Re: The Ecosystem is Moving

Moxie Marlinspike, the creator of Signal gave a talk at 36C3 on Saturday titled “The ecosystem is moving”.

The Fahrplan description of that talk reads as follows:

Considerations for distributed and decentralized technologies from the perspective of a product that many would like to see decentralize.

Amongst an environment of enthusiasm for blockchain-based technologies, efforts to decentralize the internet, and tremendous investment in distributed systems, there has been relatively little product movement in this area from the mobile and consumer internet spaces.

This is an exploration of challenges for distributed technologies, as well as some considerations for what they do and don’t provide, from the perspective of someone working on user-focused mobile communication. This also includes a look at how Signal addresses some of the same problems that decentralized and distributed technologies hope to solve.

https://fahrplan.events.ccc.de/congress/2019/Fahrplan/events/11086.html

Basically the talk is a reiteration of some arguments from a blog post with the same title he posted back in 2016.

In his presentation, Marlinspike basically states that federated systems have the issue of being frozen in time while centralized systems are flexible and easy to change.

As an example, Marlinspike names HTTP/1.1, which was released in 1999 and on which we are stuck on ever since. While it is true that a huge part of the internet is currently running on HTTP 1.0 and 1.1, one has to consider that its successor HTTP/2.0 was only released in 2015. 4 / 5 years are not a long time to update the entirety of the internet, especially if you consider the fact that the big browser vendors announced to only make their browsers work with HTTP/2.0 sites when they are TLS encrypted.

Marlinspike then goes on listing 4 expectations that advocates of federated systems have, namely privacy, censorship resistance, availability and control. This is pretty accurate and matches my personal expectations pretty well. He then argues, that Signal as a centralized application can fulfill those expectations as well, if not better than a decentralized system.

Privacy

Privacy is often expected to be provided by the means of data ownership, says Marlinspike. As an example he mentions email. He argues that even though he is self-hosting his emails, “each and every mail has GMail at the other end”.

I agree with this observation and think that this is a real problem. But the answer to this problem would logically be that we need to increase our efforts to change that by reducing the number of GMail accounts and increasing the number of self-hosted email servers, right? This is not really an argument for centralization, where each and every message is guaranteed to have the same service at the other end.

I also agree with his opinion that a more effective tool to gain privacy is good encryption. He obviously brings the point that email encryption is unusable, (hinting to PGP probably), totally ignoring modern approaches to email encryption like autocrypt.

Censorship resistance

Federated systems are censorship resistant. At least that is the expectation that advocates of federated systems have. Every time a server gets blocked, the user just simply switches to another server. The issue that Marlinspike points out is, that every time this happens, the user loses his entire social graph. While this is an issue, there are solutions to this problem, one being nomadic identities. If some server goes down the user simply migrates to another server, taking his contacts with him. Hubzilla does this for example. There are also import/export features present in most services nowadays thanks to the GDPR. XMPP offers such a solution using XEP-0277.

But lets take a look at how Signal circumvents censorship according to Marlinspike. He proudly presents Domain Fronting as the solution. With domain fronting, the client connects to some big service which is costly to block for a censor and uses that as a proxy to connect to the actual server. While this appears to be a very elegant solution, Marlinspike conceals the fact that Google and Amazon pretty quickly intervened and stopped Signal from using their domains.

With Google Cloud and AWS out of the picture, it seems that domain fronting as a censorship circumvention technique is now largely non-viable in the countries where Signal had enabled this feature.

https://signal.org/blog/looking-back-on-the-front/

Notice that above quote was posted by Marlinspike himself more than one and a half years ago. Why exactly he brings this as an argument remains a mystery to me.

Update: Apparently Signal still successfully uses Domain Fronting, just with content delivery networks other than Google and Amazon.

And even if domain fronting was an effective way to circumvent censorship, it could also be applied to federated servers as well, adding an additional layer of protection instead of solely relying on it.

But what if the censor is not a foreign nation, but instead the nation where your servers are located? What if the US decides to shutdown signal.org for some reason? No amount of domain fronting can protect you from police raiding your server center. Police confiscating each and every server of a federated system (or even a considerable fraction of it) on the other hand is unlikely.

Availability

This brings us nicely to the next point on the agenda, availability.

If you have a centralized service than you want to move that centralized service into two different data centers. And the way you did that was by splitting the data up between those data centers and you just halved your availability, because the mean time between failures goes up since you have two different data centers which means that it is more likely to have an outage in one of those data centers in any given moment.

Moxie Marlinspike in his 36c3 talk “The Ecosystem is Moving”

For some reason Marlinspike confuses a decentralized system with a centralized, but distributed system. It even reads “Centralized Service” on his slides… Decentralization does not equal distribution.

A federated system would obviously not be fault free, as servers naturally tend to go down, but an outage only causes a small fraction of the network to collapse, contrary to a total outage of centralized systems. There even are techniques to minimize the loss of functionality further, for example distributed chat rooms in the matrix protocol.

Control

The advocates argument of control says that if a service provider behaves undesirably, you simply switch to another service provider. Marlinspike rightfully asks the question how it then can be that many people still use Yahoo as their mail provider. Indeed that is a good question. I guess the only answer I can come up with is that most people probably don’t care enough about their email to make the switch. To be honest, email is kind of boring anyways 😉

XMPP

Next Marlinspike talks about XMPP. He (rightfully) notes that due to XMPPs extensibility there is a morass of XEPs and that those don’t really feel consistent.

The XMPP community already recognized the problem that comes with having that many XEPs and tries to solve this issue by introducing so called compliance suites. These are annually published documents that contain a list of XEPs that are considered vitally important for clients or servers. These suites act as maps that point a way through the XEP jungle.

Next Marlinspike states that the XMPP protocol still fails to be a suitable option for mobile devices. This statement is plain wrong and was already debunked in a blog post by Daniel Gultsch back in 2016. Gultsch develops an XMPP client for Android which is totally usable and generally has lower battery consumption than Signal has. Conversations implements all of the XEPs listed in the compliance suites to be required for mobile clients. This shows that implementing a decent mobile client for a federated system can be done and there is a recipe for it.

What Marlinspike could have pointed out instead is that the XMPP community struggles to come up with a decent iOS client. That would have been a fair argument, but spreading FUD about the XMPP protocol as a whole is unfair and dishonest.

Luckily the audience of the talk didn’t fully buy into Marlinspikes weaker arguments as demonstrated by some entertaining questions during the QA afterwards.

What Marlinspike is right about though is that developing a federated system is harder than doing a centralized service. You as the developer have control over the whole system and subsequently over the users. However this is actually the reason why we, the community of decentralized systems and federated protocols do what we do. In the words of J.F. Kennedy, we do these things…

…not because they are easy, but because they are hard…

… or simply because they are right.

Closer Look at the Double Ratchet

In the last blog post, I took a closer look at how the Extended Triple Diffie-Hellman Key Exchange (X3DH) is used in OMEMO and which role PreKeys are playing. This post is about the other big algorithm that makes up OMEMO. The Double Ratchet.

The Double Ratchet algorithm can be seen as the gearbox of the OMEMO machine. In order to understand the Double Ratchet, we will first have to understand what a ratchet is.

Before we start: This post makes no guarantees to be 100% correct. It is only meant to explain the inner workings of the Double Ratchet algorithm in a (hopefully) more or less understandable way. Many details are simplified or omitted for sake of simplicity. If you want to implement this algorithm, please read the Double Ratchet specification.

A ratchet tool can only turn in one direction, hence it is eponymous for the algorithm.
Image by Benedikt.Seidl [Public domain]

A ratchet is a tool used to drive nuts and bolts. The distinctive feature of a ratchet tool over an ordinary wrench is, that the part that grips the head of the bolt can only turn in one direction. It is not possible to turn it in the opposite direction as it is supposed to.

In OMEMO, ratchet functions are one-way functions that basically take input keys and derives a new keys from that. Doing it in this direction is easy (like turning the ratchet tool in the right direction), but it is impossible to reverse the process and calculate the original key from the derived key (analogue to turning the ratchet in the opposite direction).

Symmetric Key Ratchet

One type of ratchet is the symmetric key ratchet (abbrev. sk ratchet). It takes a key and some input data and produces a new key, as well as some output data. The new key is derived from the old key by using a so called Key Derivation Function. Repeating the process multiple times creates a Key Derivation Function Chain (KDF-Chain). The fact that it is impossible to reverse a key derivation is what gives the OMEMO protocol the property of Forward Secrecy.

A Key Derivation Function Chain or Symmetric Ratchet

The above image illustrates the process of using a KDF-Chain to generate output keys from input data. In every step, the KDF-Chain takes the input and the current KDF-Key to generate the output key. Then it derives a new KDF-Key from the old one, replacing it in the process.

To summarize once again: Every time the KDF-Chain is used to generate an output key from some input, its KDF-Key is replaced, so if the input is the same in two steps, the output will still be different due to the changed KDF-Key.

One issue of this ratchet is, that it does not provide future secrecy. That means once an attacker gets access to one of the KDF-Keys of the chain, they can use that key to derive all following keys in the chain from that point on. They basically just have to turn the ratchet forwards.

Diffie-Hellman Ratchet

The second type of ratchet that we have to take a look at is the Diffie-Hellman Ratchet. This ratchet is basically a repeated Diffie-Hellman Key Exchange with changing key pairs. Every user has a separate DH ratcheting key pair, which is being replaced with new keys under certain conditions. Whenever one of the parties sends a message, they include the public part of their current DH ratcheting key pair in the message. Once the recipient receives the message, they extract that public key and do a handshake with it using their private ratcheting key. The resulting shared secret is used to reset their receiving chain (more on that later).

Once the recipient creates a response message, they create a new random ratchet key and do another handshake with their new private key and the senders public key. The result is used to reset the sending chain (again, more on that later).

Principle of the Diffie-Hellman Ratchet.
Image by OpenWhisperSystems (modified by author)

As a result, the DH ratchet is forwarded every time the direction of the message flow changes. The resulting keys are used to reset the sending-/receiving chains. This introduces future secrecy in the protocol.

The Diffie-Hellman Ratchet

Chains

A session between two devices has three chains – a root chain, a sending chain and a receiving chain.

The root chain is a KDF chain which is initialized with the shared secret which was established using the X3DH handshake. Both devices involved in the session have the same root chain. Contrary to the sending and receiving chains, the root chain is only initialized/reset once at the beginning of the session.

The sending chain of the session on device A equals the receiving chain on device B. On the other hand, the receiving chain on device A equals the sending chain on device B. The sending chain is used to generate message keys which are used to encrypt messages. The receiving chain on the other hand generates keys which can decrypt incoming messages.

Whenever the direction of the message flow changes, the sending and receiving chains are reset, meaning their keys are replaced with new keys generated by the root chain.

The full Double Ratchet Algorithms Ratchet Architecture

An Example

I think this rather complex protocol is best explained by an example message flow which demonstrates what actually happens during message sending / receiving etc.

In our example, Obi-Wan and Grievous have a conversation. Obi-Wan starts by establishing a session with Grievous and sends his initial message. Grievous responds by sending two messages back. Unfortunately the first of his replies goes missing.

Session Creation

In order to establish a session with Grievous, Obi-Wan has to first fetch one of Grievous key bundles. He uses this to establish a shared secret S between him and Grievous by executing a X3DH key exchange. More details on this can be found in my previous post. He also extracts Grievous signed PreKey ratcheting public key. S is used to initialize the root chain.

Obi-Wan now uses Grievous public ratchet key and does a handshake with his own ratchet private key to generate another shared secret which is pumped into the root chain. The output is used to initialize the sending chain and the KDF-Key of the root chain is replaced.

Now Obi-Wan established a session with Grievous without even sending a message. Nice!

The session initiator prepares the sending chain.
The initial root key comes from the result of the X3DH handshake.
Original image by OpenWhisperSystems (modified by author)

Initial Message

Now the session is established on Obi-Wans side and he can start composing a message. He decides to send a classy “Hello there!” as a greeting. He uses his sending chain to generate a message key which is used to encrypt the message.

Principle of generating message keys from the a KDF-Chain.
In our example only one message key is derived though.
Image by OpenWhisperSystems

Note: In the above image a constant is used as input for the KDF-Chain. This constant is defined by the protocol and isn’t important to understand whats going on.

Now Obi-Wan sends over the encrypted message along with his ratcheting public key and some information on what PreKey he used, the current sending key chain index (1), etc.

When Grievous receives Obi-Wan’s message, he completes his X3DH handshake with Obi-Wan in order to calculate the same exact shared secret S as Obi-Wan did earlier. He also uses S to initialize his root chain.

Now Grevious does a full ratchet step of the Diffie-Hellman Ratchet: He uses his private and Obi-Wans public ratchet key to do a handshake and initialize his receiving chain with the result. Note: The result of the handshake is the same exact value that Obi-Wan earlier calculated when he initialized his sending chain. Fantastic, isn’t it? Next he deletes his old ratchet key pair and generates a fresh one. Using the fresh private key, he does another handshake with Obi-Wans public key and uses the result to initialize his sending chain. This completes the full DH ratchet step.

Full Diffie-Hellman Ratchet Step
Image by OpenWhisperSystems

Decrypting the Message

Now that Grievous has finalized his side of the session, he can go ahead and decrypt Obi-Wans message. Since the message contains the sending chain index 1, Grievous knows, that he has to use the first message key generated from his receiving chain to decrypt the message. Because his receiving chain equals Obi-Wans sending chain, it will generate the exact same keys, so Grievous can use the first key to successfully decrypt Obi-Wans message.

Sending a Reply

Grievous is surprised by bold actions of Obi-Wan and promptly goes ahead to send two replies.

He advances his freshly initialized sending chain to generate a fresh message key (with index 1). He uses the key to encrypt his first message “General Kenobi!” and sends it over to Obi-Wan. He includes his public ratchet key in the message.

Unfortunately though the message goes missing and is never received.

He then forwards his sending chain a second time to generate another message key (index 2). Using that key he encrypt the message “You are a bold one.” and sends it to Obi-Wan. This message contains the same public ratchet key as the first one, but has the sending chain index 2. This time the message is received.

Receiving the Reply

Once Obi-Wan receives the second message and does a full ratchet step in order to complete his session with Grevious. First he does a DH handshake between his private and the Grevouos’ public ratcheting key he got from the message. The result is used to setup his receiving chain. He then generates a new ratchet key pair and does a second handshake. The result is used to reset his sending chain.

Obi-Wan notices that the sending chain index of the received message is 2 instead of 1, so he knows that one message must have been missing or delayed. To deal with this problem, he advances his receiving chain twice (meaning he generates two message keys from the receiving chain) and caches the first key. If later the missing message arrives, the cached key can be used to successfully decrypt the message. For now only one message arrived though. Obi-Wan uses the generated message key to successfully decrypt the message.

Conclusions

What have we learned from this example?

Firstly, we can see that the protocol guarantees forward secrecy. The KDF-Chains used in the three chains can only be advanced forwards, and it is impossible to turn them backwards to generate earlier keys. This means that if an attacker manages to get access to the state of the receiving chain, they can not decrypt messages sent prior to the moment of attack.

But what about future messages? Since the Diffie-Hellman ratchet introduces new randomness in every step (new random keys are generated), an attacker is locked out after one step of the DH ratchet. Since the DH ratchet is used to reset the symmetric ratchets of the sending and receiving chain, the window of the compromise is limited by the next DH ratchet step (meaning once the other party replies, the attacker is locked out again).

On top of this, the double ratchet algorithm can deal with missing or out-of-order messages, as keys generated from the receiving chain can be cached for later use. If at some point Obi-Wan receives the missing message, he can simply use the cached key to decrypt its contents.

This self-healing property was eponymous to the Axolotl protocol (an earlier name of the Signal protocol, the basis of OMEMO).

Acknowledgements

Thanks to syndace and paul for their feedback and clarification on some points.

Shaking Hands With OMEMO: X3DH Key Exchange

This is the first part of a small series about the cryptographic building blocks of OMEMO. This post is about the Extended Triple Diffie Hellman Key Exchange Algorithm (X3DH) which is used to establish a session between OMEMO devices.
Part 2: Closer Look at the Double Ratchet

In the past I have written some posts about OMEMO and its future and how it does compare to the Olm encryption protocol used by matrix.org. However, some readers requested a closer, but still straightforward look at how OMEMO and the underlying algorithms work. To get started, we first have to take a look at its past.

OMEMO was implemented in the Android Jabber Client Conversations as part of a Google Summer of Code project by Andreas Straub in 2015. The basic idea was to utilize the encryption library used by Signal (formerly TextSecure) for message encryption. So basically OMEMO borrows almost all the cryptographic mechanisms including the Double Ratchet and X3DH from Signals encryption protocol, which is appropriately named Signal Protocol. So to begin with, lets look at it first.

The Signal Protocol

The famous and ingenious protocol that drives the encryption behind Signal, OMEMO, matrix.org, WhatsApp and a lot more was created by Trevor Perrin and Moxie Marlinspike in 2013. Basically it consists of two parts that we need to further investigate:

  • The Extended Triple-Diffie-Hellman Key Exchange (X3DH)
  • The Double Ratchet Algorithm

One core principle of the protocol is to get rid of encryption keys as soon as possible. Almost every message is encrypted with another fresh key. This is a huge difference to other protocols like OpenPGP, where the user only has one key which can decrypt all messages ever sent to them. The later can of course also be seen as an advantage OpenPGP has over OMEMO, but it all depends on the situation the user is in and what they have to protect against.

A major improvement that the Signal Protocol introduced compared to encryption protocols like OTRv3 (Off-The-Record Messaging) was the ability to start a conversation with a chat partner in an asynchronous fashion, meaning that the other end didn’t have to be online in order to agree on a shared key. This was not possible with OTRv3, since both parties had to actively send messages in order to establish a session. This was okay back in the days where people would start their computer with the intention to chat with other users that were online at the same time, but it’s no longer suitable today.

Note: The recently worked on OTRv4 will not come with this handicap anymore.

The X3DH Key Exchange

Let’s get to it already!

X3DH is a key agreement protocol, meaning it is used when two parties establish a session in order to agree on a shared secret. For a conversation to be confidential we require, that only sender and (intended) recipient of a message are able to decrypt it. This is possible when they share a common secret (eg. a password or shared key). Exchanging this key with one another has long been kind of a hen and egg problem: How do you get the key from one end to the other without an adversary being able to get a copy of the key? Well, obviously by encrypting it, but how? How do you get that key to the other side? This problem has only been solved after the second world war.

The solution is a so called Diffie-Hellman-Merkle Key Exchange. I don’t want to go into too much detail about this, as there are really great resources about how it works available online, but the basic idea is that each party possesses an asymmetric key pair consisting of a public and a private key. The public key can be shared over insecure networks while the
private key must be kept secret. A Diffie-Hellman key exchange (DH) is the process of combining a public key A with a private key b in order to generate a shared secret. The essential trick is, that you get the same exact secret if you combine the secret key a with the public key B. Wikipedia does a great job at explaining this using an analogy of mixing colors.

Deniability and OTR

In normal day to day messaging you don’t always want to commit to what you said. Especially under oppressive regimes it may be a good idea to be able to deny that you said or wrote something specific. This principle is called deniability.

Note: It is debatable, whether cryptographic deniability ever saved someone from going to jail, but that’s not scope of this blog post.

At the same time you want to be absolutely sure that you are really talking to your chat partner and not to a so called man in the middle. These desires seem to be conflicting at first, but the OTR protocol featured both. The user has an IdentityKey, which is used to identify the user by means of a fingerprint. The (massively and horribly simplified) procedure of creating a OTR session is as follows: Alice generates a random session key and signs the public key with her IdentityKey. She then sends that public key over to Bob, who generates another random session key with which he executes his half of the DH handshake. He then sends the public part of that key (again, signed) back to Alice, who does another DH to acquire the same shared secret as Bob. As you can see, in order to establish a session, both parties had to be online. Note: The signing part has been oversimplified for sake of readability.

Normal Diffie-Hellman Key Exchange

From DH to X3DH

Perrin and Marlinspike improved upon this model by introducing the concept of PreKeys. Those basically are the first halves of a DH-handshake, which can – along with some other keys of the user – be uploaded to a server prior to the beginning of a conversation. This way another user can initiate a session by fetching one half-completed handshake and completing it.

Basically the Signal protocol comprises of the following set of keys per user:

IdentityKey (IK)Acts as the users identity by providing a stable fingerprint
Signed PreKey (SPK)Acts as a PreKey, but carries an additional signature of IK
Set of PreKeys ({OPK})Unsigned PreKeys

If Alice wants to start chatting, she can fetch Bobs IdentityKey, Signed PreKey and one of his PreKeys and use those to create a session. In order to preserve cryptographic properties, the handshake is modified like follows:

DH1 = DH(IK_A, SPK_B)
DH2 = DH(EK_A, IK_B)
DH3 = DH(EK_A, SPK_B)
DH4 = DH(EK_A, OPK_B)

S = KDF(DH1 || DH2 || DH3 || DH4)

EK_A denotes an ephemeral, random key which is generated by Alice on the fly. Alice can now derive an encryption key to encrypt her first message for Bob. She then sends that message (a so called PreKeyMessage) over to Bob, along with some additional information like her IdentityKey IK, the public part of the ephemeral key EK_A and the ID of the used PreKey OPK.

Visual representation of the X3DH handshake

Once Bob logs in, he can use this information to do the same calculations (just with swapped public and private keys) to calculate S from which he derives the encryption key. Now he can decrypt the message.

In order to prevent the session initiation from failing due to lost messages, all messages that Alice sends over to Bob without receiving a first message back are PreKeyMessages, so that Bob can complete the session, even if only one of the messages sent by Alice makes its way to Bob. The exact details on how OMEMO works after the X3DH key exchange will be discussed in part 2 of this series 🙂

X3DH Key Exchange TL;DR

X3DH utilizes PreKeys to allow session creation with offline users by doing 4 DH handshakes between different keys.

A subtle but important implementation difference between OMEMO and Signal is, that the Signal server is able to manage the PreKeys for the user. That way it can make sure, that every PreKey is only used once. OMEMO on the other hand solely relies on the XMPP servers PubSub component, which does not support such behavior. Instead, it hands out a bundle of around 100 PreKeys. This seems like a lot, but in reality the chances of a PreKey collision are pretty high (see the birthday problem).

OMEMO does come with some counter measures for problems and attacks that arise from this situation, but it makes the protocol a little less appealing than the original Signal protocol.

Clients should for example keep used PreKeys around until the end of catch -up of missed message to allow decryption of messages that got sent in sessions that have been established using the same PreKey.

OMEMO

The OMEMO logo – a clownfish

Recently there was a lot of news coverage of an alleged „backdoor“ in WhatsApp, the proprietary messaging application owned by Facebook. WhatsApp deployed OpenWhisperSystem’s Signal-protocol roughly a year ago. Now a researcher showed, that WhatsApp’s servers are able to register a new device key for a user, so that messages that the user did not read yet (the ones with only one checkmark) are re-encrypted for the new key, so they can be read by WhatsApp (or whoever registered the key). There were a lot of discussions going on about whether this is a security flaw, or careful design.

I also read a lot of articles suggesting alternatives to WhatsApp. Often mentioned was of course Signal, a free open source messenger by OpenWhisperSystems, the creators of the Signal-protocol, which does not suffer from WhatsApps “vulnerability”. Both WhatsApp and Signal share one major flaw: Both create a “walled garden” for their users. That means that you can only write WhatsApp messages to other WhatsApp users. Same goes for Signal. Since Signal depends on proprietary Google libraries, it cannot be used on mobile phones without Google Play services.

Every now and then the news mention another alternative, the XMPP network.

Conversations is a free libre XMPP client for Android, which introduced the OMEMO protocol for end-to-end encryption roughly two years ago. OMEMO is basically the Signal-protocol adapted to XMPP. Since there are many different XMPP servers that can be used with many different clients, the user has a choice, which software they want to use to communicate to their friends. The issue is, there are not too many clients supporting OMEMO at the moment. But what clients are able to do OMEMO at the moment?

For Android there is Conversations of course and very recently ChatSecure for iOS was released in version 4, which brought OMEMO support. So it looks good on the mobile front (Sorry WindowsPhone).

For the desktop there is Gajim, an XMPP client written in python, which offers OMEMO support as a plugin. This works well on Linux and Windows. I admit, this is not a lot compared to OTR or GPG – but wait, there is more 😉

Currently I am writing on my bachelors thesis about the OMEMO protocol. As part of this, I am working on a Smack module that hopefully will enable messenger apps based on the Smack library (eg. Xabber, Zom, Jitsi, Kontalk…) to encrypt messages with OMEMO.

Simultaneously another student is developing a Pidgin plugin and yet another one is implementing OMEMO for the console based XMPP client Profanity. You can find a quick overview of the state of OMEMO deployment on https://omemo.top.

Update (kind of, its two years later :D): It appears, that the original article by The Guardian has been amended due to its author massively overestimating the severity of the “flaw”.