Welcome to the show, ladies and gentlemen. We have upgraded from the last video where I did the balloon pop hair color and now we have an entire space covered in plastic. Hopefully I don't get color over everything again and have to redo my flooring again. It was a lot. If you didn't see that video, I'm sorry. It was a great video. So today I thought it would be a great idea to finally do sports gun hair color. It was highly requested in the last video. Listen, I've actually tried a squirt gun before. If you were a true OG, you would know that except it wasn't to this scale. Okay? Am I echoing? No, okay. It's not that big in here, but it is large. But yeah, I'm gonna guess color some hair with a squirt gun and hopefully something good comes out of this and I don't go crazy like the last time I did some stuff like this. It's okay. Let's do it. All right, Regina. What? This is my favorite. What is this? What in the hell? We're shooting hair color through all of these and I just don't really know how that's gonna work, but maybe you've put a little thought into it. Yeah, okay. Good, thanks. Maybe you should wave the camera up and down. What am I creating with these water guns? Got it. One is. Uh-huh. The other one is shadow moving. Oh, we lost, we lost some plastic. Why don't you show me the references and we'll come right back. And you guys will see the references right now. Regina, I don't know how you expect me to do any of that, but I can guarantee you it's not gonna look anything like that, but why don't we just get into this shit? I can at least try it. I mean, I don't think that's gonna be possible, but thank you for believing in me that I can create that look with a squirt gun, Regina. It's not gonna happen. Let's just begin. I mean, do I have an outfit? Similar outfit to last time, except that I now have a black shoe. I don't know, I'm kind of vibing with the look right now, but maybe I'll just add the sunglasses.  The worker glasses? What do you call these things? Sunglasses? Protective glasses. Scientific protection utility glasses is the official name. It's always important you have a good look when you're doing something new. Helps bring confidence to yourself. It helps you feel alive and cool and brand new. So I'm making, are you recording? All right, I'm making the rules, Regina. I'm making the rules now. So I think that I should start close. Let's not make this too hard for me because I also have to learn how to, actually I was gonna say learn how to squirt it. I was gonna say learn, I was gonna say, I was gonna say that I should learn how to squirt a squirt gun, but I actually, if we recall, at Coachella, I had quite an iconic picture of me squirting a squirt gun, so I actually do know how to do it.  Hi, Miss Manny Quinn. You are gonna be getting a whole new look today. What are you, what are we doing? Glad you asked.  Your sister was the first person to get balloon pop hair color, and now you are the second. Second's almost as good as first, but you're a little concerned about the outcome of it. Me too. I don't know if it's gonna look good, to be honest with you, and I am sorry in advance, but you can say anything. So let's get started. We're doing a little layer of hair first, and I gotta pick a squirt gun here. Should I go with the biggest one first or the smallest one? I don't know. Maybe we'll start off small. How am I gonna get anything into this gun?  I'm gonna start off with blue. I wanna see the most effect first. Oh, this does work. I'm feeling this might not actually come out of it though. Did I put a lot in or just like a little bit? By the way, this is X-Mono color mix with water. Maybe too much water. I don't know. This is not a real gun, by the way. Please, YouTube do not take my video down. I promise the squirt gun, see it's orange and cute. Just like I was in high school. And are we going to be covering her face so I can protect it from the color? No. Is it going to get all over her? Yes. Do I care? No, because she has a plastic face. Let me do a little test run here. Oh! Yes! Wait, this is more fun than I thought I was gonna be. Ah! E! I wish I could do this in the salon. Anyways, okay. Oh! Wait. Is this the moment? Wait.   Oh my God, I'm obsessed. Sayonara! How are you trying to keep it clean? Oh, you didn't get anything on your posies. Good girl. You want a kiss? You gonna be a good girl tonight? Yeah, thank you. Just don't walk over there, okay? Cause it's bad for you. Yes, there's monsters over there, so don't do that. Should I do a lot more color on this first layer, or should I just like, I am kind of liking the effect that the Squirt Gun is giving, like that kind of dotted effect going on? So yeah, I thought we agreed on that. No, no more. Come on, you lost your privileges. Come on, Missy. All right, dope. So I think that I'm gonna put this baby down, but this works well. There are way bigger Squirt Guns for me to try though. Oh! Yep, we are definitely gonna need the booties for this. I figured out that I can't walk over there, or else I'm going to track more paint on my floors and stain them even more. So I thought it'd be a good idea to put a piece of plastic down and kind of shuffle my way over to section the hair now. Listen, I will say this is 10 times easier than doing the balloon pop color. You can't force me to do that again. Oh, but we will. We will force you because balloons are the best. So our sectioning, again, it's very complicated today.  Yeah, I feel like I can make this look kind of like tie-dye. Like I'm literally not doing the inspo pictures because I can't do that. But I feel like we also need to get this head farther away from me now and try to do something with a bigger Squirt Gun. I feel like the bigger ones have more range. That's what my brain is telling me today, and that is what my childhood is telling me. So let's move this back. Oh, there's color all over my hands now too. Why is hair color so messy? Why? One moment, just gotta get back to my floor. There we go. I usually say the best for last, but this one just looks so pretty and so cute and so me. Actually, that's a lie. This one kind of seems more of my style right now, but this one also seems really fun. So maybe we'll do this one first and then this one.  Feels like this is gonna take a lot of color. This yellow looks like water. Okay, so we gotta pump this.  Okay, so let's get this next layer. This okay with a little bit of the mixes together because it's gonna make it green. Oh, wait, those two layers together look so cool. Brad, do not walk on the plastic. I want to look at it up close so bad, but I can't. Oh, this looks so cool though. Oh, this thing ate the color up. That was like a whole thing of color. Gone, but worth it. This is the vibe.  I am feeling inspired. I'm feeling awake and alive. Oh, don't do it, Brad. Don't do it. Get a shuffle. Not the Balenciacas. Okay, next layer. I think that we need to do like a pink, you know, and I feel like I want more of that squirt effect. Maybe I should do a smaller one. Like one that doesn't pump like that because it's a little aggressive. I like aggressive, but maybe not everything needs to be that aggressive today. Kind of live on the edge today. It's just a little me living on the edge. This is a dope squirt gun. Can I do more videos like this guys? Like I really have fun doing it. If you could also enjoy it, that would be so good for me. Even if you don't actually enjoy it, just pretend. Let's see the range on this baby. Hello? I think we have a faulty gun. I think I clogged the hose. Shit, not the fire extinguisher. Sorry, you guys. This one just doesn't seem like it's going to happen today. This is not going to work. This hole's too small and it's just not going to happen, which is really sad for them. So hopefully that one works a bit better. No fear. The fireman is here. I also don't know if this is going to work, but we can only try and hope for the best in life. Children's toys dispense air color. Uh oh, I am making a mess. The best part about this one is that it is a backpack. Get ready for a cute outfit in three, two. All right, baby. Come on. Work for me. Yes, yeah. It works. Oh, okay. It's really hard to aim. Let me get the other side. Oh, we're running out of color. I have two more squirts to go. Oh, imagine if this was a real person. I would actually make it 10 times more fun. You're next. Okay, now I'm just getting aggressive with it. I ain't going to stop. Okay. Hello, Miss Manny Quinn. How are we feeling to- Don't you do it. I know you're about to do it. Don't do it. Miss Manny Quinn, hi. How are you feeling today? You're hanging in there. Okay. You look good, honestly. Like, the color is giving. It is giving fun. It is giving punchy. It is giving young. It is giving vibrant. It is giving healthy. And I don't have the patience to be sectioning your hair anymore. So that is the section you're going to get, okay? Lovely.  The poor thing is about to get completely drenched in color.  How did I not see this one? How am I going to fill this though? Oh, it really does. It has to go through the front. Oh, I got it. We got to load this thing up from the front and then push it out. Oh, this just feels dangerous. And I like that.  Oh my God. Oh, feels like a relatively bad idea, but all good things start with bad ideas. It is time for the stream machine. Hydrobolic water launcher.  Let's try her out. Oh, hold on. Why do these things just keep getting spookier? That was every last trip of the color that I put in there. It got everywhere. Besides where I actually wanted it, I guess that'll do. This is number one. This one was really fun and aggressive. Actually, if this had water in it, 10 out of 10. The floor honestly looks cooler than her head. Her head does look kind of cool, though. We have a few more squirt guns.  Mm-hmm, gotta make sure we get the front of your head, babe. The water pistol. Let's do some blue, cause she needs some more color on the head. I gotta fill this baby up. We have a lot of surface area to color. Yeah. The straight part of me comes out when I do things like this, like when I play with toy guns. Oh, it is getting a little harder to aim, I will say, with this being so far away. Oh, oh my God. I'm getting closer. I'm cheating. Oh, yes, yes. Look at how cool the floor looks. Regina, can you turn her head? Just grab her little nose and turn it. Watch out. We're out of ammo, guys.  Do some super green. We're loaded. Okay. Oh my God. We need another layer down. We gotta finish this baby off. Oh, I am so sorry. Are you able to breath miss?  I'm surprised when I fall asleep, I don't feel scared to be in the same house as these dolls that I torture. It's all fun and games though. It is time to break out Team Magnus. This one is by far the most chic of all of them and it obviously gets the color purple all.  Oh, it's too much for me. What kind of squirt do we think this is gonna be? Like a shh, or a shh. I think it's more of a shh, but that's just me. Sharp and skinny. Oh, I was right. I was right. This thing's got a lot of aim to it. Shit. Oh. I knew this one was gonna be the best. I knew it.  Hello. She's gonna get a lot of purple on here. I guess the whole thing is gonna be purple on the top. Oh, we're running out of color. I think I got it. I think I did it. Wait, no, she needs one more thing. She needs more yellow. Are you kidding? She think I'm gonna leave those blank spaces like that? No. Take the little one for last. You didn't forget about Yula, baby. Hey. Hey. Boop, boop, boop, boop, boop, boop, boop, boop. All the blonde sections are now obviously turning yellow, but like it looks 10 times better now. Just a little bit more on those blonde sections. And then I think her color might be good. I'm definitely cheating, but it's fine. Oh, girl. The front of your hair is not looking too cute. I found more green. I like the collage sort of abstract moment going on. This is great. I'm putting the square guns down. That color combo on the front, I'm not totally sure of. But underneath, it's giving rainbow amazingness. And then the top is giving a little bit like pukey colors. But nevertheless, we will see soon what the results are. I'll see you then. She has been washed and blow dried. And I hope you're ready for some sickening results because that's what you're gonna get. No. I just want to publicly apologize to this mini Quinn. I actually didn't realize that I covered your entire face with color and you look really bad. Next time I might consider covering your face, but I don't know. We can't guarantee anything in these games. Her hair color looks really bad and I would never do this again. Like, what is this? Ew. Ew.  It's a disaster. It's so spotty. I actually kind of hate everything about it. If you're considering, I know some of you are doing the squirt gun hair color. Don't. This could be you. And I wouldn't want that for you. Yeah. So like we have like a coontail. If you all know what that is, like going on. And then we got some random, just it's so random and bad, but that is the results. I did have a lot more fun doing this than the balloon pop color that is for sure. So I am going to rate this technique a seven out of 10 because the fun that I had doing it was high, but the results were low. Anyways, that's all for today, guys. Make sure you check out my hair color line links right down below and don't do this to yourself. That's all for today. Thank you so much for watching.  I'll see you next time. Bye.


Hello, welcome to track one to his clock talk. Hope you learned something new about SMB. This is William Martin. So as introduced, my name is William Martin. For anyone who saw me yesterday, it's going to be pretty familiar. I'm an OSCP. I'm a pentester based out of Charlotte, North Carolina. I'm a supervisor at RSM US LLP. And this is my second time presenting at DEF CON, first time as yesterday. So lessons learned from yesterday is that if you've got any questions about this talk, want me to clarify or expand or get in contact with me, take a note of the Twitter handle right now that's the best way you're going to be able to reach me. So it's a quick breach. Anyways, so before we get started, I want to make sure all the right people are in the room. We're going to be talking about SMB and SMB based man in the middle of attacks. And for red teamers, this is useful to, you know, add a new kind of attack to your tool set, add a new technique to your arsenal. And for blue teamers, you want to know how to stop the red teamers from using what they learned today. And for like the three guys curious about SMB, it's also for you. That guy right there. Thank you. So first things first, I want to clarify some terminology. When I mentioned SMB server, do not think of like a server 2012 or 2008, it is any Windows PC connected, typically connected to a domain. Every Windows PC runs an SMB server by default, but when you're in a domain typically that ports opened up so that anyone can talk to it. So when I say SMB server on client, it can be a Windows 7 to Windows 7, 2012 to 2012, there is no connotation tied to the actual operating system. So what is SMB? In a nutshell, it's a way to, you know, access files remotely as Microsoft solutions for network-based file sharing, file management.  What I want to clarify is that through this talk, I'm going to be talking about SMB 1 and SMB versions 2 and versions 3. Now, back when Vista was released, Microsoft pretty much did an entire rework of the SMB protocol. Originally it was based on an IBM system, and that's what we call like NTLM, and Microsoft uses NTLM everywhere, so the names always get mixed up. But SMB version 1 is what we're typically familiar with for like, you know, MS-17010 and things like that. SMB version 2 and 3 is an entire rework of the SMB protocol, and within that there are different versions, they're called dialects. So 2.0.2 is the first version of SMB 2.3, and then you got 2.1, then you got 3.0, and then 3.0.2 and et cetera. So, a typical of this change in SMB looks like this. Someone says, hey, what's in this folder? And SMB will reply, you got documents, desktop, and you know, some not password file. So, we love it past the hash, we love it for system enumeration, and we love it for spidering shares and hunting for sensitive data, such as like, you know, the C-password vulnerability and SysFold, and obviously for MS-17010. Now, the premise of this talk, and the origin of this talk, is SMB signing, particular how it defeats my absolute favorite attack. My favorite attack is the NTLM relay attack, especially against SMB servers. If anyone has used impact, it's the NTLM relay stuff, PY tool, you know, that is it. And I'll tell you, the attack works like this. A victim says, hey, where is my network share? An attacker says, hey, I'm totally that network share. Victim says, cool, let me log in. We then relay that to some random server we pick and say, hey, let me log in as this dude. Server says, yeah, that's cool. Just hash your password with this challenge. We send that back to the victim. They comply. We forward that on to the server. Server lets us log in and then we kick the victim. We ghost them. And once we have that connection, we can enumerate the system, we can exit commands, we can dump it, that's now our box. If the person's a local admin.  Signature is required. Now, I had a bit of confusion. I just manipulated the entire authentication process for this victim, yet they have somehow established a secret or trust between each other unbeknownst to me. So I didn't know how could they have done that. Where was there some kind of like public key, you know, certificate kind of thing going on? I had no idea. So when I looked up what is SMB signing, I got vague descriptions.  So naturally, like most of you, I Google it. Now I got it's answers like it stops man and middle attacks. Stops man and middle attacks. Trust us, it stops man and middle attacks. It's Microsoft solutions to stop man and middle attacks. That's about it. That's all the information I could find. So I knew that it protects the integrity of SMB messages, because we edited it after signing is enabled, we get screwed. It's required by default on DCs. It occurs only after the authentication process.  So I dove into the MSND docs.  And I saw things like this. And I saw things like that for a while, quite a while. But eventually I found the answer to what SMB signing actually is. And we're gonna dive into that. At the end of the authentication phase, both the client and the server will share the same session-based key, just a 16 byte value. They then use that value to generate other keys to then sign the messages. Now, the goal of what we're about to cover is where does that key come from and how can we compromise it? By the way, that's what a signature looks like for anyone who hasn't used Wireshark on a DC. So the session-based key actually depends on what authentication mechanism is used. So let's talk through NTLMV2, also my favorite type of authentication. There are three messages in NTLMV2. There's a negotiate, a challenge, and an authentication. So negotiate just says, hey, I wanna log in. And they set some empty parameters. Like you can see in this capture, there is no username. There's no workstation. There's no domain name. It just says I wanna initiate this conversation. One flag that can be in this message is called the negotiate key exchange flag. And we're gonna get into that later. But in a nutshell, what that means is that once both the client and the server established that shared session-based key, they're gonna change it again. But that's what that flag means. We'll get to that.  And this contains the server challenge information, like the host name, domain name at DNS name, stuff like that. The authentication message contains a lot of stuff. The username, the domain, the client challenge, the NT proof string, which in a nutshell is the hash generated by the client. A bunch of response server versions, things that are in plain text that we don't particularly care about. And an encrypted new session-based key. If you look in this message, you'll see there's a session key value like B485 to whatever. That only exists there if the negotiate key change flag was set earlier. That is the encrypted version of the new session-based key. But if they didn't negotiate that, that value's gonna be empty.  So, I thought it was very technical. But let's get down to how the keys are actually generated. And we need to know what HMAX and CMAX are before we can get into that. In a nutshell, they are message authenticating, no, authentication code algorithms. You can think of them, if you're familiar with password salting, you can think of them like a salt where you have a message and you're gonna hash that message. But while you're hashing it, you're gonna include a secret value that only those that secret value can throw in that hashing algorithm to create the same hash. So in HMAX or CMAX, the underlying protocol might vary like some use AES and some use like SHAF 256. But in a nutshell, their goal is to hash the message in addition to like some secret information. So, let's actually walk through generating those session base keys. So, step one is we need the NT response. That is the user's NT hash. So it goes from plain text to NT hash. Step two, we take all of the information from the server challenge and we put that together and we use the HNAC algorithm with the password, with that hash password to the NT hash. And then we have our session base key, which is the NT response, hashed again, again, your password hashed again in addition to all of this server information that you already hashed. All together it looks like that. The key takeaway though is the highlighted information is the only information we don't have in this exchange. To generate the keys that protect all SMB sessions, we just need the user's password, which is great, because they're always secure, we can never crack them. That was my response when I found out that the key concept protecting all these connections was just their password. I mean, think about if TLS was protected not by some random long string generated through the connection established phase, but instead like the dude's password on the website he's connected to. So, the key logic works like this. You have the password, gets converted to the NT hash, gets combined with all that authentication data, and then that generates the session base key. Once you've got that session base key, you can use that to then sign packets, or in other versions of SMB, you can use that to generate the keys to sign the packets. Long story short, this is the value we care about. So, as I mentioned earlier, if that flag is set and you generate that key, you're just gonna use it to decrypt this one and that becomes the new one. So, with that knowledge now of how those session base keys are generated, I want to go back to my favorite attack, the NTLM v2 relay attack, and show where that trust is established and I know there are some Microsoft guys or AD admins in here who are gonna laugh at this for leaving this step out. So, here's what it looked like. We just sent the challenge response, we just sent the authentication message to the server. The victim at this point, before the server replies, has already gathered all the information required to generate that session base key. So, he's cool. The server doesn't have the user's password, unless you're connecting to a DC itself. So, the server actually sends all of that data off to the DC through a mandatory encrypted channel. Please trust me on that one. And the DC will reply if it's a valid login and if it is, the DC will generate the same key in the same way that the victim did and provide that to the server. That's the trusted secret that we don't get. So, I know you're all thinking, what about Kerberos? So, Kerberos is a bit more difficult to get into. Starting from step zero, when the user logs into their workstation, they log in and they send a request to the Kerberos server to believe the DC. Kerberos replies saying, hey, encrypt this timestamp with your password so I know it's legitimate. We send the encrypted timestamp and the Kerberos server replies with our TGT, which is our session key. We're gonna use that for most everything on the domain. We're gonna use that for future communication with the DC. We're gonna use that to request tickets to other resources on the network. Such as when we wanna connect to something called a file server one, just a random file server and the DC will reply with an encrypted service session key in that packet. We'll send the ticket we just received off to the file server. File server will, assuming it's valid, will reply and say, hey, cool, you're good. And if there is extended security, it will reply with another encrypted session key. Which altogether looks like this. Password turns into the Kerberos session key we got when we first logged into Kerberos. That we use to decrypt the service session key we get when we ask for a ticket to a file server. And if they're using that extended logic, we use that last key to decrypt the now new key provided from the file server. These keys are then used to sign the SMB messages. These are the SMB session keys. And the algorithm used to generate these keys and to generate the signatures is very based on the version of SMB. So there's version one, which is MD5. Versions two and 2.1 kind of beeped it up a little bit with SHA-256. And versions three and 311 really beeped it up with AES-128. So now that we know the only thing protecting these sessions is the integrity and the complexity of the user's password, let's go after it. So first things first, we just talked about how to kind of break SMB signing keys and how to break signed SMB connections. But when SMB signing isn't used or we have that, it's essentially HTTP without HPS. If encryption's not used, we can steal copies of files passed over the wire with or without the keys. And encryption's not used by default. If signing is not used, it's fair game. You can replace every file with an identical link that executes our code. You can swap out the contents of legitimate files passed over the network. You can inject fake files into directories and that helps with social engineering. And if signing is used and we know the password, then we can do all of the above. Plus, we can also backdoor some stuff pulled from the DC by the user. So in SMB version one, they don't really use signing by default. And in SMB version two, three, the case is pretty much the same. Unless somebody requires signing on one of the sides, no one uses signing. So we just talked about how to break signing most of the time it's not even in place per the Nessus reference. Also SMB version one, there is no encryption. So for those plain text files passed over the network, we can just grab them. SMB version two and three, it supports encryption version three, but it's not enabled by default. And enabling it is a bit of a pain. So chances are, you can also, regardless, steal files passed over the network. Broken down, there are various versions of SMB and they're supported on various types of operating system. Like Vista came out with SMB version two and that was the first one to come out with it with 202. Then you've got the latest and greatest server 2016 using 311 and Windows 10 using 311. Everyone else uses something earlier. Or rather not earlier, in between those. Notable exceptions in all of this is that DCs require SMB signing by default. Windows 10 2016 have protected paths that always require signing if they're connected to a path that matches these paths. So anything that's like something SysFall or something NetLog on, the client's gonna require signing regardless of what the server says. And that's through a process called UNT hardening. One other notable exception is that if a client supports SMB version three and that's 302 or 311, then regardless of if signing is used or not at the end of the authentication phase, they're gonna send a message to the server saying, hey, just make sure we're all on the same page. Here's the information you gave me during the negotiation phase. Is this still cool? And that's a signed message. So the server now has a way to kind of verify that no one messed with it in between. Even if they're not using signing for any of the subsequent messages. Only catch here is that in that message, it's the one that verifies we're all on the same page. It covers everything except for the authentication mechanisms used. So even with that, you can still downgrade them to NTLMB2 and get away with it. So on the other end of the spectrum, SMB 311 is a beast. And I'll give kudos to Ned Pyle on that one. The SMB keys, rather than just being based on the authentication mechanism used, it's also based on the hash of every packet passed back and forth during the negotiation and authentication. So if you edit anything, then the server and the client are not gonna have the same keys and the connection's gonna drop. So not bad on that one. So to recap, it's used on DCs and on 10 and 2016 on those paths. Encryption's only on SMB3, but it's a manual process. Every dialect up except for 311 can be downgrade on NTLMB2 and signing and encryption keys are at the root based on the user's password. So let's attack that. I built SMBetray, and the goal is just to build a tool to really take advantage of these man-made vulnerabilities. The attacks we've been running before are like the relay attack I described, where we're enumerating the system if we're putting ourselves in between a victim and a server or we're trying to pop it if they have LA. But if they don't have either of those, that's pretty much where the road ends for us on SMB attacks, except for MS-17 or patch-related vulnerabilities. So I wanted to take the focus instead of relaying or putting ourselves to the focus on the server. I wanted to go back on the client. I wanted to go back on the HTTP mindset of attacking the client. So the biggest obstacle in all of that was putting ourselves in the position to attack the client. So we wanted to be right there. We want to be between my buddy Damian's in the crowd. We want to be between Damian and his DC, his file share, and his other file share because many users have multiple. We didn't want to just pick between, you know, being in between Damian and his DC, and that's it. So we're missing a lot of data there. So when I was trying to build this tool and I was trying to put it on top of Man of the Middle framework, I kind of had two options. The first one was through the use of an arbitrary upstream server. A lot of these Man of the Middle tools will use an arbitrary upstream server as a way of misstability. Long story short, you receive a connection during like an ARP cache poisoning attack. IP tables will redirect that connection right back to you. And then in the socket layer, you will then forward it on to wherever you want. The catch is when you're at that layer, you don't have the original destination of the connection you just hijacked. So if Damian was trying to connect to his DC and I intercepted that connection, I might be redirecting him to some random file share I picked. And on his end, that's not going to be what he wants, so he's going to drop the connection and it might not give me all the things I want. I want him using that connection so I can take advantage of every opportunity. I want him downloading files so I can steal them over the wire. The other opportunity for a man-made tool to kind of take advantage of that was the use of Net Filter Queue. Net Filter Queue really gets down to the kernel level and allows you to edit those packets and intercept those packets live time. So you don't have to worry about losing the destination information as you're pointing this intercept. So you can put yourself in between all of those servers. Only catch is that when you're putting yourself in between all those servers, Python is what I was using and Python would just snowball, it would drag. What would seem very quick to us was eons for QCP. So this only solution that I found to do a full transparent man-made middle attack was killing me because it wasn't fast enough, it wasn't parsing the data fast enough to pass the information back on. So I tried to combine them so I get the solution that I wanted. I created a little library called EBClib which I was kind of playing on, there was EdoCap and then there was BetterCap so cheekishly I put EBC for even BetterCap as a man-made middle TCP kind of framework. So it gives you all of the freedom of a transparent proxy built on NFQ where you can just say, hey, put myself in between Damian and whatever he's talking to without editing it or edit if I choose to with the connection stability of like a BetterCap with an upstream proxy. And that's the technical of how it works. Long story short, you get the packet. NFQ rather than trying to edit the packet the entire time do it and do whatever attack you intended instead it just performs one task which it does pretty quickly and that's why the connection doesn't drop. NFQ will get the packet, it will just take the source and the destination information and then store it in a shared piece of memory and then pass it on. That gets redirected like the first type of man-made middle attack to a TCP server. And with there you have the stability of TCP. That TCP server will reach out to that shared memory, find out where this dude was actually trying to go to and then builds that connection dynamically out there. So once you receive a connection that exists it just passes through to the TCP server like business as usual. So now that we compare ourselves in between the server that we want to hit and the user, let's go ahead and let's start attacking them. Let's downgrade the dialect and the authentication mechanism is used. Let's steal the passive files that I've been harping on. Let's inject some files and swap out some content and let's replace files with an identical link so that when they click it, it launches that thing. And of course, if we know the password for the user, let's leverage that information to break those session keys. So the way as the betray is broken down kind of looks like this. We put ourselves in between the victim and whatever server they want, even multiple servers at a time. The victim will say, hey, what's in this folder? And that request occurs simply when you open up a folder in a share and it starts listing out all the files and folders in there. We pass that on to the receiving server. Receiving server will reply saying here, file one, file two. We'll get that and if we know the keys or it's an insecure session, we'll throw in our own file in there or we'll modify the details of the files that were just listed like their file size. The user might request one of the files we just lied about instead of was in that folder. Now, instead of passing that on to the server because the server would reply with an error saying that file doesn't exist, we send them a convenient function, SMB, called an echo. SMB loves to keep its messages in sync. Each request and response has a numeric ID. So if I say I'm gonna pick on Damian again, if I say hi Damian, that has a message of one, when he replies, that's a message ID of one. That conversation is concluded. If I say another thing to him, message ID two, he replies message ID two. That helps verify that we haven't missed anything in this conversation. But if the user just requested a file that does not exist and we're not gonna pass that on to the server, there will now be a discrepancy in how they talk to each other.  So to keep them in sync, for every request that is completely forged or malicious by the victim that we're handling, we're gonna send an echo request to the destined server. When the server replies to that echo, we've now incremented the messages again and now we're gonna reply to the victim with whatever we wanted. And that way, when they continue their conversation with each other, no one will identify that they've been swindled, old word. So now let's show a brief demo of what this is gonna look like. So assume we've done an ARP cache poisoning attack on this victim and we're between them and a switch. On the other end of the switch, it's gonna be like a DC and there's gonna be just some file share. So first things first, we're just logging into a user's workstation to show you what a non-attack scenario looks like, what his average PC sees. He's got a file share, a map drive called some network share and there are some files in there. Keep a mental note of the files that you see because we're gonna be injecting some and removing some. Cool. So now we're gonna launch the ARP cache poisoning attack to really put ourselves in between him and whatever he wants to talk to. And also note, the server that he just connected to, one of the files in his map network drive requires SMB signing. File containing a lot of pop credentials.  And we're gonna load these credentials into the tool itself. It's just gonna use them and when it sees a connection coming from that user, it's gonna try to leverage those credentials to pop the SMB signing keys. The attack we're running is gonna be a link swap all attack as well as an inject files. Inject files intuitively just injects files. Makes files appear in the directory that don't actually exist in the directory. And the link swap all is any file at all. We're gonna replace it with instead a link that will run whatever we want. In this case, we're just running calc.  So calc was easy enough. So now Paul Davis is gonna log back into his PC. You can see we capture his hash. Then in the background, you can see that we, it's reported that we broke his session base key through both NTLMV2 and it's cut off a little bit, but it says Kerberos. And now it shows that we just injected some files. So click me, inject me, seems legit, all those. The text file that we opened up earlier is now a link. And when opened, we'll run whatever we want. In this case, it was calc. Inject me, a totally fictitious file that doesn't exist on the server he thinks he's talking to is now there. And any file, thank you. Any file that this user is now downloading or opening, either directly or indirectly, through back end processes and Windows, we will be passively stealing a copy of. And to show the impact of that, I'm gonna run the attack again.  And the only thing I'm gonna do is I'm gonna passively steal stuff.  So we're removing the credentials and we're just gonna listen passively. As it turns out, when Windows starts up, it downloads a lot of useful information from the DC. And if you are lucky enough to be running attack like this, or if you lost your client or you lost your victim to convince them to reboot their PC, you might just be able to capture all of these valuable pieces of information from the DC. I recorded this demo on a PC from 2012, so it's not gonna be the quickest thing. PC just started up and we've already intercepted some connections. Paul Davis is logging in and we're now stealing some data from the group policy, including the registry.poll file, which contains a lot of valuable information in terms of registry setting configured for the users on the domain. If you want to take a photo, it will be posted this evening. So now that we just kind of demonstrated that SMB keys are based on passwords and that even without the password, we can still intercept and modify a lot of connections. And we can especially download some useful information from the group policy. How do we stop this from happening? Netpile is the guy who I would argue is in charge of SMB globally. Disable SMB once. Second thing, even though we're just demonstrating that you can defeat SMB signing, that's by no means any excuse not to require it. There is, and for those who haven't run Nessa scans, there's an option to just support SMB signing and there is one to require it always. And I highly recommend you require it always unless you're running XP systems, you're going to be able to support that. So SMB version three introduced encryption. And I would love to see organizations really start pushing this thing out. Any SMB three client supports it. So if you're running anything later than Windows seven in your org, you can put encryption pretty much everywhere you want. And it is actually more efficient than signing the messages. So if you, you can support encryption or you can require it. So if you support it, then SMB three negotiations protected. If they negotiate that you can support encryption, they're going to encrypt the session. So UNC hardening is one of the features used by default by Windows 10 and 2016 to protect the SysFall and the Netlogon shares for any connection going out to something that looks like that. But you can manually require that on other shares or any other kind of path. So if you know in your organization that there's a very specific file share that your user connecting to that you want to make sure it's pretty locked down, you can lock down from the server side by requiring signatures or requiring encryption. But you can also lock it down on the client side, prevent them from connecting to rogue servers by throwing in this UNC hardening saying, hey, if you're connecting to this server or a server that looks like this, do XYZ. And I hate to say this because as a pen tester, I love NCLM, but NCLM really is outdated. It was made near the 90s. I was made near the 90s. So if you can run through audits in your organization, see where NCLM is used. And if you can't disable it just carte blanche, out of those properties of carte blanche, if you can't disable it across the org, then find out where it's used and then restrict it just to those systems. For me, that screws me over, but I guess we're all here for security. Kerberos fast armoring is an interesting thing. We showed that if we know the user's password, we can intercept their Kerberos authentication phase and steal their Kerberos session key from the initial logon and then use that to steal their Kerberos ticket session keys from every subsequent request. That can be protected, but it requires Kerberos fast armoring, which in a nutshell, any request going to the Kerberos server is first locked up with the, man, I'm hoping my details right, with the machine accounts Kerberos tickets, which means unless you can pop the machine account password with that obscenely large password, you're not gonna be able to modify or intercept that Kerberos session key even if you know the password. So huge precautions when enabling fast. It requires Windows 8 and 2012 to layer throughout the environment. Just like SMB signing, it can be supported or it can be required. If you just support it, we're gonna take advantage of the benevolence of the server and just downgrade clients. But if you require it, then you better make sure that all your clients can connect to it, otherwise you're gonna break them. They're not gonna be able to talk to the DC. So Microsoft has great documentation on how to push out a fast armoring and I'd highly recommend you going through the procedure of pushing this out through your organization. You know, always use passwords and not passwords. A lot of the SMB signing crap that we just covered in terms of breaking the keys were lies that we compromised their password. So push out strong passwords. Push out strong passwords and require SMB signing and you're a lot better than you were at the beginning of this talk. Even if you don't do all the other complicated and involved things like fast armoring. So that pretty much leaves us to like a Q and A, but right now I wanna acknowledge that a few people have contributed on this talk. Ned Pyle is Principal Program Manager at Microsoft and it was awesome. I did my own research on MSFDN and I said, hey, to the best of my knowledge, here's how SMB works and here are the various circumstances that it behaves. Is this cool? And he was awesome in terms of providing feedback and giving me direction on yes and no things so I didn't give you guys misinformation. So he was awesome. Matthew George also worked side by side with Ned on this one to kind of spot check me on this. And Core Security for the Impact Library for which all of SMBitray is based on and I use their library when I was trying to figure out more on how SMB signing works. So that's about it.


Hello, everyone, and welcome. This is Melissa Armo with the stock swash and reviewing FDX. Really nice drop off and move in this. Again, if you did this, I had called the two puts in this on the 18th in the day trade. This is the day that it had the earnings gap down. Fell, low in here was 148.50. It was, there were nice profitable moves if you got out of them this day. And again, booking profits is important in this market. But this fell then again on Friday and then gap down this morning. Actually today it opened at 147.54. This is traveling down and low today was 146.35 or 33 there. I mean, this is obviously if you held onto this you're getting paid here more today. I called the 152.50 puts and the 150 puts. So I mean, this is continuing. I mean, this is quite a ways through the strike here. So anybody that held this got paid, again, in this type of market environment where the market's very volatile, I do think it's important to take profits, either a portion of profits or the whole thing. But if anyone held this down, this drop down today and very well to be lower. So good luck everybody, anyone that's in it and congratulations if you got this bigger move and the drop off in here through the break. And I'll be watching this to see if anything else is going on in this. But I mean, I think that this is pretty much played out here for this period. But really nice move in FDX like the gap and we'll see what the next week brings. Thanks everyone. If you're interested in the options newsletter, email me at Melissa at thestockshwish.com.


So there's an odd kind of paradox in the global health situation where some countries have bid farewell to the COVID-19 pandemic. Some countries are still reeling from the after effects of it. And of course, the World Health Assembly was one opportunity for a large number of countries to bring their concerns on board and also to trash out what is being called as a pandemic treaty. We discussed these issues previously during the Executive Board meeting of the World Health Organization and today we're returning to Jyotsna Singh from the People's Health Movement who was actually in Geneva attending all the events and the conferences and she's going to give us an update on what's happening right now. Jyotsna, welcome. Thank you. So Jyotsna, the biggest issue it seems from our discussions which we've had over the last few weeks is that the funding of the World Health Organization and money matters as you said are actually crucial right now, why is that? Absolutely. So the thing is it is about an overall direction in which the global health governance is moving when it comes to talking about where the funding and the resources for any initiative will come from. So I'll begin with the WHO itself. So this is an organization which is a multilateral organization which means that primarily it is the governments which are part of it who form the organization and other people have more of an observer status though they are allowed to speak on the floor of the assembly. But if a voting is concerned and other aspects are concerned it is the governments who do it. However what's happening earlier say till the 1980s most of the money for running WHO used to come from the governments. So there is a ratio according to your population and your per capita income, your GDP, some money is earmarked that every government is supposed to give this much of money to run the organization. Now this is called core funding and all the countries decide together along with the WHO secretariat where will the money be spent. So it was in 1970s that there was this famous conference took place in Almaty which is now in Kazakhstan then in USSR where it was decided that the main focus in the world is going to be and with the leadership of WHO it is going to be primary healthcare because it is an estimate that if people are able to bring their needs early on to the health system then 80% of the ailments can be taken care of and then you go to the higher forms of tertiary care or secondary care only after that. However so but all of this had to happen but then we started to see that the WHO's funding direction shifted. So it started to shift to donors which became majorly the flamethrower capitalist organizations say the Rockefeller Foundation, the Bill and Melinda Gates Foundation has emerged over the years and today when we talk about as much as 83% of WHO's funding comes from these donors and what is the problem? They come with a very project based mentality. They decide where the WHO will spend the money and it is rather than questioning the structural problems they would spend on vertical programs. So I am spending the money only on HIV program or only on polio. Now whether it actually strengthens the public health system or not that is really not there worry in that sense. You can see those words in the documents but what we see happening on the ground is something very different. In fact this this time when I was in Geneva a friend I was talking to and she said that in South Africa and this is her real life experience so a pen was needed in another room and it was present in one of the rooms in one of the wards in the same health facility but it could not be given because it had come under the head of the HIV AIDS program. A simple pen to write with. Yes so you start to decide things so minutely and so the understanding is not comprehensive care at all and it all happens so we do need I mean it is not to say that we did not need these programs to happen but to divorce them from the strengthening of the health systems becomes a problem and with donors the point is that they are very specific about the outcomes so they are giving money for something very specific and they want very specific outcomes within a very narrow schema of things. So this is what is happening in since 90s so now the problem is that WHO actually has very less autonomy in deciding what it would like to do. Alright and when I say WHO I actually mean the WHO secretariat and the countries together because they decide and that is why the world health assemblies are important but then it is all happening at the back door etc etc so this year what happened there was a sustainable financing report which was put forth for discussion by the WHO secretariat the director general and it took two years for a committee to arrive at it. Now the committee itself correctly said that so much of funding earmarked funding coming which is for a specific purposes not giving flexibility to WHO is a problem correct analysis but when he saw the recommendation this time it said that earmarked funding is one form of funding that WHO will take it is really dangerous it is dangerous more dangerous than before because earlier there was this entire move to recognize the problem but now it is institutionalizing earmarked funding now the countries especially the rich countries who some of them something like US who favor earmarked funding they will take back to their parliament and say now WHO approves of earmarked funding and that's what we are going to give that's what Bill and Melinda Gates Foundation will give because US as a country also gives a lot of earmarked funding so that has become the problem and therefore a lot of organizations especially four organizations did a press conference there in Geneva People's Health Movement Society for International Development Third World Network and Public Services International all of them came together because they recognized this is going to be a disaster for WHO. So Jyotsna are there countries which are actually attempting to change the direction which the WHO seems to be headed in and how have what are the crucial issues on which there are differences between the developed world and the poorer countries what are the core issues here? So there was a story which was with Geneva Health files broke right during the WHO and it showed that it was the US the US government which pressurized WHO to bring in earmarked funding they said we will not let it pass the report pass unless you have it so yes this is where the developed world stands right and in our conversations and I will not name the country because they have asked us not to name them but a known representative from an African nation told us that they were not in favor of earmarked funding they actually tried to push for flexible funding because they say that it is the poorer nations who suffer more because the issues of the poorer nations say Ebola in Africa it should be one of the priorities to work on we don't get to work on it and issues like intellectual property etc which have harmed Ebola treatment reaching African nations all of that has happened so but he was very clear that these problems exist and we are not even though we push for not having earmarked funding and flexible funding so that we have an equal say because WHO otherwise works on one country one vote absolutely but then so what is happening is that those very principles on which WHO was formed in the 1950s are being questioned and it is serious WHO should also take it very seriously so you know when we hear a phrase like the pandemic treaty it sounds like the WHO the member countries are actually moving towards solving a very big problem I mean the world was really under covid and it was a very difficult time is that really the case no doesn't so I mean whether it will happen or not is a different question whether it will okay it is going in the direction of solving a problem or not is a different question altogether so pandemic accord as it is called is being discussed and again coming back to the funding part of it yes again the way we are saying the overall direction is something which is becoming a problem because the financial mechanism so there is a pandemic fund that the G20 countries not at the WHO but the group of 20s they have formed which again consists of most of the developed countries and some developing countries like India and all so which is actually based out of World Bank so this is the fund where countries will put the money and they will see how to go about things in future which is such a problem and it is giving a lot of anxiety to continents like Africa I will come back to it again and some of the Latin American countries because they are not in favor of something of this sort because what they are saying is and I think this is going to become one of the points on which some of the developing countries at least or the developing countries blocks are not going to agree and I hope not easily and I hope they will not agree at all not easily for sure they won't which is that you should have a fund of course we need to create a pool of funds for pandemic and it is not only during the pandemics this fund will be used but also to see how to avoid pandemics and if it happens how to have equitable distribution of vaccines medicines and other response the response as they say exactly there should not be travel bans put arbitrarily and all of that so all of that but then the money will should be able to come from this one they they are saying that we can have it should be the WHO which actually decides how much fund and how to use it and even if World Bank because it has as they say experience in using it so these countries some of the south global south countries are saying but the decisions of how to use the fund has to come from the world health assembly kind of a grouping and it cannot be a few countries deciding about it and they also say that it is not enough to have a few nations decide where there is one representation of one country in that group because the developed countries and overpowered them absolutely so it has to be everyone's say when it comes to decide what will be the fund used for and how will the distribution happen so that is one part right yeah and if I can come there are there is another thing on which I know at least the African countries are going to really put their foot down that they will not accept which is access and benefit sharing now ABS in short right which it is called which basically means that if companies and it's mostly companies private companies they make use of a pathogen that has arisen from a particular country and have made treatments or vaccines using that then everybody should have access to the benefit also so the access not only to the pathogens say the virus or the bacteria but also access to the products that come out of using them because some country has actually shared the genetic sequencing and etc using that but then they don't get access to the cures or the remedies no no we saw it in the case of South Africa South Africa was the first one who said about Omicron and they actually shared the genetic genetic sequencing but what did South Africa get a travel ban though the same virus during covid was present in many countries but western countries did not face the travel ban it was such an unequal travel ban that the countries of the global south faced and instead of saying that okay it is good this is what South Africa has done and then the vaccines that now come which will save people from Omicron should reach South Africa and other countries that did not happen and we have seen this in so many cases we have seen this in Ebola we have seen this when Indonesia shared a particular sequencing and Indonesia is not the one which got it in fact Ebola that is what there was this report by MSF they also launched it during the World Health Assembly it clearly shows that so in 2020 two Ebola treatments were approved by the US FDA and we have had outbreaks of Ebola in African nations over the past two years right yes we all know that African nations do not have access to those treatments all the treatments all the treatments are being hooded by the US because the government has bought it they think that if people in their country fall sick then they should get to access those medicines this is what pandemic preparedness and response that is happening all right so so and people are saying that the accord that we want should go absolutely opposite to this right but the WHO already is supposed to have or has a system to deal with health emergencies and you earlier told me that the pandemic treaty or the pandemic accord and the IHR are proceeding in parallel are they replicating the process are they wasting hard-earned funds what is going on there so yeah so there are two things yes initially when the pandemic accord was being discussed and EU was the one which was pushing for it from the beginning and by the way that started even when the COVID was we were in the middle of COVID into 2021 that's right right and that's when they started to discuss about the future pandemic of course then that's where also the inequality comes because the developing world was reeling under COVID worse even that time but well so this civil society organizations and activists said even that time that when we are talking about amending the international health regulations which got kicked in in 2005 after the SARS right COVID that the SARS virus spread that happened so but then there was a lot of push and now we are in a situation where we have two accords being discussed okay so this is where we are but so the thing is again now the problem is the developed countries have more resources you always see more delegates for them from these countries coming in so they talk about two things together all the time they have but with developing countries it becomes difficult to really negotiate on so many fronts at the same time so that is one but again as I'm saying that is happening so on IHR there is in some countries a little less focus there is more focus on pandemic treaty because that has become the famous that's right the word now because of COVID but yes so both are going on and it similar issues are coming up in both because they are quite similar processes whether the intellectual property barriers will be addressed or not whether access and benefit sharing will happen or not and how will we manage the funds so these issues are coming up in both what we have heard is that the developing countries are saying there is a possibility because next year 77th WHA is the one where the pandemic accord is supposed to be finalized but they're saying that what we will say is that we cannot decide one of them first and then leave the second of them to happen later so if pandemic accord is is being discussed then IHR amendments have to be finalized in the same assembly or the other way around because they are saying if they are able to discuss properly in one and get some I mean pushed for their demands and if they are accepted all right they are not confident in the second one that will happen all right and if it doesn't happen then they will be at the losing end all right so either both right or none all right so and but again the point is that this is what they are aiming for and hopefully it will happen in that fashion so I sort of gleaned two things from what you say that the developing world is actually hoping to get what it needs just because the developed countries the wealthy countries are getting what they want you know that's sort of a sad situation but the other thing I sort of understand from what you say is that it is the poorer countries which are more progressive would that be a correct estimate I think it would be yes because as I said that when you talk to the delegates from tsunami bia both swana or the afro block block as a whole you do here because you do you see what happened with Africa during covid like it was the continent which suffered the most and now you have mRNA hub coming up in South Africa but it is just too little too late the mRNA hub would be for the vaccine for the vaccines yes and there was a lot of push that we should have this facility in Africa and throughout covid it didn't happen and now this is happening so hopefully I mean it is it's that's what I'm saying too little too late because maybe some of the new vaccines South Africa will be able to produce but not for the pandemic when it was needed the most so and Africa just none of the countries could achieve a very good level of vaccination so of course their experience and what they are taking very progressive positions because they know their continent can't go through something similar again then we are also seeing good positions coming from some of the Latin American countries and that is because of the change in political dynamics there we have more progressive comments and now with Lula becoming Brazil's premier again and Brazil's famous slogan now is Brazil is back and science is back and a lot a lot of things so you do hear the the slogan in even in these meetings so at WHA we heard that and Brazil has actually so so Brazilian statements if you see there they do take positions which are more progressive and about excellent benefit sharing IP barriers should be removed they do say that they actually brought a resolution which is health for indigenous people so Brazil now does not have only a health ministry they have a vice minister for health for indigenous people so who would focus on that and they were present very actively advocating for indigenous people's rights in the assembly that they did that and in we had interviewed him for people's dispatch and he very clearly said that we want to use the word indigenous people because it has connotations of colonization and it is not just about any community it is about community which communities which got discriminated against or displaced in massive numbers because of the coming of the colonizers so it is actually we are fighting back the colonization so that was good so brazil is doing these things and of course it is easy to talk to them for the civil society and columbia is another country which takes chili as well so we are seeing some of those countries because of their political this thing so yeah so we are hoping that next year when the pandemic accord actually becomes the thing to talk about we will have these progressive positions come out and they do not compromise because otherwise we won't be able to deal with yet another pandemic hopefully it doesn't happen right and it is not only about a pandemic it is also about how do you ensure it does not happen it also gets related to many other health emergencies because IHR is not only about pandemic right it also responds to something like what happened in turkey and earthquake and the earthquake floods in Pakistan Ebola absolutely so it kicks in for all those things so we do need a strong IHR there is no doubt about it now so it's not the IHR like the pandemic accord would work only if the intellectual property rights are relaxed is would that be a correct estimate that's essential to making everything will work only then so because whether you talk about likelihood of that's happening I think those are very different discussions should not be as I said that we would like to see health as treat us as a comprehensive thing and not one by one so whether we talk about non-communicable diseases we have been talking about infectious diseases but non-communicable diseases also the kind of I mean you see and and then I guess you're right this gets reflected in WHO's documents also so if you do not have medicines say for cancers cancer medicines are just so costly medicines for rare diseases are so costly now if WHO wants to put in those recommendations in its documents which would say that you know everyone should have access to these medicines and all and put forth proper policy guidelines right it is difficult to do if your medicines are so costly absolutely and intellectual property is the barrier the problem is it is not only WHO but the TRIPS agreement which actually decides these things which is the trade related aspects of intellectual property that is actually hosted in the World Trade Organization which works very differently than than the WHO it is a very closed body and it is largely the amount of influence transnational corporations and have WHO also has but much less compared to how WTO works so we would like WHO to sort of take more progressive positions and see to it that it does pressure as WTO to behave better when it comes to health it is about lives at the end of the day right Jyotsna thanks so much for joining us with that and as you heard Jyotsna just tell us it's a big fight for the developing countries to get access to basic health care and in fact to push the WHO towards a more progressive public health oriented system for health care thanks very much for watching us


Čakaj, imaš več, mnogo, za organizacij, da imaš zelo. Vsih, ki imam tudi tukaj, je... nekaj, da je tukaj od vsega matriča teori. Tukaj, da je tukaj vsega matriča teori, je zelo, da je vsega matriča teori, da je tukaj vsega matriča teori, da je tukaj vsega matriča teori, da je vsega matriča teori. I zelo, da sam jih je zelo, da sem daz sentagonalne skrana, na zelo, da sem jih ga predmelyljučna mat. Vsega, da sem jih ga predmelylčna matem, tudi je zač japovljanje sprem, eskud je poča, da se nisem, bolj saj. Aspečno, da sem jih ga predmelylčna matem, da sem jih ga predmelylčna matem. Protočno, da bi je je vneno, zelo s jednog branča in zelo so prikratili, da je najbolj spodobno, kako se vedno počkala. Taj počkala je ne pozdravila, kaj ste prikratili. Zelo počkala se, ko mi je povedila v kanve, na bajneri kvadratičke formu, je to, da je jedna situacija, kaj je tudi template, tudi konvej tapograf. Konvej inventat, tudi tapograf, imam tukaj, prvi, početno početno početno, kaj je bajneri kvadratičke formu, kaj je vse početno vse. Now you can view this as a quantum problem, you can see the Laplace-Biltrami on the flat torus, then corresponding spectrum is quadratic form, and then you ask in what is the spectrum, it means that what are the values of this quadratic form. So it's quite natural from integrable system, quantum integrable system point of view, it corresponds to the question of flat torus, which is clearly integrable in on sense, so this was the question of konvej, so I will start with explaining konvej tapograf and then I will talk about direction I can from and this is Markov equation and and then I will study some function which is describing the growth in the corresponding dynamics which is SL2Z, PSL2Z maybe better to say dynamics. Now why is SL2Z is here, because if you consider usual dynamical system deterministic one, you can view this as action of Z, simply you take a mapping and you iterate it, so it's just autology. Now you can take other group, infinite group and what I'm suggesting is to take as PSL2Z, modular group and there are many many reasons for this, I hope to explain maybe there are many interesting examples and one of them is konvej and the second is which was I think realized later was Markov equation and so I will describe some function and then I will explain how, because I think it's beautiful, the proof is based on links with hyperbolic geometry although at the end of the days and with bit of analysis of feather or grom of stable norm, so I realize that I have chosen criminal amount of material, so I will probably have to rush through sometimes, but I hope to get to explain the message eventually which is I think it's important. So this is the paper which is joined paper mainly with my PhD student Katie Spalding and with Alfonso Sorrentino, it's now published so the main material is there. So what was the idea of konvej? It's quite nice actually, so you can see the binary quadratic form and the point is actually it's not konvej was not the first, it goes back to 19th century and it was the student of Riemann I think it will come the name who used this idea. You should use not a basis but superbasis. Superbasis are three vectors such that e1 and e2 is a basis but you add also e3 which is such that the sum is superbasis and if you have that's one thing this idea was known konvej added one more thing which is conceptually it looks like trivial thing but actually it's very, very conceptually important step he said that one should consider not vectors but lax vectors mainly you have to consider vectors up to sin e1 and then every if you can see the so-called lax vectors then every basis gives rise to two superbasis and these are here for example so for example if you take e1, e2 then you have e1, e2 and e1 plus e2 or minus, minus it does matter remember that lax or you can consider e1 minus e2 so superbasis are living in the vertices of this of this binary graph so this is what is konvejt apograf konvejt apograf is just the all superbasis presented in a very clever way so that vertices so lax vectors are living in the complement to the binary t on the plane it's not just binary t ok so now this kind of tree of course was known before sometimes it's called fairy tree and fairy tree is is the representing all the fraction where at each point you have this is a median it's called if you add fraction naively 2 plus 1 3, 1 plus 1 is 2 I mean that's fairy addition but in fact of course it's nothing else but projectivization of pitch yes it doesn't matter sum is zero that's the rule so the rule is very simple sum is zero so superbasis is a kind of you have two and then one vector is so this is a kind of superbasis it's quite natural in a way ok or you can draw it like this if you want up to SL2Z are superbasis that's correct edges are basis and complement are lax vectors so this are basic so this is what convey topograph now you can use it in many many ways that's my point as soon as I realize that actually we have after that we can ask some question which I'm going to ask so once we have it so now let me look at this in a different way and this is very very important point of view let's look at the edge so you have one one here one to here let's put a matrix here one one one one one two it's a SL2 metric and if you take positive part for example this is a monoid SL2N it's a matrices which is dimension determinant one with positive integers so you can view this positive half of the tree as SL2NN means that non-negative only entries there are no elliptic elements of SL2Z so it's a kind of SL2N rather than this another thing so let's forget about all the labels let's look at this as a planner tool and graph what are the symmetry of this graph the symmetry of this graph is you can rotate by pi over middle of this by 2pi over 3 so the symmetry is Z2 free product with Z3 which is nothing else but PSL2Z so that's why it is actually and this convey did explain this beautifully so he clearly realized that this is a very very important object even if you forget about all this if you consider this as a planner graph of arithmetic because the symmetry of this graph is PSL2Z so basically now let me say a little bit about this so binary quadratic form you have 3k efficient so if you know the values on basis it's not enough to recover this but if you know the values on the super basis then you have 3 numbers and this is exactly the thing so you recover so C is the value on the E1 plus E2 so if you know A, B and C you know H of course and you know the whole thing so the action of SL2Z when you change the basis then it's changing the how the form look like but the values also of this satisfy this arithmetic progression rule which is nothing else but parallelogram rule sometimes it's called right so if you know U plus V then it's a kind of definition of quadratic form if you want you need homogeneity but that's all what you need to know and then it's quadratic form so then you have this conveying which is playing important role but growing it grows forever doesn't matter so maybe I'll skip this detail so this is an example so this is a kind of question goes to Gauss which integer can be represented as a sum of two squares and the usual thing is of course deep results you have to factorize look at the prime numbers 1 mod 4, 1 mod 3 and then you know this by Gauss but for this you have to know factorization and factorization is hard problem I mean if you know factorization then of course so convey saying basically well let's do it easily I mean let's do the following let me visualize them so let's start this and then apply this rule for example 2 plus 1 is 3 times 2 6 minus 1 is 5 is 3 just local rules only you grow the values and then you will have the tree which knows all the values well up to total squares but nevertheless that was the idea of convey and because of convey lem if you want to know up to the million numbers you stop when the number will be larger than million then you know everything about the values so it's totally different approach to the classical but anyway and so this is the value so one thing I'd like to mention this because it's really beautiful yes if quadratic form is indefinite it's not of course related to the spectral problem but nevertheless convey river it's beautiful object namely you have both positive and negative numbers and if you exclude 0 there are no zeros on this picture and river is dividing the convey topography into two parts in one is positive and another negative and he showed that it's periodic also convey is periodic it's related to periodic continued fraction expansion of quadratic rational and this is the thing so now going back to Markov it's daifantine analysis so you have it's a story of the most rational numbers so every number can be approximated by p over q with 1 over q square less than 1 over q square that's continued fraction theory question can we reduce this c one is always possible can we do it better the answer is yes and the possible values of c are known to be Lagrange spectrum sometimes called and reserving for Markov top of the spectrum is less than one thought so let me show you the most irrational number with largest possible c c is a function of alpha and it turned out that the spectrum is discrete top of the spectrum is discrete so golden ratio is a champion so you can always take c is less than 1 you can take it 1 over root 5 but then if you fix it 1 over root 5 it will be golden ratio but if you exclude golden ratio and equivalent equivalent means that the tail not consistent with 1 in continued fraction then it will be silver ratio which is root 2 and then bronze ratio if you never seen this story you would be surprised it's clear that there is something going on that's a bronze ratio that's the third most rational number and then there is something here so this is the thing if you never seen it you should of course think what's going on because here this is diagonal of pentagon this is diagonal of square there is no geometry here there is deep arithmetic which was discovered by Markov and this is a beautiful paper it's actually master thesis and this is a relation between this question and the following differential equation it's called Markov equation it's x squared plus y squared c x y z and then he showed that all a solution, integer solution 1 1 1 is obviously a solution and then you notice that this equation is quadratic in z so therefore if you know two roots if you fix x and y then with respect to z it's quadratic equation so if you know one root z then you know the second one using vieta 3 x y minus z for example if you have 1 1 2 in the end do permutation then 1 times 2 times 3 6 minus 1 5 so what I drawn here is actually I used convey topograph to represent it I think I don't know who was the first to realize that one can use convey topograph I mean it's I learned it from I think Volodya Falk first so it came from Taichmuller theory and from this but they didn't use convey topograph they just said that it's natural way to represent them now there is a unicity conjecture which is still open saying that every mark of number appears only in one mark of triple so for example 2 appear many times it appear in 1 1 2 and 1 2 5 but only once it appear as the largest one in 1 1 2 so you have as many triples as many numbers so this mark of numbers are the most but the conjecture is still open so now what was the discovery of this wonderful mark of is that mark of spectrum means that the values of c bigger than one thought top of the spectrum is discrete and that's exactly the values of mu and m are mark of numbers which are all the numbers which appear in mark of triples so this is the thing and this is if you want to know the explicit form then if you know xyz mark of triple then you can construct this rational number by the way this is 9z2 minus 4 9z2 minus 4 so just to show you again just second this list 9 times 5 squared minus 4 225 minus 4 that's the meaning of this so this is the third mark of number so this is the list of most rational number ranked by mark of constant what is the minimal the most rational number is the larger the largest possible c you have anyway so this is now story growth the growth of mark of numbers was studied by Don Zagir in 1982 and this is I think there is still some question remaining to this asymptotic behavior but this is basically what happens if you put them on the line so from this perspective they are growing on the tree and this is the tree and again to grow the tree you are using local rule so for example 2 times 5 times 3 is 30 minus 129 and then you start growing 3 times product minus 2 will be 433 so this is the thing so it's not natural yes if you order them in this order then this is m1, m2, m3, m4 just order them in increasing order so the fifth number will be 29 and this is how it's natural I should say that what Don Zagir is doing is quite natural because you want to know how they grow in the increasing but from dynamics point of view I mean from convey point of view it's natural to look at them at the tree so basically what Don Zagir and Markov essentially also doing put them all on the line order them and then you will have Markov spectrum now from the dynamical point of view they are growing on the tree so it's natural to see how they grow on the tree that's a good question I don't think so it's terminology this is the definition it's all possible c for given alpha you have c what are the values they used to call Markov spectrum it's not clear the top of the spectrum is discrete I mean the set we should say probably set it's discrete and it's explicit integrable part of the spectrum the bottom is presumably continuous it's feeling from zero to some number which is called Friedman number I think so it's continuous but in between it's counter like set it's very complicated I think it's still a lot of questions but usually people call the whole spectrum is Lagrange spectrum for some reason I don't understand why but Markov is reserved for the integrable part which is top discrete spectrum and it's kind of suggestive that maybe but I don't know it's a bit like Riemann zeros I don't know, speculate but no but it's common to call it Markov spectrum the set it's a set of these things now what is the idea of it was the idea of Don's idea and we will use it too so there is much better actually equation than this if you add four nines then it will be integrable and this surface is actually well known classical surface from 19th century it's called Kelly cubic it's a cubic with maximal number of conic singularity four and this is one of the version of them now what's special about cubic because it's a kind of rational degenerate you can parameterize it explicitly you can parameterize it explicitly by kosh and then you reduce this equation cannot be reduced to the linear form but if you do this change of variable you reduce one of them at least to the Euclid equation A plus B equal to C linearizable explicitly linearization okay so it's only but you have to spoil it by four nines of course you have to forget about arithmetic at that point but if you're interested in growth then it's fine and that was Don Zagir used but actually this observation I don't think he knew this but Mordell in the theory of Diphantine equation noticed this already in 1953 so people that actually it's much better because he used it normalization which is integer anyway so this is the kind of thing and this is what behind it that's all what is related to integrability it's close to integrable equation so to study growth you can use this and therefore you can reduce it to Euclid equation and Euclid equation means that so this is but Euclid equation is very simple if you have A and B here you put A plus B here 3, 5, 8 and so on and because koš reduces basically not for this equation but for modified for Mordell equation as we call it then it's just koš minus 1 explicit linearization so this is linear equation here so this is tricky Markov equation it's very related only asymptotically approximately but if you add four nines then it's and we want to use fairy tree of course fairy or convey topography if you want and then now what's the question what is the growth you should label first of all the path so to work on the tree you have always two way to go left or right and let's label the path by a continued fraction basically c0 is number of left tones if it's 1 then it's if it's 0 put 0 and then c1 it's how many right tones after that right, right, right left, left, left and so on this is the thing I mean you may say that why don't you put 0 and 1 left 0, right 1 then it will be kind of diadic this is another way and this is you will see to switch from one picture to another you need this Minkowski question mark function which I will mention at the end gosh it's fast so right right so as I said SL2Z PSL2Z is acting on the whole tree on the convey tree and the four it's acting on the solution of this and it's acting PSL2Z is Z2 product free product with Z3 Z3 is cyclic rotation Z2 is disinvolution Markov and the orbit of 111 is Markov orbit it's just one as PSL2Z orbit okay so we the whole story of Markov is about one PSL2Z orbit so SL2Z is acting on the tree and if you take one element then it's there is Kanta and Laray and Iwasaki Ohara they studied dynamics of action of SL2Z on this but for a given element, right we want to study the so basically they pick up A and then iterate it A square, a cube and so on usual dynamics so we want to study growth along the path and so this is actually historically for some reason we define we were interested in Markov dynamics so you have to take double logarithm in order to make it finite so now the thing is that you can it's equivalent so these are 3 equivalent definition this is from Markov and this is from Euclid Cn remember A plus B equal to C so you can use usual logarithm because of so this is integrable limit basically integrable modification you are using or you can use growth of spectral radius spectral radius of A so which is exactly so you may say that we looking at the growth of average of topological entropy on the Markov spectrum so it's the same and we using simply this observation as now coming back to this quadratic form so you can view these values of quadratic form along the path and then the answer is that then you will have twice the same function except with two exception exception are the ends of the river convey river which is so quadratic form you have hyperbolas and hyperbolas has asymptotes and asymptotes have they define corresponds to two points on absolute alpha and alpha alpha plus minus so river is flowing is a kind of you can view this as geodesics so yeah that's another thing convey topography you can view what model discrete of discrete hyperbolic plane and I think this was probably I've heard that this was an idea already of Gromov at the point of view so therefore it's interesting that absolute so you can view this disk as a punker model of hyperbolic plane now what is discrete so this is a kind of skeleton and this is a very clever skeleton because the absolute is the same you see because to go to infinity you need to choose path and path is labeled by continuous fraction continuous fraction real numbers you will have exactly the same absolute so it looks like much smaller set but it has the same absolute at infinity so this convey topography is actually very clever and this is a geodec so the river in this picture is just geodesics coming from one hyperbola end of hyperbola to another so this is the thing so if you start here then everywhere else you can go it's twice lambda except this when if you go along the river you have zero growth so this is anyway so I have to skip now so let me maybe go to the main point so the main point is that I would like to advocate that lambda of x is probably very important function with very interesting property that's the main message actually so first of all it's a pgl2z invariant so you may say that it's real modular function but people usually when say they modular you assume some analytic property and you will see that there are no analytic property it exists only in absolute and whether it's related to anything inside it's not clear so lambda of x is almost everywhere zero but host of dimension of its support is one actually it was pointed out by Michael Maghi to us so the Leppunov spectrum of this form it takes all the value from zero to log phi in spite of being zero almost everywhere it takes all the value from zero to log phi and and this log phi corresponds of course to the golden path and golden path so you remember this left, right, left, right path that's the maximum value and this is the most important thing because at some point we were lost so you have a function which is a cell to z invariant it means that it's zero at every rational number but on the other hand there are quadratic rational for example it's not zero I mean how would you ask about analytic property and the answer is the following choose a special set and if you restrict on a special set and the special set is of course the most rational numbers which Markov studied, right so they correspond to it's a cell to z invariant so therefore it's a kind of function if you want on the quotient of absolute by cell to z which is nasty space, right how would you work with them so the idea was carefully orbits and order them carefully then you will see some structure and that what we managed to see we realized that if you can see if you can look at at the most rational number in fair parameterization it's continuous and convex continuous and convex function continuous and convex and then result based on hyperbolic geometry now I think it's a beautiful piece but I think I have to skip but let me just flash something so this is uniformization theorem so what is the main object you take T2 and T2 of course the best metric is flat but if you make a puncture then the metric become incomplete by uniformization theorem there is constant curvature metric here unique which is conformally equivalent to this this is what you get is you will have hyperbolic torus punctured hyperbolic torus and it's important that this is equianharmonic means that this is rhombus and this is 60 degrees so you take flat metric make a puncture is not complete anymore introduce complete hyperbolic metric it's uniquely defined by this after that you can see the simple geodesics non-self-intersection geodesics and mark of numbers are cosh of their length this is beautiful observation due to Garshkov and Kohn so maybe I'll skip this in fifties this is how it proved and it goes back to really skip this this is another thing which we have used it's Harvey Kohn observed we actually introduced themselves we call it quantum mark of quantum Euclid 3 but it's actually when we realized that Kohn introduced it so you basically replace A plus B equal to C by AB equal to C in B are 2 by 2 matrices and if you start with a particular matrices like this then Kohn showed then you will have this Kohn tree a very beautiful actually object now they are related to usual mark of tree this one by taking one thought of trace one thought of trace for example 1 this is the thing and this is a really beautiful object it will play also some role and they actually generate a special subgroup of SL2z which is commutator commutator of SL2z is generated by these two matrices and this is actually explicit uniformization of these torus I was talking about so it's really beautiful piece of geometry happened in 1950s in hyperbolic geometry and then that's contribution of Volodyfok as I said I learned about this stuff he rediscovered probably this convey representation for Markov I don't know who was the first anyway he definitely knew this so he introduced this function psi of p over q and remember that we have labeling of Markov numbers by comparing by rational numbers 1 for example is function m of 0 2 is m of 0 1 half, 5 is 0 1 thought so now we are ordering them not according to the growth but according to the position on the tree and then you have as many Markov numbers as many rational numbers positive rational numbers and then you take m of p over q 3 half and this 3 half and cos minus 1 is coming from this integrable modification of course remember that was cos 3 half so this was fork observation that this function actually is quite nice m of p of q is tricky but if you take cos it's still bad and this is what I never understood this coefficient I knew about this fork's function but I couldn't understand this was a kind of contradiction this 1 over q it was clear that it's crucial but I couldn't understand why I mean it's anyway so if you add this 1 over q which was clever thing to do then the function is extended and continuous convex function so now this is our observation so it turned out that lambda our function lambda evaluated at the most irrational number corresponding to m Markov number m of p of q so this is m of p of q is integer and this is the most rational number this quadratic rational I have written explicit formula for sorry p of q I mean this is what I tried to explain here it's given by this so 1 is m of 0 1 on this ferry 3 and this is addition ferry addition it's just labelling by conveyed apograf if you want because these are conveyed apograf but I'm writing this in the usual way so this is different parameterization of course not like Zagir did and 1 and 2 and 3 in order it's a parameterization by p of q and if you add this 1 over q so this is that was the crucial observation that lambda if you evaluate on this most rational number then you have one half of fork function and that means that it can be extended if you choose carefully these orbits and if you order them properly and if you put them together it will be convex function so this is and moreover corresponding matrix on the ferry 3 because you have to climb is precisely the matrix from the con tree everything suddenly fit together marker results orbits results con observation yes the limit on absolute you have real number and you can go there between on this tree and this is the limit of course of this and we want to know what is the average growth of topological entropy along on this tree and the claim is that if you if you choose special mark of and numbers and then yes sorry and if you choose this special most rational number then lambda on them is nothing else and you need this q this q is crucial the q which fork put the whole thing works and we have found some generalization now I have to let me skip the federal grom of stable norm I'm afraid so basically this is another interpretation if you know this then the fork function is another interpretation it's half of the restriction of stable norm for on the first homology of this hyperbolic torus on the line and if you restrict norm on the line then of course you have convex continuous function so this is explanation it's restriction of the norm of certain norm and this is and as a result we prove something about fork function which was not known to fork namely that it's differentiable at all rational numbers so it's quite peculiar function psi even when we carefully chosen the representative we made it maximally regular it's still not differentiable at any rational number I mean it's quite peculiar and this is everything was prepared by Bangert and McShane and Trivin in 90s so just the last my message my message is that we are looking at special function as complex analytic function but I read actually it was talked by Hadamar in 1930s in the first congress of Soviet mathematician I think in Kharkov 1930s and he spoken about special real function it was a kind of a side remark he said that was surprised that he essentially mentioned exactly these two function which I knew and this is two example I want to point out so this is one Weierstrass introduced it in 1996 but he said that he heard that Riemann actually produced but it's it's debatable whether there is no records of Riemann considering this function but anyway it's usually called Weierstrass function and this is the thing it's signed by pi k squared x divided by pi k squared k squared so it's very so and that function was started he produced it to remember that in 1990s it's before I think he was produced the function which is differential nowhere started with more interesting example from my point of view and he considered this only because somebody said that Riemann actually considered this and then Kharkov did study this and then it's until now so the answer is that it's differentiable at every only rational points and very specific rational points for example at all rational point and irrational point is not differentiable so this is one example another example is due to Minkowski again we rediscovered this function because we need it you can label the path either by binary 01 or by continued fraction and the difference is exactly this Minkowski question mark function and I didn't know this actually this remarkable function I did not know this because he denoted this by question mark I don't know how would you know this but anyway so eventually we found the reference and it was Minkowski geometry I mean the famous book and then he mentioned this question mark function and this is exactly this homeomorphism 01 with 01 which was started by Zohar and Salem and it's very interesting it's continuous both ways it's homeomorphism of 01 in contrast to devil staircase which is not homeomorphism so it's strictly increasing but derivative is zero almost everywhere and basically my idea is that maybe maybe lambda and psi and fork function psi belong to the similar list because they have you see many natural interpretation and it's what we notice is probably a little bit of their remarkable property but they are it's really require presumably like in all these cases you see it require proper analysis from people who doing real analysis so it's a kind of special real valued function which has peculiar property Thanks