then compute the shared secret $S$ as well, using the multiplication of the same two key exchanges:

• $A^b$, the ephemeral key exchange
• $v^{ub}$, the other key exchange involving the hashed password and the two ephemeral public keys

The final step is for both sides to hash the shared secret and use it as the session key $K = H(S)$. Key confirmation can then happen after both sides make successful use of this session key. (Without key confirmation, you’re not sure if the other side managed to perform the PAKE.)

## Should I use SRP today?

The SRP scheme is a much better way to handle user passwords, but it has a number of flaws that make the PAKE protocol less than ideal. For example, someone who intercepts the registration process can then easily impersonate Alice as the password is never directly used in the protocol, but instead the salted hash of the password which is communicated during the registration process.

This was noticed by multiple security researchers along the years. Matthew Green in 2018 wrote Should you use SRP?, in which he says:

Lest you think these positive results are all by design, I would note that there are [five prior versions] of the SRP protocol, each of which contains vulnerabilities. So the current status seems to have arrived through a process of attrition, more than design.

After noting that the combination of multiplication and addition makes it impossible to implement in elliptic curve groups, Matthew Green concludes with:

In summary, SRP is just weird. It was created in 1998 and bears all the marks of a protocol invented in the prehistoric days of crypto. It’s been repeatedly broken in various ways, though the most recent [v6] revision doesn’t seem obviously busted — as long as you implement it carefully and use the right parameters. It has no security proof worth a damn, though some will say this doesn’t matter (I disagree with them.)

Furthermore, SRP is not available in the last version of TLS (TLS 1.3).

Since then, many schemes have been proposed, and even standardized and productionized (for example PAK was standardized by Google in 2010) The IETF 104, March 2019 - Overview of existing PAKEs and PAKE selection criteria has a list:

In the summer of 2019, the Crypto Forum Research Group (CFRG) of the IETF started a PAKE selection process, with goal to pick one algorithm to standardize for each category of PAKEs (symmetric/balanced and asymmetric/augmented):

Two months ago (March 20th, 2020) the CFRG announced the end of the PAKE selection process, selecting:

• CPace as the symmetric/balanced PAKE (from Björn Haase and Benoît Labrique)
• OPAQUE as the asymmetric/augmented PAKE (from Stanislaw Jarecki, Hugo Krawczyk, and Jiayu Xu)

Thus, my recommendation is simple, today you should use OPAQUE!

If you want to learn more about OPAQUE, check out chapter 11 of my book real world cryptography.

2 comments

# Alternatives to PGP posted May 2020

As part of my book's chapter on end-to-end encryption I've been writing about the horrors of PGP.

As a recap of what's bad with PGP:

• No authenticated encryption. This is my biggest issue with PGP personally.
• Receiving a signed message means nothing about who sent it to you (see picture below).
• Usability issues with GnuPG (the main implementation).
• Discoverability of public keys issue.
• Bad integration with emails.
• No forward secrecy.

For more, see my post on a history of end-to-end encryption and the death of PGP.

(excerpt from the book Real World Cryptography)

The latter two I don't care that much. Integration with email is doomed from my point of view. And there's just not way to have forward secrecy if we want a near-stateless system.

Email is insecure. Even with PGP, it’s default-plaintext, which means that even if you do everything right, some totally reasonable person you mail, doing totally reasonable things, will invariably CC the quoted plaintext of your encrypted message to someone else (we don’t know a PGP email user who hasn’t seen this happen). PGP email is forward-insecure. Email metadata, including the subject (which is literally message content), are always plaintext. (Thomas Ptatcek)

OK so what can I advise to my readers? What are the alternatives out there?

For file signing, Frank Denis wrote minisign which looks great.

For file encryption, I wrote eureka which does the job. There's also magic wormhole which is often mentioned, and does some really interesting cryptography, but does not seem to address a real use-case (in my opinion) for the following reason: it's synchronous. We already have a multitude of asynchronous ways to transfer files nowadays (dropbox, google drive, email, messaging, etc.) so the problem is not there. Actually there's really no problem... we just all need to agree on one way of encrypting a file and eureka does just that in a hundred lines of code.

(There is a use-case for synchronous file transfer though, and that's when we're near by. Apple's airdrop is for that.)

For one-time authenticated messaging (some people call that signcryption) which is pretty much the whole use-case of PGP, there seems to be only one contender so far: saltpack. The format looks pretty great and seems to address all the issues that PGP had (except for forward secrecy, but again I don't consider this a deal breaker). It seems to only have two serious implementations: keybase and keys.pub. Keybase a bit more involved, and keys.pub is dead simple and super well put. Note that age and rage (which are excellent engineering work) seem to try to address this use case. Unfortunately they do not provide signing as Adam Caudill pointed out. Let's keep a close eye on these tools though as they might evolve in the right direction. To obtain public keys, the web of trust (signing other people keys) hasn't been proven to really scale, instead we are now in a different key distribution model where people broadcast their public keys on various social networks in order to instill their identity to a specific public key. I don't think there's a name for it... but I like to call it broadcast of trust.

For encrypted communications, Signal has clearly succeeded as a proprietary solution, but everyone can benefit from it by using other messaging apps like WhatsApp and Wire or even federated protocols like Matrix. Matrix' main implementation seems to be Riot which I've been using and really digging so far. It also looks like the French government agrees with me. Same thing here, the web of trust doesn't seem to work, and instead what seems to be working is relying on centralized key distribution servers and TOFU but verify (trust the first public key you see, but check the fingerprint out-of-band later).

8 comments

# Hardware Solutions To Highly-Adversarial Environments Part 3: Trusted Execution Environment (TEE), SGX, TrustZone and Hardware Security Tokens posted April 2020

This is end of my blog post series on cryptography with hardware. I’ve written about smart cards and secure elements in part 1 and about HSMs and TPMs in part 2.

## Trusted Execution Environment (TEE)

So far, all of the hardware solutions we’ve talked about have been standalone secure hardware solutions (with the exceptions of smart cards which can be seen as tiny computers). Secure elements, HSMs, and TPMs can be seen as an additional computer.

(picture taken from The right secure hardware for your IoT deployment)

Let’s now talk about integrated secure hardware!

Trusted Execution Environment (TEE) is a concept that extends the instruction set of a processor to allow for programs to run in a separate secure environment. The separation between this secure environment and the ones we are used to deal with already (often called “rich” execution environment) is done via hardware. So what ends up happening is that modern CPUs run both a normal OS as well as a secure OS simultaneously. Both have their own set of registers but share most of the rest of the CPU architecture (and of course system). By using clever CPU-enforced logic, data from the secure world cannot be accessed from the normal world. Due to TEE being implemented directly on the main processor, not only does it mean a TEE is a faster and cheaper product than a TPM or secure element, it also comes for free in a lot of modern CPUs.

TEE like all other hardware solutions has been a concept developed independently by different vendors, and then a standard trying to play catch up (by Global Platform). The most known TEEs are Intel’s Software Guard Extensions (SGX) and ARM’s TrustZone. But there are many more like AMD PSP, RISC-V MultiZone and IBM Secure Service Container.

By design, since a TEE runs on the main CPU and can run any code given to it (in a separate environment called an “enclave”), it offers more functionality than secure elements, HSMs, TPMs (and TPM-like chips). For this reason TEEs are used in a wilder range of applications. We see it being used in clouds when clients don’t trust servers with their own data, multi-party computation (see CCF), to run smart contracts.

TEE’s goal is to first and foremost thwart software attacks. While the claimed software security seems to be really attractive, it is in practice hard to segregate execution while on the same chip as can attest the many software attacks against SGX:

Trustzone is not much better, Quarkslab has a list of paper successfully attacking it as well.

In theory a TPM can be re-implemented in software only via a TEE (which was done by Microsoft) but one must be careful as again, TEE as a concept provides no resistance against hardware attacks besides the fact that things at this microscopic level are way too tiny and tightly packaged together to analyze without expensive equipment. But by default a TEE does not mean you’ll have a secure internal storage (you need to have a fused key that can’t be read to encrypt what you want to store), or a hardware random number generator, and other wished hardware features. But every manufacturers sure has different offers with different levels of physical security and tamper resistance when it comes to chip that supports TEE.

## Hardware Security Tokens

Finally, hardware security tokens are keys that you can usually plug into your machine and that can do some cryptographic operations. For example yubikeys are small dongles that you can plug in the USB port of a laptop, and that will perform some cryptographic operations if you touch its yellow ring.

The word “token” in hardware security token comes from the fact that using it produces a “token” per-authentication request instead of sending the same credentials over and over again.

Yubikeys started as a way to provide 2nd factor authentication, usually in addition to a password, which an attacker can’t exploit in a phishing attack. The idea is that if an attacker calls your grandmother, and asks her to spell out the yubikey output, she won’t be able to. There is no output. Furthermore, modern yubikeys implement the FIDO 2 protocol which will not produce the correct response unless you are on the right webpage (if we are talking about usage for the web). The reason is that the protocol signs metadata that is linked to what’s in the url bar of your browser.

More recently laptops and mobile devices have started offering other ways to provide the same value as a hardware security token via their own secure module. For example Apple provides a biometric-protected (Touch ID or Face ID) authenticator via the secure enclave.

It’s not clear how much protection against hardware attacks your typical hardware security token has to implement since the compromise of one is not enough to authenticate as a user in most cases (unless you use one as single factor authentication). Yet yubikeys are known to have secure elements inside. Still, this doesn’t exclude software attacks if badly programmed. For example in 2013, a low-cost and non-intrusive side-channel attack managed to extract keys from a yubikey.

Cryptocurrency has similar dongles that will sign transactions for a user, but the threat model is different and they will usually have to authenticate the user in some ways and provide tamper resistance. Here is a picture of a Nano ledger.

As with any hardware solutions, attacks have been found there as well (for example one the trezor).

## Conclusion

As a summary, this 3-part blog series surveys different techniques that exist to deal with physical attacks:

• Smart cards are microcomputers that needs to be turned on by an external device like a payment terminal. They can run arbitrary java applications. Bank cards are smart cards for example.
• Secure elements are a generalization of smart cards, which rely on a set of Global Platform standards. SIM Cards are secure elements for example.
• TPMs are re-packaged secure elements plugged on personal and enterprise computers’ motherboards. They follow a standardized API (by the Trusted Computing Group) that are used in a multitude of ways from measured/secure boot with FDE to remote attestation.
• HSMs can be seen as external and big secure elements for servers. They’re faster and more flexible. Seen mostly in data centers to store keys.
• TEEs like TrustZone and SGX can be thought of secure elements implemented within the CPU. They are faster and cheaper but mostly provide resistance against software attacks unless augmented to be tamper-resistant. Most modern CPUs ship with TEEs and various level of defense against hardware attacks.
• Hardware Security Tokens are dongles like yubikeys that often repackage secure elements to provide a 2nd factor by implementing some authentication protocol (usually TOTP or FIDO2).
• There are many more that I haven’t talked about. In reality vendors can do whatever they want. We’ve seen a lot of TPM-like chips. Apple has the secure enclave, Google has Titan, Microsoft has Pluton, Atmel for example sells “crypto elements”.

Keep in mind that no hardware solution is the panacea, you're only increasing the attack's cost. Against a sophisticated attacker all of that is pretty much useless. For this reason design your system so that one device compromised doesn't imply all devices are compromised. Even against normal adversaries, compromising the main operating system often means that you can make arbitrary calls to the secure element. Design your protocol to make sure that the secure element doesn't have to trust the caller by either verifying queries, or relying on an external trusted part, or by relying on a trusted remote party, or by being self-contained, etc. And after all of that, you still have to worry about side channel attacks :)

PS: thanks to Gabe Pike for the many discussions around TEE!

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# Hardware Solutions To Highly-Adversarial Environments Part 2: HSM vs TPM vs Secure Enclave posted April 2020

In the previous post (part 1) you learned about:

• The threat today is not just an attacker intercepting messages over the wire, but an attacker stealing or tampering with the device that runs your cryptography. So called Internet of Things (IoT) devices often run into this type of threats and are by default unprotected against sophisticated attackers.
• Hardware can help protect cryptography applications in highly-adversarial environment. One of the idea is to provide a device with a tamper-resistant chip to store and perform crypto operations. That is, if the device falls in the hands of an attacker, extracting keys or modifying the behavior of the chip will be hard. But hardware-protected crypto is not a panacea, it is merely defense-in-depth, effectively slowing down and increasing the cost of an attack.
• smart cards were one of the first such secure microcontroller that could be used as a micro computer to store secrets and perform cryptographic operations with them. These are supposed to use a number of techniques to discourage physical attackers.
• the concept of a smart card was generalized as a secure element, which is a term employed differently in different domains, but boils down to a smart card that can be used as a coprocessor in a greater system that already has a main processor.
• Google having troubles dealing with the telecoms to host credit card information on SIM cards (which are secure elements), the concept of secure element in the cloud was born. In the payment space this is called host card emulation (HCE). It works simply by storing the credit card information (which is a 3DES symmetric key shared with the bank) in a secure element in the cloud, and only giving a single-use token to the user: if the phone is compromised, the attacker can only use it to pay once.

All good?

In this part 2 of our blog series you will learn about more hardware that supports cryptographic operations! These are all secure elements in concept, and are all doing sort of the same things but in different contexts. Let’s get started!

## Hardware Security Module (HSM)

If you understood what a secure element was, well a hardware secure module (HSM) is pretty much a bigger secure element. Not only the form factor of secure elements require specific ports, but they are also slow and low on memory. (Note that being low on memory is sometimes OK, as you can encrypt keys with a secure element master key, and then store the encrypted keys outside of the secure element.) So HSM is a solution for a more portable, more efficient, more multi-purpose secure element. Like some secure elements, some HSMs can run arbitrary code as well.

HSMs are also subject to their own set of standards and security level. One of the most widely accepted standard is FIPS 140-2: Security Requirements for Cryptographic Modules, which defines security levels between 1 and 4, where level 1 HSMs do not provide any protection against physical attacks and level 4 HSMs will wipe their whole memory if they detect any intrusion!

Typically, you find an HSM as an external device with its own shelf on a rack (see the picture of a luna HSM below) plugged to an enterprise server in a data center.

(To go full circle, some of these HSMs can be administered using smart cards.)

Sometimes you can also find an HSM as a PCIe card plugged into a server’s motherboard, like the IBM Crypto Express in the picture below.

Or even as small dongles that you can plug via USB (if you don’t care about performance), see the picture of a YubiHSM below.

HSMs are highly used in some industries. Every time you enter your PIN in an ATM or a payment terminal, the PIN ends up being verified by an HSM somewhere. Whenever you connect to a website via HTTPS, the root of trust comes from a Certificate Authority (CA) that stores its private key in an HSM, and the TLS connection is possibly terminated by an HSM. You have an Android or iPhone? Chances are Google or Apple are keeping a backup of your phone safe with a fleet of HSMs. This last case is interesting because the threat model is reversed: the user does not trust the cloud with its data, and thus the cloud service provider claims that its service can’t see the user’s encrypted backup nor can access the keys used to encrypt it.

HSMs don’t really have a standard, but most of them will at least implement the Public-Key Cryptography Standard 11 (PKCS#11), one of these old standards that were started by the RSA company and that were progressively moved to the OASIS organization (2012) in order to facilitate adoption of the standards.

While PKCS#11 last version (2.40) was released in 2015, it is merely an update of a standard that originally started in 1994. For this reason it specifies a number of old cryptographic algorithms, or old ways of doing things. Nevertheless, it is good enough for many uses, and specifies an interface that allow different systems to easily interoperate with each other.

While HSMs’ real goals are to make sure nobody can extract key material from them, their security is not always shining. A lot about the security of these hardware solutions really relies on their high price, the protection techniques used not being disclosed, and the certifications (like FIPS and Common Criteria) mostly focusing on the hardware side of things. In practice, devastating software bugs have been found and it is not always straight forward to know if the HSM you use is vulnerable to any of these vulnerabilities (Cryptosense has a good summary of known attacks against HSMs).

By the way, not only the price of one HSM is high (it can easily be dozens of thousands of dollars depending on the security level), in addition to an HSM you often have another HSM you use for testing, and another one you use for backup (in case your first HSM dies with its keys in it). It can add up!

Furthermore, I still haven’t touched on the elephant in the room with all of these solutions: while you might prevent most attackers from reaching your secret keys, you can't prevent attackers from compromising the system and making their own calls to the secure hardware module (be it a secure element or an HSM). Again, these hardware solutions are not a panacea and depending on the scenario they provide more or less defense-in-depth.

By the way, if it applies to your situation modern cryptography can offer better ways of reducing the consequences of key material compromise and mis-use. For example using multi-signatures! Check my blog post on the subject.

## Trusted Platform Module (TPM)

A Trusted Platform Module (TPM) is first and foremost a standard (unlike HSMs) developed in the open by the non-profit Trusted Computing Group (TCG). The latest version is TPM 2.0, published with the ISO/IEC (International Organization for Standardization and the International Electrotechnical Commission).

A TPM complying with the TPM 2.0 standard is a secure microcontroller that carries a hardware random number generator also called true random number generator (TRNG), secure memory for storing secrets, cryptographic operations, and the whole thing is tamper resistant. If this description reminds you of smart cards, secure element, and HSMs well… I told you that everything we were going to be talking about in this chapter were going to be secure elements of some form. (And actually, it’s common to see TPMs implemented as repackaging of secure elements.)

You usually find a TPM directly soldered to the motherboard of many enterprise servers, laptops, and desktop computers (see picture below).

Unlike solutions that we’ve seen previously though, a TPM does not run arbitrary code. It offers a well-defined interface that a greater system can take advantage of. Due to these limitations, a TPM is usually pretty cheap (even cheap enough that some IoT devices will ship with one!).

Here is a non-exhaustive list of interesting applications that a TPM can enable:

• User authentication. Ever heard of the FBI iPhone fiasco? TPMs can be used to require a user PIN or password. In order to prevent low entropy credentials to be easily bruteforced, a TPM can rate limit or even count the number of failed attempts.
• Secure boot. Secure boot is about starting a system in a known trusted state in order to avoid tampering of the OS by malware or physical intrusion. This can be done by using a platform’s TPM and the Unified Extensible Firmware Interface (UEFI) which is the piece of code that launches an operating system. Whenever the image of a new boot loader or OS or driver is loaded, the TPM can store the associated expected hash and compare it before running the code, and failing if the hash of the image is different. If you hold a public key you can also verify that a piece of code has been signed before running it. This is a gross over-simplification of how secure boot works in practice, but the crypto is pretty straight forward.
• Full disk encryption (FDE). This allows to store the key (or encrypt the key) that encrypts all data on the device at rest. If the device has been proven to be in a known good state (via secure boot) and the user authenticates correctly, the key can be released to decrypt data. When the devices is locked or shut down, the key vanishes from memory and has to be released by the TPM again. This is a must feature if you lose, or get your device stolen.
• Remote attestation. This allows a device to authenticate itself or prove that it is running specific software. In other words, a TPM can sign a random challenge and/or metadata with a key that can be tied to a unique per-TPM key (and is signed by the TPM vendor). Every TPM comes with such a unique key (called an endorsement key) along with the vendor’s certificate authority signature on the public key part. For example, during employee onboarding a company can add a new employee’s laptop’s TPM endorsement key to a whitelist of approved devices. Later, if the user wants to access one of the company’s service, the service can request the TPM to sign a random challenge along with hashes of what OS was booted to authenticate the user and prove the well-being of the user’s device.

There are more functionalities that a TPM can enable (there's afterall hundreds of commands that a TPM implements) which might even benefit user applications (which should be able to call the TPM).

Note that having a standard is great for inter-operability, and for us to understand what is going on, but unfortunately not everyone use TPMs. Apple has the secure enclave, Microsoft has Pluton, Google has Titan.

Perhaps, on a darker note, it is good to note that TPMs have their own controversies and have also been subjected to devastating vulnerabilities. For example the ROCA attack found that an estimated million TPMs (and even smart cards) from the popular Infineon vendor had been wrongly generating RSA private keys for years (the prime generation was flawed).

To recap, you’ve learned about:

• HSMs. They are external, bigger and faster secure elements. They do not follow any standard interface, but usually implement the PKCS#11 standard for cryptographic operations. HSMs can be certified with different levels of security via some NIST standard (FIPS 140-2).
• TPMs. They are chips that follow the TPM standard, more specifically they are a type of secure element with a specified interface. A TPM is usually a secure chip directly linked to the motherboard and perhaps implemented using a secure element. While it does not allow to run arbitrary programs like some secure elements, smart cards, and HSMs do, it enables a number of interesting applications for devices as well as user applications.

That’s it for now, check this blog again to read part 3 which will be about TEEs!

Many thanks to Jeremy O'Donoghue, Thomas Duboucher, Charles Guillemet, and Ryan Sleevi who provided help and reviews!

6 comments

# Hardware Solutions To Highly-Adversarial Environments Part 1: Whitebox Crypto vs Smart Cards vs Secure Elements vs Host-Card Emulation (HCE) posted March 2020

If at some point you realize that doing cryptography means having to manage long-term keys, it means you’re standing in the world of key management.

Makes sense right?

In these lands, you are going to run into scenarios where attackers can be quite close to your applications. I call these highly-adversarial environments.

Imagine using your credit card on an ATM skimmer (a doodads that a thief can place on top of the card reader of an ATM in order to copy the content of your credit card, see picture bellow); downloading an application on your mobile phone that compromises the OS; hosting a web application in a colocated server shared with a malicious customer; managing highly-sensitive secrets in a data center that gets breached; and so on.

These scenarios suck, and are very counterintuitive to most cryptographers. This is because cryptography has come a long way since the historical “Alice wants to encrypt a message to Bob without Eve intercepting it”. Nowadays, it’s often more like “Alice wants to encrypt a message to Bob, but Alice is also Eve”.

The key here is that in these scenarios, there’s not much that can be done cryptographically (unless you believe in whitebox crypto) and hardware can go a long way to help.

OK, so now we have a whole world of new doohickeys to learn about, and there’s a lot of thingamabob believe me (hence the dense title). It can be quite confusing to learn about all of this, so here we go: my promise is that by the end of this blogpost series you’ll have a better understanding of what are all these different hardware solutions.

Keep in mind that none of these solutions are pure cryptographic solutions: they are all defense-in-depth (and sometimes dubious) solutions that serve to hide secrets and their associated sensitive cryptographic operations. They also all have a given cost, meaning that if a sophisticated attacker decides to break the bank, there’s not much we can do (besides raising the cost of an attack).

OK let's get started.

## Obfuscation

By definition obfuscation has nothing to do with security: it is the act of scrambling something so that it still work but is hard to understand. So for the laugh, let’s first mention whitebox cryptography which attempts to “cryptographically” obfuscate the key inside of an algorithm. That’s right, you have the source code of some AES-based encryption algorithm with a fixed key, and it encrypts and decrypts fine, but the key is mixed so well with the implementation that it is too confusing for anyone to extract the key from the algorithm. That's the theory. Unfortunately in practice, no published whitebox crypto algorithm has been found to be secure, and most commercial solutions are closed-source due to this fact (security through obscurity kinda works in the real world). Again, it’s all about raising the cost and making it harder for attackers.

All in all, whitebox crypto is a big industry that sells dubious products to businesses in need of DRM solutions. On the more serious side, there is a branch of cryptography called Indistinguishability obfuscation (iO) that attempts to do this cryptographically (so for realz). iO is a very theoretical, impractical, and so far not-really-proven field of research. We’ll see how that one goes.

(Timeline of whitebox cryptography, taken from Matthieu Rivain’s slides)

## Smart Cards

OK, whitebox crypto is not great, and worse: even if you can’t extract the key, you can still copy the program instead of trying to extract the key (and use it to do whatever cryptographic operation it features). It would be great if we could prevent people from copying secrets from sensitive devices though, or even prevent them from seeing what’s going on when the device performs cryptographic operations. A smart card is exactly this. It’s what you commonly find in credit cards, and is activated by either inserting it into, or using Near-field Communication (NFC) by getting the smart card close enough to, a payment terminal (also called Point of Sale or PoS terminal).

Smart cards are pretty old, and started as a practical way to get everyone a pocket computer. Indeed, a smart cart embarks a CPU, memory (RAM, ROM and EEPROM), input/output, hardware random number generator (so called TRNGs), etc.) unlike the not-so-smart cards that only had data stored in them via a magnetic stripe (which in turn can be easily copied via the skimmers I talked about previously). Today, it seems like the same people all have a much more powerful computer in their pockets, so smart cards are probably going to die. (Rob Wood is pointing to me that more than a quarter of the US still doesn’t have a smart phone, so there’s still some time before this prophecy come to fruition.)

Smart cards mix a number of physical and logical techniques to prevent observation, extraction, and modification of its execution environment and some of its memory (where secrets are stored). But as I said earlier, it’s all about how much money you want an attacker to be spending, and there exist many techniques that attempt at breaking these cards:

• Non-invasive attacks such as differential power analysis (DPA) analyze the power consumption of the smart card while it is doing cryptographic operations in order to extract the associated keys.
• Semi-invasive attacks require access to the chip’s surface to mount attacks such as differential fault analysis (DFA) which use heat, lasers, and other techniques to modify the execution of a program running on the smart card in order to leak the key via cryptographic attacks (see my post on RSA signature fault attacks for an example).
• Finally invasive silicon attacks can modify the circuitry in the silicon itself to alter its function and reveal secrets.

## Secure Elements

Smart cards got really popular really fast, and it became obvious that having such a secure blackbox in other devices could be useful. The concept of a secure element was born: a tamper-resistant microcontroller that can be found in a pluggable form factor like UUICs (SIM cards required by carriers to access their 3G/4G/5G network) or directly bonded on chips and motherboards like the embedded SE (eSE) attached to an iPhone’s NFC chip. Really just a small separate piece of hardware meant to protect your secrets and their usage in cryptographic operations.

SEs are an evolution of the traditional chip that resides in smart cards, which have been adapted to suit the needs of an increasingly digitalized world, such as smartphones, tablets, set top boxes, wearables, connected cars, and other internet of things (IoT) devices. (GlobalPlatform)

Secure elements are a key concept to protect cryptographic operations in the Internet of Things (IoTs), a colloquial (and overloaded) term to refer to devices that can communicate with other devices (think smart cards in credit cards, SIM cards in phones, biometric data in passports, garage keys, smart home sensors, and so on).

Thus, you can see all of the solutions that will follow in this blogpost series as secure elements implemented in different form factors, using different techniques, and providing different level of defense-in-depth.

If you are required to use a secure element (to store credit card data for example), you also most likely have to get it certified. The main definition and standards around a secure element come from GlobalPlatform, but there exist more standards like Common Criteria (CC), NIST’s FIPS, EMV (for Europay, Mastercard, and Visa), and so on. If you’re in the market of buying secure microcontrollers, you will often see claims like “FIPS 140-2 certified” and “certified CC EAL 5+” next to it. Claims that can be obtained after spending some quality time, and a lot of money, with licensed certification labs.

## Host Card Emulation (HCE)

It’s 2020, most people have a computer in their pocket: a smart phone. What’s the point of a credit card anymore? Well, not much, nowadays more and more payment terminals support contactless payment via the Near-field Communication (NFC) protocol, and more and more smartphones ship with an NFC chip that can potentially act as a credit card.

NFC for payment is specified as Card Emulation. Literally: it emulates a bank card. Banks allow you to do this only if you have a secure element.

Since Apple has full control over its hardware, it can easily add a secure element to its new iPhones to support payment, and this is what Apple did (with an embedded SE bonded to the NFC chip since the iPhone 6). iPhone users can register a bank card with the Apple wallet application, Apple can then obtain the card’s secrets from the issuing bank, and the card secrets can finally be stored in the eSE. The secure element communicates directly with the NFC chip and then to NFC readers, thus a compromise of the phone OS does not impact the secure element.

Google, on the other hand, had quite a hard time introducing payment to Android-based mobile phones due to phone vendors all doing different things. The saving technology for Google ended up being a cloud-based secure element called Host Card Emulation (HCE) introduced in 2013 in Android 4.4.

How does it work? Google stores your credit card information in a secure element in the cloud (instead of your phone), and only gives your phone access to short-lived single-use PAN (card numbers). (Note that some Android devices do have an eSE that can be used instead of HCE, and some SIM cards can also be used as secure elements for payment.) This concept of replacing sensitive long-term information with short-lived tokens is called tokenization. Sending a random card number that can be linked to your real one is great for privacy: merchants can’t track you as it’ll look like you’re always using a new card number. If your phone gets compromised, the attacker only gets access to a short-lived secret that can only be used for a single payment. Tokenization is a common concept in security: replace the sensitive data with some random stuff, and have a table secured somewhere safe that maps the random stuff to the real data.

Wikipedia has some cool diagram to show what’s going on whenever you pay with Android Pay or Apple Pay:

Although Apple theoretically doesn't have to use tokenization, since iPhones have secure elements that can store the real PAN, they do use it in order to gain more privacy (it's afterall their new bread and butter).

In part 2 of this blog series I’ll cover HSMs, TPMs, and much more :)

(I would like to thank Rob Wood, Thomas Duboucher, and Lionel Rivière for answering my many questions!)

PS: I'm writing a book which will contain this and much more, check it out!

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# Coronavirus and cryptography posted March 2020

The coronavirus is shaking the world, on its multiple layers, and cryptography hasn't been spared.

The IACR announced on March 14th that multiple conferences were postponed:

FSE 2020, which was supposed to be held in Athens, Greece, during 22-26 March 2020, has been postponed to 8-12 November 2020.

PKC 2020, which was supposed to be held in Edinburgh, Scotland, during 4-7 May 2020, has been postponed.

EUROCRYPT 2020, which was supposed to be held in Zagreb, Croatia, during 10-14 May 2020, has been postponed.

While some others were not:

No changes have been made at this time to the schedule of CRYPTO 2020, CHES 2020, TCC 2020, and ASIACRYPT 2020, but we will continue to closely monitor the situation and will inform members if changes are needed.

While many workplaces (including mine) are moving to a WFH (work from home) model, will conferences follow?

It seems to be the case at least for Consensus 2020, a cryptocurrency conference organized by coindesk, which is moving to an online model:

Consensus 2020 will now be a completely virtual experience, where attendees from all over the world can participate online at no charge.

On a more dramatic note it seems like several participants of EthCC, which was held in Paris almost a week ago, have contracted the virus. A google spreadsheet has been circulating in order to self-report and figure out who else could have potentially contracted the virus. Even Vitalik Buterin is rumored to have had mild COVID-19 symptoms. Nobody is out of reach.

On a lighter note, my coworker Kostas presented on proofs of solvency at the lightning talks of Real World Crypto 2020. With his merkle tree-like construction he hopes to make governments accountable when they count the number of people who counted positive to the virus.

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# EdDSA, Ed25519, Ed25519-IETF, Ed25519ph, Ed25519ctx, HashEdDSA, PureEdDSA, WTF? posted March 2020

## The Edwards-curve Digital Signature Algorithm (EdDSA)

You've heard of EdDSA right? The shiny and new signature scheme (well new, it's been here since 2008, wake up).

Since its inception, EdDSA has evolved quite a lot, and some amount of standardization process has happened to it. It's even doomed to be adopted by the NIST in FIPS 186-5!

First, some definition:

• EdDSA stands for Edwards-curve Digital Signature Algorithm. As its name indicates, it is supposed to be used with twisted Edwards curves (a type of elliptic curve). Its name can be deceiving though, as it is not based on the Digital Signature Algorithm (DSA) but on Schnorr signatures!
• Ed25519 is the name given to the algorithm combining EdDSA and the Edwards25519 curve (a curve somewhat equivalent to Curve25519 but discovered later, and much more performant).

EdDSA, Ed25519, and the more secure Ed448 are all specified in RFC 8032.

## RFC 8032: Edwards-Curve Digital Signature Algorithm (EdDSA)

RFC 8032 takes some new direction from the original paper:

• It specifies a malleability check during verification, which prevents ill-intentioned people to forge an additional valid signature from an existing signature of yours. Whenever someone talks about Ed25519-IETF, they probably mean "the algorithm with the malleability check".
• It specifies a number of Ed25519 variants, which is the reason of this post.
• Maybe some other stuff I'm missing.

To sign with Ed25519, the original algorithm defined in the paper, here is what you're supposed to do:

1. compute the nonce as HASH(nonce_key || message)
2. compute the commitment R = [nonce]G with G the generator of the group.
3. compute the challenge as HASH(commitment || public_key || message)
4. compute the proof S = nonce + challenge × signing_key
5. the signature is (R, S)

where HASH is just the SHA-512 hash function.

At a high-level this is similar to Schnorr signatures, except for the following differences:

• The nonce is generated deterministically (as opposed to probabilistically) using a fixed nonce_key (derived from your private key, and the message M. This is one of the cool feature of Ed25519: it prevents you from re-using the same nonce twice.
• The challenge is computed not only with the commitment and the message to sign, but with the public key of the signer as well. Do you know why?

Important: notice that the message here does not need to be hashed before being passed to the algorithm, as it is already hashed as part of the algorithm.

Anyway, we still don't know WTF all the variants specified are.

## PureEdDSA, ContextEdDSA and HashEdDSA

Here are the variants that the RFC actually specifies:

• PureEdDSA, shortened as Ed25519 when coupled with Edwards25519.
• HashEdDSA, shortened as Ed25519ph when coupled with Edwards25519 (and where ph stands for "prehash").
• Something with no name we'll call ContextEdDSA, defined as Ed25519ctx when coupled with Edwards25519.

All three variants can share the same keys. They differ only in their signing and verification algorithms.

By the way Ed448 is a bit different, so from now on I'll focus on EdDSA with the Edwards25519 curve.

Ed25519 (or pureEd25519) is the algorithm I described in the previous section.

Easy!

Ed25519ctx (or ContextEd25519) is pureEd25519 with some additional modification: the HASH(.) function used in the signing protocol I described above is re-defined as HASH(x) = SHA-512(some_encoding(flag, context) || x) where:

• flag is set to 0
• context is a context string (mandatory only for Ed25519ctx)

In other words, the two instances of hashing in the signing algorithm now include some prefix. (Intuitively, you can also see that these variants are totally incompatible with each other.)

Right out of the bat, you can see that ContextEd25519 big difference is just that it mandates some domain separation to Ed25519.

Ed25519ph (or HashEd25519), finally, builds on top of ContextEd25519 with the following modifications:

• flag is set to 1
• context is now optional, but advised
• the message is replaced with a hash of the message (the specification says that the hash has to be SHA-512, but I'm guessing that it can be anything in reality)

OK. So the big difference now seems that we are doubly-hashing.

## Why HashEdDSA and why double hashing?

First, pre-hashing sucks, this is because it kills the collision resistance of the signature algorithm. In PureEdDSA we assume that we take the original message and not a hash. (Although this is not always true, the caller of the function can do whatever they want.) Then a collision on the hash function wouldn't matter (to make you create a signature that validates two different messages) because you would have to find a collision on the nonce which is computed using a secret (the nonce key).

But if you pre-hash the message, then finding a collision there is enough to obtain a signature that validates two messages.

Thus, you should use PureEdDSA if possible. And use it correctly (pass it the correct message.)

Why is HashEdDSA a thing then?

The EdDSA for more curves paper which was the first to introduce the algorithm has this to say:

The main motivation for HashEdDSA is the following storage issue (which is irrelevant to most well-designed signature applications). Computing the PureEdDSA signature of M requires reading through M twice from a buffer as long as M, and therefore does not support a small-memory “InitUpdate-Final” interface for long messages. Every common hash function H0 supports a smallmemory “Init-Update-Final” interface for long messages, so H0 -EdDSA signing also supports a small-memory “Init-Update-Final” interface for long messages. Beware, however, that analogous streaming of verification for long messages means that verifiers pass along forged packets from attackers, so it is safest for protocol designers to split long messages into short messages to be signed; this splitting also eliminates the storage issue.

## Why am I even looking at this rabbit hole?

Because I'm writing a book, and it'd be nice to explain what the hell is going on with Ed25519.

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# What's a key exchange? posted March 2020

I've been writing about cryptography for a book for a year now, and it has brought me some interesting challenges. One of them is that I constantly have to throw away what I've learned a long time ago, and imagine what it feels like not to know about a concept.

For example what are key exchanges?

The most intuitive explanation that I knew of (up until recently) was the one given by the wikipedia page on key exchanges. You might already know about it (unless you're reading this post to learn about key exchanges). It's a picture that involves paint. Take a look at it, but don't try to understand what is going on if you don't know about key exchanges yet. You can come back to it later.

I thought this was great. At least until I tried to explain key exchanges to my friends using this analogy. Nobody got it.

Nobody.

The other problem was that I couldn't use colors to explain anything in my book, as it'll be printed in black & white.

So I sat on the sad realization that I didn't have a great explanation for key exchanges, this for a number of months, and that until a more intuitive idea came to my mind.

The idea goes like this. Imagine that Alice and Bob wants to share a secret, but are afraid that someone is intercepting their communications. What they do is that they go to the store and buy the same bottle of generic soda.

Once home, they both start a random timer and shake their respective bottles until their timer end.

What they obtain are some shaked, pressurized, ready to gush out bottles of sodas. Each of the bottles will release a different amount of pressure.

After that, they swap bottles. Now Alice has the bottle of Bob, and Bob has Alice's bottle.

What do they do now? They restart their timers and shake the other person's bottle for the same amount of time.

Shake shake shake!

What do they finally obtain? Try to guess.

If I did my job correctly, then I gave you an intuition of how key exchanges work. Both Alice and Bob should now have two bottle of sodas that will release the same pressure once opened. And that's the secret!

And even if I steal the two bottles, I can't get a bottle that combines both bottles' pressure.

I recap the whole flow in the picture below:

Did you know about key exchanges before? Did you get it? Or did you think the painting example made more sense?

Please tell me in the comment!

This is probably what I'll include in my book as an introduction of what key exchanges are, unless I find a better way to explain it :)

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