Ever since the Invisible Salamanders paper was published, there has been a quiet renaissance within my friends and colleagues in applied cryptography for studying systems that use Authenticated Encryption with Associated Data (AEAD) constructions, understanding what implicit assumptions these systems make about the guarantees of the AEAD mode they chose to build upon, and the consequences of those assumptions being false.

I’ve discussed Invisible Salamanders several times throughout this blog, from my criticisms of AES-GCM and XMPP + OMEMO to my vulnerability disclosures in Threema.

Five years after Invisible Salamanders, it’s become clear to me that many software developers do not fully appreciate the underlying problem discussed in the Invisible Salamanders paper, even when I share trivial proof-of-concept exploits.

Background

Fast AEAD constructions based on polynomial MACs, such as AES-GCM and ChaCha20-Poly1305, were designed to provide confidentiality and integrity for the plaintext data, and optionally integrity for some additional associated data, in systems where both parties already negotiated one shared symmetric key.

The integrity goals of the systems that adopted these AEAD constructions were often accompanied by performance goals–usually to prevent Denial of Service (DoS) attacks in networking protocols. Verification needed to be very fast and consume minimal resources.

In this sense, AEAD constructions were an incredible success. So successful, in fact, that most cryptographers urge application developers to use one of the fast AEAD modes as the default suggestion without looking deeper at the problem being solved. This is a good thing, because most developers will choose something stupid like ECB mode in the absence of guidance from cryptographers, and AEAD modes are much, much safer than any hand-rolled block cipher modes.

The problem is, that one tiny little assumption that both parties (sender, recipient) for a communication have agreed on exactly one symmetric key for use in the protocol.

Fast MACs Are Not Key-Committing

Cryptographers have concluded that AEAD constructions based on polynomial MACs–while great for performance and rejection of malformed packets without creating DoS risks–tend to make the same assumption. This is even true of misuse-resistant modes like AES-GCM-SIV and extended-nonce constructions like XSalsa20-Poly1305.

When discussing this implicit assumption of only one valid key in the systems that use these AEAD modes, we say that the modes are not key-committing. This terminology is based on what happens when this assumption is false.

Consequently, you can take a single, specially crafted ciphertext (with an authentication tag) and decrypt it under multiple different keys. The authentication tags will be valid for all keys, and the plaintext will be different.

Art: Swizz

What does this look like in practice?

Consider my GCM exploit, which was written to generate puzzle ciphertexts for the DEFCON Furs badge challenge a few years ago. How it works is conceptually simple (although the actual mechanics behind step 4 is a bit technical):

1. Generate two keys.
   There’s nothing special about these keys, or their relationship to each other, and can be totally random. They just can’t be identical or the exploit is kind of pointless.
2. Encrypt some blocks of plaintext with key1.
3. Encrypt some more blocks of plaintext with key2.
4. Calculate a collision block from the ciphertext in the previous two steps–which is just a bit of polynomial arithmetic in GF(2^128)
5. Return the ciphertext (steps 2, 3, 4) and authentication tag calculated over them (which will collide for both keys).

A system that decrypts the output of this exploit under key1 will see some plaintext, followed by some garbage, followed by 1 final block of garbage.

If the same system decrypts under key2, it will see some garbage, followed by some plaintext, followed by 1 final block of garbage.

For many file formats, this garbage isn’t really a problem. Additionally, a bit more precomputation allows you to choose garbage that will be more advantageous to ensuring both outputs are accepted as “valid” by the target system.

For example, choosing two keys and a targeted nonce may allow both the valid plaintext and garbage blocks to begin with a PDF file header.

If you’re familiar with the file polyglot work of Ange Albertini, you can use this to turn the Invisible Salamanders problem into an artform.

And this is just the simple attack!

The Invisible Salamanders paper outlined a more advanced variant (with a proof of concept) in Section 3.2, which doesn’t suffer from nearly as much garbage data as the simple attack.

As Bruce Schneier often says, “Attacks only get better, they never get worse.”

Why is it called Invisible Salamanders?

The proof-of-concept used in the paper involved sending one picture (of a salamander) over an end-to-end encrypted messaging app, but when the recipient flagged it as abusive, the moderator saw a different picture.

https://www.youtube.com/watch?v=3M1jIO-jLHI

Thus, the salamander was invisible to the moderators of the encrypted messaging app.

As for the choice of a “salamander”, I’ve been told by friends familiar with the research that was inspired by the original name of the Signal Protocol being “Axolotl”.

But, like, who cares about these details besides me? It’s a cute and memorable name.

What are the consequences of violating the “one key” assumption?

That depends entirely on what your system does!

In Database Cryptography Fur the Rest of Us, I discussed the use of AEAD modes to prevent confused deputy attacks. This works great, but if you’re building an application that supports multi-tenancy, you suddenly have to care about this issue again.

An earlier design for OPAQUE, a password authenticated key exchange algorithm, was broken by a partitioning oracle attack due to building atop AEAD modes that are not key-committing. This let an attacker recover passwords from Shadowsocks proxy servers with a complexity similar to a binary search algorithm.

These are two very different impacts from the same weakness, which I believe is a significant factor for why the Invisible Salamanders issue isn’t more widely understood.

Sometimes violating the “one key” assumption that went into fast AEAD modes based on Polynomial MACs completely destroys the security of your system.

Other times, it opens the door for a high-complexity but low-impact behavior that simply violates the principle of least astonishment but doesn’t buy the attacker anything useful.

They Just Don’t Get It

The Invisible Salamanders issue is relevant in any system that uses symmetric-key encryption where more than one key can be valid.

This includes, but is not limited to:

• Multi-tenant data warehouses
• Group messaging protocols
  
  • It’s sometimes tempting to discount group messaging as a relevant consideration if your experience is “emulated groups atop 1-to-1 messaging”, but there are protocols that establish a Group Key (i.e., RFC 9420) and then use that for all group messages.

  
  

• Envelope encryption schemes with multiple wrapping keys
• Bearer tokens (such as JSON Web Tokens) in systems that utilize Key IDs

Systems can mitigate this issue by introducing an explicit key commitment scheme (based on a cryptographic hash rather than a polynomial MAC) or by using a committing cipher mode (such as AES + HMAC, if done carefully).

However, most of the time, this advice falls on deaf ears whenever this concern is brought up by a cryptography engineer who’s more aware of this issue.

“Abuse reporting? We don’t have no stinking abuse reporting!”

The most common misunderstanding is, “We don’t have a report abuse feature, so this issue doesn’t affect us.”

This is because the Invisible Salamanders talk and paper focused on how it could be leveraged to defeat abuse reporting tools and bypass content moderation.

In my experience, many security teams would read the paper and conclude that it only impacts abuse reporting features and not potentially all systems that allow multiple symmetric keys in a given context.

Another Exploit Scenario

Imagine you’re building a Data Loss Prevention product that integrates with corporate file-sharing and collaboration software (e.g. ownCloud) for small and medium businesses.

One day, someone decides to ship an end-to-end encryption feature to the file-sharing software that uses AES-GCM to encrypt files, and then encrypts the keys to each recipient’s public key. This is basically the envelope encryption use-case above.

So, you dutifully update your integration to act as another “user”, whose public key must be included in all E2EE transfers, and will block download of ciphertexts it cannot decrypt OR contains sensitive information.

And this works, until an insider threat clever enough to abuse the Invisible Salamanders issue comes along.

In order for said insider threat (e.g., a senior business analyst) to leak sensitive data (e.g., anything that would be useful for illegal insider trading) to another person that shouldn’t have access to it (e.g., a store clerk that’s talking to the press), they just have to do this:

1. Encrypt the data they want to exfiltrate using key1.
2. Encrypt some innocuous data that won’t trigger your DLP product, using key2.
3. Ensure that both messages encrypt to the same ciphertext and authentication tag.
4. Give their recipient key1, give everyone else (including your DLP software) key2.

Bam! File leaked, and everyone’s none the wiser, until it’s too late. Let’s actually imagine what happens next:

A random store clerk has leaked sensitive data to the press that only a few analysts had access to.

The only communication between the analyst and the store clerk is a file that was shared to all employees, using the E2EE protocol. No emails or anything else were identified.

Your DLP product didn’t identify any other communications between these two, but somehow the store clerk has the data on their desktop.

A detailed forensics analysis may eventually figure out what happened, but by then, the damage is done and your product’s reputation is irrecoverably damaged.

All because the hypothetical E2EE protocol didn’t include a key-commitment mechanism, and nobody identified this deficit in their designs.

This isn’t to endorse DLP solutions at all, but rather, to highlight one of the many ways that the Invisible Salamander issue can be used creatively by clever attackers.

Art: AJ

“Couldn’t you do the same with steganography?”

No, the attack is very different from stego.

Stego is about hiding a message in plain sight, so that only the person that knows where/how to look can find it.

The Invisible Salamanders attack lets you send one ciphertext through a network then selectively decrypt it to one of two plaintexts, depending on which key you reveal to each participant.

In the Invisible Salamanders paper and talk, they used this to send “abusive” messages to a recipient that the moderator would not see. Thus, invisible.

In one, the message is always emitted to anyone who knows how to find it. In the other, the attacker selects which you see, even if you have mechanisms to ensure you’re seeing the same ciphertext. It’s not a subtle difference.

Mitigation Techniques

There are multiple ways to mitigate the risk of Invisible Salamanders in a cryptosystem.

1. Use HMAC, or (failing that) something built atop cryptographic hash functions, rather than a Polynomial MAC.
2. Use an AEAD cipher designed with multi-recipient integrity as a security goal.
3. Compute a non-invertible, one-way commitment of the encryption key.

A trivial mitigation looks like this:

class SoatokExampleEncryptor { const NEW_ENCRYPT_KEY = 'myProtocol$encryptKey'; const NEW_COMMITMENT = 'myProtocol$commitment'; public function __construct(#[SensitiveParameter] private string $key) {} /** * Let's assume we're starting with a simple AES-GCM wrapper */ public function legacyEncrypt(string $plaintext, string $assocData = ''): string { $nonce = random_bytes(12); $tag = ''; $ciphertext = openssl_encrypt( $plaintext, 'aes-256-gcm', $this->key, OPENSSL_RAW_DATA, $nonce, $tag, $assocData ); return $nonce . $ciphertext . $tag; } /** * An improved function looks something like this */ public function newEncrypt(string $plaintext, string $assocData = ''): string { // Avoid birthday bound issues with 256-bits of randomness $longerNonce = random_bytes(32); // Derive a subkey and synthetic nonce $tmp = hash_hkdf('sha512', $this->key, 44, self::NEW_ENCRYPT_KEY . $longerNonce); $encKey = substr($tmp, 0, 32); $nonce = substr($tmp, 32); // New: Key commitment $commitment = hash_hkdf('sha512', $this->key, 32, self::NEW_COMMITMENT . $longerNonce); // Most of this is unchanged $tag = ''; $ciphertext = openssl_encrypt( $plaintext, 'aes-256-gcm', $encKey, OPENSSL_RAW_DATA, $nonce, $tag, $assocData ); return $longerNonce . $commitment . $ciphertext . $tag; }}

And then the decryption logic would recalculate the commitment, and compare it with the stored value, in constant-time.

It’s important that the commitment be stored with the ciphertext, rather than bundling it with the key.

(It may be worthwhile to also include the commitment in the associated data, to add a mechanism against downgrade attacks.)

The Lesson to Learn

If you’re building a network protocol that uses AEAD to encrypt data over an insecure network (e.g., WireGuard), keep up the good work.

If you’re doing anything more involved than that, at the application layer, pause for a moment and consider whether your system will ever need multiple valid symmetric keys at once.

And, if the answer is “yes”, then you should always explicitly add a key-commitment mechanism to your system design.

(Hire a cryptographer if you’re not sure how to proceed.)

In my opinion, hemming and hawing over whether there’s a significant impact to the Invisible Salamanders issue is a worse use of your time than just solving it directly.

Eventually, I expect a new generation of AEAD modes will be standardized that explicitly provide key-commitment.

When these new designs are standardized, widely supported, and sufficiently trusted by experts, feel free to update my advice to “prefer using those modes” instead.

Header art: Harubaki, CMYKat, and a photo by Brian Gratwicke. Poorly photoshopped by myself.

https://soatok.blog/2024/09/10/invisible-salamanders-are-not-what-you-think/

#AEAD #AESGCM #InvisibleSalamanders #randomKeyRobustness #symmetricCryptography

Dhole Moments

2020-05-13 10:00:22

If you’re reading this wondering if you should stop using AES-GCM in some standard protocol (TLS 1.3), the short answer is “No, you’re fine”.

I specialize in secure implementations of cryptography, and my years of experience in this field have led me to dislike AES-GCM.

This post is about why I dislike AES-GCM’s design, not “why AES-GCM is insecure and should be avoided”. AES-GCM is still miles above what most developers reach for when they want to encrypt (e.g. ECB mode or CBC mode). If you want a detailed comparison, read this.

To be clear: This is solely my opinion and not representative of any company or academic institution.

What is AES-GCM?

AES-GCM is an authenticated encryption mode that uses the AES block cipher in counter mode with a polynomial MAC based on Galois field multiplication.

In order to explain why AES-GCM sucks, I have to first explain what I dislike about the AES block cipher. Then, I can describe why I’m filled with sadness every time I see the AES-GCM construction used.

What is AES?

The Advanced Encryption Standard (AES) is a specific subset of a block cipher called Rijndael.

Rijndael’s design is based on a substitution-permutation network, which broke tradition from many block ciphers of its era (including its predecessor, DES) in not using a Feistel network.

AES only includes three flavors of Rijndael: AES-128, AES-192, and AES-256. The difference between these flavors is the size of the key and the number of rounds used, but–and this is often overlooked–not the block size.

As a block cipher, AES always operates on 128-bit (16 byte) blocks of plaintext, regardless of the key size.

This is generally considered acceptable because AES is a secure pseudorandom permutation (PRP), which means that every possible plaintext block maps directly to one ciphertext block, and thus birthday collisions are not possible. (A pseudorandom function (PRF), conversely, does have birthday bound problems.)

Why AES Sucks

Art by Khia.

Side-Channels

The biggest reason why AES sucks is that its design uses a lookup table (called an S-Box) indexed by secret data, which is inherently vulnerable to cache-timing attacks (PDF).

There are workarounds for this AES vulnerability, but they either require hardware acceleration (AES-NI) or a technique called bitslicing.

The short of it is: With AES, you’re either using hardware acceleration, or you have to choose between performance and security. You cannot get fast, constant-time AES without hardware support.

Block Size

AES-128 is considered by experts to have a security level of 128 bits.

Similarly, AES-192 gets certified at 192-bit security, and AES-256 gets 256-bit security.

However, the AES block size is only 128 bits!

That might not sound like a big deal, but it severely limits the constructions you can create out of AES.

Consider the case of AES-CBC, where the output of each block of encryption is combined with the next block of plaintext (using XOR). This is typically used with a random 128-bit block (called the initialization vector, or IV) for the first block.

This means you expect a collision after encrypting (at 50% probability) blocks.

When you start getting collisions, you can break CBC mode, as this video demonstrates:

https://www.youtube.com/watch?v=v0IsYNDMV7A

This is significantly smaller than the you expect from AES.

Post-Quantum Security?

With respect to the number of attempts needed to find the correct key, cryptographers estimate that AES-128 will have a post-quantum security level of 64 bits, AES-192 will have a post-quantum security level of 96 bits, and AES-256 will have a post-quantum security level of 128 bits.

This is because Grover’s quantum search algorithm can search unsorted items in time, which can be used to reduce the total number of possible secrets from to . This effectively cuts the security level, expressed in bits, in half.

Note that this heuristic estimate is based on the number of guesses (a time factor), and doesn’t take circuit size into consideration. Grover’s algorithm also doesn’t parallelize well. The real-world security of AES may still be above 100 bits if you consider these nuances.

But remember, even AES-256 operates on 128-bit blocks.

Consequently, for AES-256, there should be approximately (plaintext, key) pairs that produce any given ciphertext block.

Furthermore, there will be many keys that, for a constant plaintext block, will produce the same ciphertext block despite being a different key entirely. (n.b. This doesn’t mean for all plaintext/ciphertext block pairings, just some arbitrary pairing.)

Concrete example: Encrypting a plaintext block consisting of sixteen NUL bytes will yield a specific 128-bit ciphertext exactly once for each given AES-128 key. However, there are times as many AES-256 keys as there are possible plaintext/ciphertexts. Keep this in mind for AES-GCM.

This means it’s conceivable to accidentally construct a protocol that, despite using AES-256 safely, has a post-quantum security level on par with AES-128, which is only 64 bits.

This would not be nearly as much of a problem if AES’s block size was 256 bits.

Real-World Example: Signal

The Signal messaging app is the state-of-the-art for private communications. If you were previously using PGP and email, you should use Signal instead.

Signal aims to provide private communications (text messaging, voice calls) between two mobile devices, piggybacking on your pre-existing contacts list.

Part of their operational requirements is that they must be user-friendly and secure on a wide range of Android devices, stretching all the way back to Android 4.4.

The Signal Protocol uses AES-CBC + HMAC-SHA256 for message encryption. Each message is encrypted with a different AES key (due to the Double Ratchet), which limits the practical blast radius of a cache-timing attack and makes practical exploitation difficult (since you can’t effectively replay decryption in order to leak bits about the key).

Thus, Signal’s message encryption is still secure even in the presence of vulnerable AES implementations.

Hooray for well-engineered protocols managing to actually protect users.
Art by Swizz.

However, the storage service in the Signal App uses AES-GCM, and this key has to be reused in order for the encrypted storage to operate.

This means, for older phones without dedicated hardware support for AES (i.e. low-priced phones from 2013, which Signal aims to support), the risk of cache-timing attacks is still present.

This is unacceptable!

What this means is, a malicious app that can flush the CPU cache and measure timing with sufficient precision can siphon the AES-GCM key used by Signal to encrypt your storage without ever violating the security boundaries enforced by the Android operating system.

As a result of the security boundaries never being crossed, these kind of side-channel attacks would likely evade forensic analysis, and would therefore be of interest to the malware developers working for nation states.

Of course, if you’re on newer hardware (i.e. Qualcomm Snapdragon 835), you have hardware-accelerated AES available, so it’s probably a moot point.

Why AES-GCM Sucks Even More

AES-GCM is an authenticated encryption mode that also supports additional authenticated data. Cryptographers call these modes AEAD.

AEAD modes are more flexible than simple block ciphers. Generally, your encryption API accepts the following:

1. The plaintext message.
2. The encryption key.
3. A nonce (: A number that must only be used once).
4. Optional additional data which will be authenticated but not encrypted.

The output of an AEAD function is both the ciphertext and an authentication tag, which is necessary (along with the key and nonce, and optional additional data) to decrypt the plaintext.

Cryptographers almost universally recommend using AEAD modes for symmetric-key data encryption.

That being said, AES-GCM is possibly my least favorite AEAD, and I’ve got good reasons to dislike it beyond simply, “It uses AES”.

The deeper you look into AES-GCM’s design, the harder you will feel this sticker.

GHASH Brittleness

The way AES-GCM is initialized is stupid: You encrypt an all-zero block with your AES key (in ECB mode) and store it in a variable called . This value is used for authenticating all messages authenticated under that AES key, rather than for a given (key, nonce) pair.
Diagram describing Galois/Counter Mode, taken from Wikipedia.
This is often sold as an advantage: Reusing allows for better performance. However, it makes GCM brittle: Reusing a nonce allows an attacker to recover H and then forge messages forever. This is called the “forbidden attack”, and led to real world practical breaks.

Let’s contrast AES-GCM with the other AEAD mode supported by TLS: ChaCha20-Poly1305, or ChaPoly for short.

ChaPoly uses one-time message authentication keys (derived from each key/nonce pair). If you manage to leak a Poly1305 key, the impact is limited to the messages encrypted under that (ChaCha20 key, nonce) pair.

While that’s still bad, it isn’t “decrypt all messages under that key forever” bad like with AES-GCM.

Note: “Message Authentication” here is symmetric, which only provides a property called message integrity, not sender authenticity. For the latter, you need asymmetric cryptography (wherein the ability to verify a message doesn’t imply the capability to generate a new signature), which is totally disparate from symmetric algorithms like AES or GHASH. You probably don’t need to care about this nuance right now, but it’s good to know in case you’re quizzed on it later.

H Reuse and Multi-User Security

If you recall, AES operates on 128-bit blocks even when 256-bit keys are used.

If we assume AES is well-behaved, we can deduce that there are approximately different 256-bit keys that will map a single plaintext block to a single ciphertext block.

This is trivial to calculate. Simply divide the number of possible keys () by the number of possible block states () to yield the number of keys that produce a given ciphertext for a single block of plaintext: .

Each key that will map an arbitrarily specific plaintext block to a specific ciphertext block is also separated in the keyspace by approximately .

This means there are approximately independent keys that will map a given all-zero plaintext block to an arbitrarily chosen value of (if we assume AES doesn’t have weird biases).

Credit: Harubaki

“Why Does This Matter?”

It means that, with keys larger than 128 bits, you can model the selection of as a 128-bit pseudorandom function, rather than a 128-bit permutation. As a result, you an expect a collision with 50% probability after only different keys are selected.

Note: Your 128-bit randomly generated AES keys already have this probability baked into their selection, but this specific analysis doesn’t really apply for 128-bit keys since AES is a PRP, not a PRF, so there is no “collision” risk. However, you end up at the same upper limit either way.

But 50% isn’t good enough for cryptographic security.

In most real-world systems, we target a collision risk. So that means our safety limit is actually different AES keys before you have to worry about reuse.

This isn’t the same thing as symmetric wear-out (where you need to re-key after a given number of encryptions to prevent nonce reuse). Rather, it means after your entire population has exhausted the safety limit of different AES keys, you have to either accept the risk or stop using AES-GCM.

If you have a billion users (), the safety limit is breached after AES keys per user (approximately 262,000).

“What Good is H Reuse for Attackers if HF differs?”

There are two numbers used in AES-GCM that are derived from the AES key. is used for block multiplication, and (the value of with a counter of 0 from the following diagram) is XORed with the final result to produce the authentication tag.

The arrow highlighted with green is HF.

It’s tempting to think that a reuse of isn’t a concern because will necessarily be randomized, which prevents an attacker from observing when collides. It’s certainly true that the single-block collision risk discussed previously for will almost certainly not also result in a collision for . And since isn’t reused unless a nonce is reused (which also leaks directly), this might seem like a non-issue.

Art by Khia.

However, it’s straightforward to go from a condition of reuse to an adaptive chosen-ciphertext attack.

1. Intercept multiple valid ciphertexts.
   
   • e.g. Multiple JWTs encrypted with {"alg":"A256GCM"}

   
   

2. Use your knowledge of , the ciphertext, and the AAD to calculate the GCM tag up to the final XOR. This, along with the existing authentication tag, will tell you the value of for a given nonce.
3. Calculate a new authentication tag for a chosen ciphertext using and your candidate value, then replay it into the target system.

While the blinding offered by XORing the final output with is sufficient to stop from being leaked directly, the protection is one-way.

Ergo, a collision in is not sufficiently thwarted by .

“How Could the Designers Have Prevented This?”

The core issue here is the AES block size, again.

If we were analyzing a 256-bit block variant of AES, and a congruent GCM construction built atop it, none of what I wrote in this section would apply.

However, the 128-bit block size was a design constraint enforced by NIST in the AES competition. This block size was during an era of 64-bit block ciphers (e.g. Triple-DES and Blowfish), so it was a significant improvement at the time.

NIST’s AES competition also inherited from the US government’s tradition of thinking in terms of “security levels”, which is why there are three different permitted key sizes (128, 192, or 256 bits).

“Why Isn’t This a Vulnerability?”

There’s always a significant gap in security, wherein something isn’t safe to recommend, but also isn’t susceptible to a known practical attack. This gap is important to keep systems secure, even when they aren’t on the bleeding edge of security.

Using 1024-bit RSA is a good example of this: No one has yet, to my knowledge, successfully factored a 1024-bit RSA public key. However, most systems have recommended a minimum 2048-bit for years (and many recommend 3072-bit or 4096-bit today).

With AES-GCM, the expected distance between collisions in is , and finding an untargeted collision requires being able to observe more than different sessions, and somehow distinguish when collides.

As a user, you know that after different keys, you’ve crossed the safety boundary for avoiding collisions. But as an attacker, you need bites at the apple, not . Additionally, you need some sort of oracle or distinguisher for when this happens.

We don’t have that kind of distinguisher available to us today. And even if we had one available, the amount of data you need to search in order for any two users in the population to reuse/collide is challenging to work with. You would need the computational and data storages of a major cloud service provider to even think about pulling the attack off.

Naturally, this isn’t a practical vulnerability. This is just another gripe I have with AES-GCM, as someone who has to work with cryptographic algorithms a lot.

Short Nonces

Although the AES block size is 16 bytes, AES-GCM nonces are only 12 bytes. The latter 4 bytes are dedicated to an internal counter, which is used with AES in Counter Mode to actually encrypt/decrypt messages.

(Yes, you can use arbitrary length nonces with AES-GCM, but if you use nonces longer than 12 bytes, they get hashed into 12 bytes anyway, so it’s not a detail most people should concern themselves with.)

If you ask a cryptographer, “How much can I encrypt safely with AES-GCM?” you’ll get two different answers.

1. Message Length Limit: AES-GCM can be used to encrypt messages up to bytes long, under a given (key, nonce) pair.
2. Number of Messages Limit: If you generate your nonces randomly, you have a 50% chance of a nonce collision after messages.
   However, 50% isn’t conservative enough for most systems, so the safety margin is usually much lower. Cryptographers generally set the key wear-out of AES-GCM at random nonces, which represents a collision probability of one in 4 billion.

These limits are acceptable for session keys for encryption-in-transit, but they impose serious operational limits on application-layer encryption with long-term keys.

Random Key Robustness

Before the advent of AEAD modes, cryptographers used to combine block cipher modes of operation (e.g. AES-CBC, AES-CTR) with a separate message authentication code algorithm (e.g. HMAC, CBC-MAC).

You had to be careful in how you composed your protocol, lest you invite Cryptographic Doom into your life. A lot of developers screwed this up. Standardized AEAD modes promised to make life easier.

Many developers gained their intuition for authenticated encryption modes from protocols like Signal’s (which combines AES-CBC with HMAC-SHA256), and would expect AES-GCM to be a drop-in replacement.

Unfortunately, GMAC doesn’t offer the same security benefits as HMAC: Finding a different (ciphertext, HMAC key) pair that produces the same authentication tag is a hard problem, due to HMAC’s reliance on cryptographic hash functions. This makes HMAC-based constructions “message committing”, which instills Random Key Robustness.

Critically, AES-GCM doesn’t have this property. You can calculate a random (ciphertext, key) pair that collides with a given authentication tag very easily.

This fact prohibits AES-GCM from being considered for use with OPAQUE (which requires RKR), one of the upcoming password-authenticated key exchange algorithms. (Read more about them here.)

Better-Designed Algorithms

You might be thinking, “Okay random furry, if you hate AES-GCM so much, what would you propose we use instead?”

I’m glad you asked!

XChaCha20-Poly1305

For encrypting messages under a long-term key, you can’t really beat XChaCha20-Poly1305.

• ChaCha is a stream cipher based on a 512-bit ARX hash function in counter mode. ChaCha doesn’t use S-Boxes. It’s fast and constant-time without hardware acceleration.
• ChaCha20 is ChaCha with 20 rounds.
• XChaCha nonces are 24 bytes, which allows you to generate them randomly and not worry about a birthday collision until about messages (for the same collision probability as AES-GCM).
• Poly1305 uses different 256-bit key for each (nonce, key) pair and is easier to implement in constant-time than AES-GCM.
• XChaCha20-Poly1305 uses the first 16 bytes of the nonce and the 256-bit key to generate a distinct subkey, and then employs the standard ChaCha20-Poly1305 construction used in TLS today.

For application-layer cryptography, XChaCha20-Poly1305 contains most of the properties you’d want from an authenticated mode.

However, like AES-GCM (and all other Polynomial MACs I’ve heard of), it is not message committing.

The Gimli Permutation

For lightweight cryptography (n.b. important for IoT), the Gimli permutation (e.g. employed in libhydrogen) is an attractive option.

Gimli is a Round 2 candidate in NIST’s Lightweight Cryptography project. The Gimli permutation offers a lot of applications: a hash function, message authentication, encryption, etc.

Critically, it’s possible to construct a message-committing protocol out of Gimli that will hit a lot of the performance goals important to embedded systems.

Closing Remarks

Despite my personal disdain for AES-GCM, if you’re using it as intended by cryptographers, it’s good enough.

Don’t throw AES-GCM out just because of my opinions. It’s very likely the best option you have.

Although I personally dislike AES and GCM, I’m still deeply appreciative of the brilliance and ingenuity that went into both designs.

My desire is for the industry to improve upon AES and GCM in future cipher designs so we can protect more people, from a wider range of threats, in more diverse protocols, at a cheaper CPU/memory/time cost.

We wouldn’t have a secure modern Internet without the work of Vincent Rijmen, Joan Daemen, John Viega, David A. McGrew, and the countless other cryptographers and security researchers who made AES-GCM possible.

Change Log

• 2021-10-26: Added section on H Reuse and Multi-User Security.

https://soatok.blog/2020/05/13/why-aes-gcm-sucks/

#AES #AESGCM #cryptography #GaloisCounterMode #opinion #SecurityGuidance #symmetricCryptography

Since the IETF’s CFRG decided to recommend OPAQUE as a next-generation Password Authenticated Key Exchange, there has been a lot of buzz in the cryptography community about committing authenticated encryption (known to the more academically inclined as Random Key Robustness), because OPAQUE requires an RKR-secure AE scheme.

Random Key Robustness is a property that some symmetric encryption modes have, where it’s not feasible to decrypt a valid (ciphertext, tag) pair into two different plaintexts if both recipients are using different keys.

To illustrate this visually:

RKR-secure ciphers don’t let people produce the same ciphertext+tag from two different plaintexts, with two different keys. You might be able to create an identical ciphertext, but the authentication tag will differ. (Art by Swizz.)

In the wake of the CFRG discussion, it became immediately clear that AES-GCM doesn’t meet this requirement.

What wasn’t immediately clear is that AES-GCM-SIV also falls short. But don’t take my word for it, Sophie Schmieg worked out the math in the linked post, which I highly recommend reading.

This isn’t to say that AES-GCM or AES-GCM-SIV are doomed, or should be deprecated. You probably don’t even care about Random Key Robustness in most of the places you’d use either algorithm! But if you are doing something where RKR actually matters, you probably care a lot. And it certainly violates the principle of least astonishment.

ChaCha20-Poly1305 won’t save you here either, since this is a property that message authentication codes based on cryptographic hash functions (e.g. HMAC) provide, but polynomial MACs (GMAC, Poly1305, etc.) do not.

So, if every standardized and widely-supported AEAD construction fails to provide RKR security, what’s a software engineer to do?Roll their own crypto?!

Don’t actually do that. (Art by Swizz.)

If you’re always on a well-tread path with a well-defined, standard threat model (i.e. client-server application accessible via TLS 1.3, possibly storing hashed passwords server-side), then rolling your own crypto isn’t just dangerous; it’s wholly unnecessary.

Coping with Non-Standard Threat Models

Systems that require Random Key Robustness do not fall within the standard threat model of AEAD cipher constructions.

However, RKR is far from the only scenario in which application developers might find themselves without a clear solution. Another example that comes up a lot:

“I need to encrypt data in a relational database, but still somehow use it in SELECT queries.”

— Far too many damn developers who haven’t heard of CipherSweet.

The first thing that you should do is clearly document your requirements and what attacks your system must protect against. Any undefined attack vector in your model should be assumed to be a vulnerability in your design. (This gets into Unknown Unknowns territory quickly.)

And then you should have a cryptographer review your design, and then have a cryptography engineer build it for you.

But where’s the fun in that?

This would be a very boring blog post if I left it at that! (Art by Khia.)

Instead of copping out with sane and reasonable advice, let’s actually walk through the process. At the end of this post, I’ll share a toy example I cooked up for this blog post.

Designing New Cryptography

First, Understand the Problem

Why don’t AES-GCM, etc. provide Random Key Robustness? Because they’re built with universal hash functions rather than cryptographic hash functions.

Cryptographic hash functions have different properties (i.e. preimage resistance and collision resistance) that make it significantly difficult to calculate two different authentication tags under two different keys. Attacking HMAC-SHA-256 in this way is about as expensive as brute forcing a 128-bit AES key. (Good luck with that!)

However, cryptographic hash functions are much slower than polynomial MACs, and using them in a construction like HMAC approximately doubles the slowness.

You might be tempted to just hash they key and the message together to save on CPU cycles, but that’s actually not safe for the hash functions nearly everybody uses (due to length extension attacks).

It logically follows that, if we had an AEAD cipher construction based on a hash function, we could have RKR security.

Now we’re getting somewhere! (Art by Khia.)

Look At Prior Art

Before the days of AES-GCM and ChaCha20-Poly1305, there were a lot of ad hoc constructions used everywhere based on AES-CBC and HMAC. (In that era, everyone used HMAC-SHA1, but don’t do that.)

However, there are a number of problems with ad hoc CBC+HMAC that we don’t want to reintroduce in modern systems:

1. If you forget to include the initialization vector in the HMAC tag, you give attackers free reign over the first 16 bytes of the decrypted plaintext without having to break the MAC.
2. The order of operations (Encrypt-then-MAC, MAC-then-Encrypt, Encrypt and MAC) matters tremendously.
3. CBC+HMAC is usually implemented in application-layer code, but the security of such a construction depends heavily on the availability and utilization of constant-time functions.
4. There is no standard format for CBC+HMAC, nor the order of operations for what gets fed into the MAC.
   
   • IV + ciphertext? Ciphertext + IV?
   • Append the MAC, or prepend it?

   
   

5. CBC+HMAC is only an AE mode, there is no room for additional authenticated data. If you try to naively shove extra data into the HMAC, now you have to worry about canonicalization attacks!
6. CBC mode requires padding (usually PKCS #7 padding), whereas cipher modes based on CTR do not.

This is among the long list of reasons why cryptographers have spent the past decade (or longer) pushing developers towards AEAD modes.

Boring cryptography is good cryptography!

You never want to hear this about your design. (Art by Khia.)

Make sure you clearly understand the risks of the components other constructions have used.

Sketch Out A First Draft

By now, it should be clear that if we have an Encrypt-then-MAC construction, where the MAC is based on a cryptographic hash function (e.g. SHA-256), we may be able to attain RKR security.

With that in mind, our sketch will probably look something like this:

• Encrypt(K1, M, N) -> C
  
  • Where Encrypt() is AES-CTR or equivalent

  
  

• Auth(K2, C, A) -> T
  
  • Where Auth() wraps HMAC-SHA2 or equivalent
  • How we feed C and A into the underlying MAC is important

  
  

• ???? -> K1, K2

We still have to define some way of splitting a key (K) into two distinct keys (K1, K2). You never want to use a cryptographic key for more than one purpose, after all.

Key-Splitting and Robustness

Your encryption key and authentication key should be different, but they should also derived from the same input key! This is mainly to protect implementors from having independent keys and accidentally creating a forgery vulnerability.

There are several different ways you can split keys:

1. Just use SHA-512(k), then cut it in half. Use one half for encryption, the other for authentication.
2. Use HMAC-SHA256(k, c1) and HMAC-SHA256(k, c2), where c1 and c2 are distinct (yet arbitrary) constants.
3. Use HKDF. This works with any secure cryptographic hash function, and was specifically designed for situations like this. HKDF also supports salting, which can be used to randomize our derived keys.

We can really pick any of these three and be safe, but I’d advise against the first option. HKDF uses HMAC under-the-hood, so either of the latter options is fine.

Can We Make it Faster?

What if, instead of HMAC-SHA256, we used BLAKE3?

BLAKE3’s performance compared with other hash functions.

BLAKE3’s advertised 6.8 GiB/s can be even faster than Poly1305 or GHASH (and BLAKE3’s speed really shines through with long messages, due to its extreme parallelism through Merkle trees).

In Favor of ChaCha over AES

It’s no secret that I’m not a fan of AES. It’s not the mathematical properties of AES that bother me, it’s the 128-bit block size and the fact that software implementations have to decide between being fast or being secure.

Me, whenever I find an insecure software AES implementation. (Art by Khia.)

ChaCha’s 256-bit security level is easier to justify: The underlying PRF state is 512 bits (which implies an approximately 256-bit security level) and the keys are always 256 bits.

Furthermore, if you’re building ChaCha and BLAKE3 in the same codebase, you could reuse some components (i.e. the compression function, G). This is very desirable if you’re trying to ship a small amount of code (e.g. embedded systems). EDIT: One of the BLAKE3 authors informed me that I’m mistaken about this: “[N]ope, not exactly the same logic (rotations in different direction)”.

Other Desirable Security Properties

Nonce Nonsense

One of the biggest problems with standard AEAD modes is that they explode gloriously when you reuse a nonce. There are two ways out of this peril:

1. Use a nonce misuse resistant AEAD construction (AES-GCM-SIV, etc.).
   
   • For prior art on nonce-misuse resistant cipher modes based on ChaCha, check out DAENCE.

   
   

2. Use large nonces (e.g. XChaCha20 uses 192-bit nonces) and generate them randomly, so the probability of nonce reuse becomes negligible.

Since we’re already planning on using a hash function to derive subkeys (one for encryption, one for authentication), it makes sense to also accept a longer nonce than our stream cipher demands. The excess bytes can be passed to our KDF without significant risk or additional overhead.

Since the IETF’s ChaCha20 variant expects a 96-bit nonce, designing our construction to support 256-bit nonces means we can pass the first 160 bits of the nonce to the KDF and the latter 96 bits to the stream cipher. You can expect a single KDF collision after 2^80 encryptions, but it will almost certainly occur with a different nonce.

Safe MAC Canonicalization

We want to ensure it’s infeasible for an attacker to feed two different (ciphertext, AAD) pairs into our construction that produce the same tag.

Simply concatenating the two values will run the risk of someone shaving off a chunk of the ciphertext and storing it in the AAD instead.

There’s always a complication! (Art by Swizz.)

The simplest solution is to either prepend or append the lengths of the components (as the little-endian octet string representation of 64-bit unsigned integers).

The choice between prepending and appending doesn’t affect security much, but appending the lengths is friendlier for streaming interfaces.

After all, in a streaming encryption/decryption interface, you might not know the lengths of the either component until you’ve finished encrypting and authenticating all of the data.

(Art by Khia.)

Putting It All Together

Now that we’ve meandered through a rough list of desirable design properties, let’s recap:

• We want to Encrypt then MAC.
• We want to use ChaCha20 (the IETF’s variant) as our stream cipher.
• We want to use keyed BLAKE3 for the KDF and MAC algorithm.
• We want to accept 256-bit nonces (160 bits for the KDF, 96 for the stream cipher).
• We want to ensure our ChaCha20 and BLAKE3-MAC keys are derived from the same input key, using some domain separation constants.
• We want to feed the data into the MAC this order:
  
  1. AAD
  2. Ciphertext
  3. Length of AAD
  4. Length of Ciphertext

  
  

• We want to ensure our authentication tags are always verified in constant-time.

That sounds like a lot. But what does it yield in terms of code size? Surprisingly very little!

You can find the JS implementation of my design on Github.

Should I Use This?

No. Don’t do it.

I mean, would your users really feel safe if you got your cryptography recommendations and implementations from a furry blogger?

This is just a toy example I put together for the sake of illustrating how a new cryptographic design might be proposed. That’s only the first step.

Ultimately, you shouldn’t use this for one simple reason: Neither my design nor my implementation have been peer reviewed.

Maybe I’ll refine it a bit and kick it over to the CFRG for consideration for inclusion with OPAQUE someday. It might turn out to be a good design. It might be vulnerable to some subtle attack I can’t even imagine right now.

Until experts tell you otherwise, it’s hazardous material and you should only play with it for educational purposes.

(Art by Swizz.)

Further Reading

I’ve written a lot about cryptography, and there are always more topics to write about than I have the time or energy to cover, so here’s a few cool blogs/etc. to check out while I slog through Rough Draft Hell.

• Cryptography Dispatches — Newsletter ran by Filippo Valsorda, cryptographer and Go security team lead.
• Bulletproof TLS Newsletter — Newsletter ran by Hanno Böck, freelance journalist, IT security expert, and AES-GCM exploiter.
• Key Material — A new blog by Sophie Schmieg (cryptographer at Google) and Sarai Rosenberg (security engineer at Pager Duty).
• Little Man In My Head — A blog by Scott Contini, a security expert who frequently posts helpful comments on /r/crypto.

Header art by Khia. The figure in the background is from this paper on Message Franking via Committing Authentication Encryption.

https://soatok.blog/2020/09/09/designing-new-cryptography-for-non-standard-threat-models/

#BLAKE3 #ChaCha20 #cryptography #randomKeyRobustness #SecurityGuidance #symmetricCryptography

Dhole Moments

2020-04-21 12:25:46

Authenticated Key Exchanges are an interesting and important building block in any protocol that aims to allow people to communicate privately over an untrusted medium (i.e. the Internet).

What’s an AKE?

At their core, Authenticated Key Exchanges (AKEs for short) combine two different classes of protocol.

1. An authentication mechanism, such as a MAC or a digital signature.
2. Key encapsulation, usually through some sort of Diffie-Hellman.

A simple example of an AKE is the modern TLS handshake, which uses digital signatures (X.509 certificates signed by certificate authorities) to sign ephemeral Elliptic Curve Diffie-Hellman (ECDH) public keys, which is then used to derive a shared secret to encrypt and authenticate network traffic.

I guess I should say “simple” with scare quotes. Cryptography is very much a “devil’s in the details” field, because my above explanation didn’t even encapsulate mutual-auth TLS or the underlying machinery of protocol negotiation. (Or the fact that non-forward-secret ciphersuites can be selected.)

AKEs get much more complicated, the more sophisticated your threat model becomes.

For example: Signal’s X3DH and Double Ratchet protocols are components of a very sophisticated AKE. Learn more about them here.

The IETF is working to standardize their own approach, called Messaging Layer Security (MLS), which uses a binary tree of ECDH handshakes to manage state and optimize group operations (called TreeKEM). You can learn more about IETF MLS here.

Password AKEs

Recently, a collection of cryptographers at the IETF’s Crypto Research Forum Group (CFRG) decided to hammer on a series of proposed Password-Authenticated Key Exchange (PAKE) protocols.

PAKEs come in two flavors: Balanced (mutually authenticated) and augmented (one side is a prover, the other is a verifier). Balanced PAKEs are good for encrypted tunnels where you control both endpoints (e.g. WiFi networks), whereas Augmented PAKEs are great for eliminating the risk of password theft in client-server applications, if the server gets hacked.

Ultimately, the CFRG settled on one balanced PAKE (CPace) and one augmented PAKE (OPAQUE).

Consequently, cryptographer Filippo Valsorda managed to implement CPace in 125 lines of Go, using Ristretto255.

I implemented the CPace PAKE yesterday with Go and ristretto255, and it felt like cheating.

📦 https://t.co/Q0kI19JOPY 📦

125 lines of code! Really happy with it and it was a lot of fun.

— Filippo Valsorda (@FiloSottile) March 29, 2020

Why So Complicated?

At the end of the day, an AKE is just a construction that combines key encapsulation with an authentication mechanism.

But how you combine these components together can vary wildly!

Some AKE designs (i.e. Dragonfly, in WPA3) are weaker than others; even if only in the sense of being difficult to implement in constant-time.

The reason there’s so many is that cryptographers tend to collectively decide which algorithms to recommend for standardization.

(n.b. There are a lot more block ciphers than DES, Blowfish, and AES to choose from! But ask a non-cryptographer to name five block ciphers and they’ll probably struggle.)

https://soatok.blog/2020/04/21/authenticated-key-exchanges/

#ake #authenticatedKeyExchange #cryptography #ECDH