S2 - Essential Tools of Modern Cryptography

Transcript

Hi. Hi. Uh, let's wait. Can't. Hi everyone. Hi everyone.

Okay. What things are going for you? I just put a message. Uh um

Okay. Uh Ma is coming in 5 minutes just to let you know that Who was the first sision funny?

So we will start in five minutes just to to let you know and uh if you didn't register for theaton as well 5 minutes I can tell you about that um you can register here we have more than 700 100 university represented which is like what the and I still have some application to to take care of like we're at

almost at 100 100 1,500 applicants like almost. That's crazy. Yeah. So cool. So if you are not register feel free to do so. Um by the way as I mentioned we will have everywhere in Ninja. We just open eights today. Uh so which is very big.

Um we will ask does the same thing in Ukraine too. Um you just open Ukraine and I like Dublan Island today and in Turkey we will have like maybe 10 10 ups too. So yeah I'm quite shocked to be honest. Even super team people from Solana are quite shocked. Oh, that's funny as well. But that's cool. That's cool. Like I mean at least we will do something cool for for the AATON and and when people put I'm just here

for prices, I just click on reject. So we will have just cool people there. Touk tok. Um, do you have any question for something whatever? Because we can wait a bit. Feel free to ask anything. I'm here. So yeah. Are you going into a like?

Oh, I saw Pola you are there but we don't have in Eurray. We don't have one in Eurray. Maybe you can go and in Buenosares. Um yeah, we have one in Egypt. Oh, you are from your grave. Okay. Polar too. Maybe you can also Hi guys. Hi. So, let's just wait. Um, I mean, I will just ping the message. Pin pin pin.

All good. >> Sure. Okay. Uh, okay. It's good. We can start in one, two minutes. or wait more as you want minister. >> Sure. Let's start in a minute or two. >> Yeah. To to wait people like I think we will be like around 30 every time. Um it's end of the day.

Uh good evening. Um yes. So uh yeah I was saying we indeed uh I was saying we will be around 30 every time. Um so just people come around 10. So that's why we are used to that. That's uh yeah we we are online not doing sing I already yet as I mention if you have any question

feel free to let us know. like she can be related to the position. Okay. Okay.

Oh, we're at 23. So, as you want. Sure thing. Um, so how do we feel after last Tuesday's lesson? Are we a bit fatigued? Uh, are we ready for more? Are there any questions? I haven't seen many questions from our chat. You can also catch your notification during during the courses because otherwise it's like kind of hard to follow, I guess. So better to get everything and defocus.

>> Yeah. Okay. So people are excited for more. That's what I like to hear. Cool. Uh let's see. I'll share my presentation with you guys. >> Guys, good. There's a lot to me. Sorry. Yeah. >> No, Ju just say hello. >> Hi. Hi.

>> Hello from Brazil. >> Yeah. Hi, Lucas. I missed you. >> Lindo. I remember you. >> Okay. You should be able to see my um my presentation for now.

>> Sure. All good. >> Perfect. Welcome to the second uh lesson this boot camp for Zen privacy. My name is Milita. I'm Zin privacy lead for that three pack and also I'm doing PhD research in zero knowledge proofs. And today um we have a lot to go through. Uh one of them for sure is uh as um as a hash function. Uh we'll go through uh other hash functions. We'll um do some examples. I'll show you how it plays a role in uh both blockchain and zk. Uh we'll look at um uh key exchange um

especially for Diffy Helman. We'll have an exercise with that as well. You see how it's how does it work um uh on a practical in a practical way. Then uh we'll take a look a bit uh to at um some symmetric cryptography methods and then as well as uh asymmetric ones and uh yeah then um then I'll ask questions. I'll see uh what you guys remember. I I I won't be uh strict. I I promise. But yeah, it's important uh to have rehearsal every now and then, especially uh because we're basically doing the

essentials of cryptography and um everything that's behind ZK and privacy uh so that you can continue on your journey as uh ZK uh um developers later. So yeah, these are our uh uh topics and uh we'll see uh why does cryptography matter? Um who knows why cryptography matters. No more shy faces. Just shoot your shot.

I like why I I know why because um so it's it's related to the the privacy of the individual and also uh the privacy of the companies. The privacy of the individual represent their freedom in society and the privacy of a company represent their their own interest related to it. So there are a lot of thing that you can't do without privacy. >> That's that's perfect. Uh we want to have uh our own personal secrets. Then we want to have corporate secrets. We want to have um development in in in

silence while not all of us are being in the same um office but we can be around the world and uh develop our own let's say protocol or or some zero knowledge uh proof um type or something like that. Yeah. So, someone else? Anyone else? >> Is privacy even important? >> Yes.

>> Yeah. I was saying cryptography apart from apart from privacy and things we deal with on blockchain today, cryptography was also an essential part of the development of the internet. the in encryption of connection between devices and it's connected is really really connected with security. It's basically about secure communication everywhere. So crypto is one of the applications of cryptography to take it a step further and make things private. It's just the same endless loop. Security privacy security privacy. That's my own take.

Perfect. Perfect. Okay. And so for us, what do we want to achieve? We want to have um security of our data. We don't want our let's say bank accounts leaked or at some instances even uh addresses and want to um want to remain our our um conversations that are over the internet private. And we want to make sure that we are um an authentic person. Uh if we are interacting with someone that that someone is also authentic. Um some of them are like it's it's popular

now around crypto Twitter. I've seen it and I have almost been a victim to one of the attacks uh because someone uh um didn't uh protect their account on uh on on Telegram. So yeah, it looked like a legitimate uh um authentic person but actually that one uh person is not in control of their account anymore unfortunately. So that is uh really important uh so that you do not um fall for some uh hack uh or installing some malware god forbid or something like that. Then uh yeah blockchain is um is uh um is using

cryptography as one of its pillars and uh we'll see um how everything works in a couple of of slides. We have a lot to cover today. So, please bear with me. It's uh uh we're going to we're going to cover a lot of topics, but um I trust in you guys and um if not um you'll have you'll have the video and you'll have questions anytime. H okay. Um hash functions uh we're using it um every day um believe it or not.

Like if you're using internet, you're using hash function as well somewhere hidden um behind um passwords you're using um or Merkel trees or something you have downloaded from the internet um every time you're using a hash function. And you know the qualities for hash function uh the biggest one actually is that for whatever input you will get fixed size output and um every time uh you get the same input you will have the same output and uh whatever output you have it's not reversible. So you cannot

tell anything from the output you have uh about the input. So you will get usually some letters and numbers um um within that hash but you cannot tell what has been hashed. You cannot even have an educated guess and even small changes will uh produce uh big changes and we'll see it further. Uh yeah. Uh one of them is um uh avalanche effect. That's how it's called. Like even if you have one small change, you will have a huge effect uh on on a digest as they call it uh we can call it uh output.

So you can see that in the first example you have input um uh named the fox. And even though we're using the same cryptographic hash function, we'll have completely different digest for um uh the second one uh which is which even contains fox but it's um um add more words. It's sentence. But for the third one that has only one letter changed there is a dramatic change uh from the second one. You see uh um the digest starts and in the case of the second uh uh example it starts with two zeros and

in the third uh example the digest starts with 8 FD um uh and um everything else but it is completely different. there are um no um similarities that can say that there is one educated guest that can say that it is um that it's um fairly similar sentence that's producing the digest and you can see in um two more following examples that once we change uh even one letter that it changes completely the digest and it's called the avalanche effect because everything changes. Even though you have one small change,

everything completely changes. That's why it's called an avalanche. Uh why do we have collision uh resistance? Um so it's um in some cases in in very rare cases you can have uh one input I mean two different inputs having um the same digest. That's called collision. And modern hash functions are designed to minimize collision and that's why we have collision resistance as one of the key function uh uh key properties of a hash function.

Um so some of the examples of hash algorithms are MD5, SHA 1, SHA 2 156 which is still in use, SHA 3 um uh there is uh Poseidon as well which is used for for ZK and um if someone is more interested in modern hash functions I can uh share um a more um deep dive list into it. Um just send me a message and you will have that included as well.

And um yeah for um as we mentioned the application of hashes uh for password storage I mean um I know that still some websites with login they do preserve passwords in plain text and it's unknown um a reason to why are they doing that they can at least hash it and store it as a hash and then once you're typing your password they can actually compare your hashes instead of plain text password uh uh preservation.

Um yeah, for uh for um for checking the file integrity uh everything that you download from the internet, you should you should check the hash for digital signatures as well. And for blockchain, >> you have a question. >> Oh yeah, tell me. Let me see. Uh, how are these hash functions uh broken? Um, I'll uh um I'll send you uh examples to how weaker hash functions look like. Um to uh an example to uh a stronger ones that are um that are uh in

modern what is much uh that that are now in use. Um usually it's um either the um initial vector that is being used or the length or the uh the fact that um with more computer power you can you can use uh uh more hashes uh to yeah someone sends Spongebob. You can you can go through uh combinations of uh for for a hash if you know the function. But yeah, like if you are interested, I can uh send you uh lists with uh with Poseidon and with SHA 3 and everything we're

using today versus MD5 and others. Just send you a message. Yeah. Let's go to I'll send you um Okay, I'm sending you um message and the chat. Okay, Trachie, just send me a message on Telegram if you mind. Okay. So, here we're going to have an example of how does um hash look like and what is actually an avalanche effect. So,

we're going to type hello. Does everyone see um shot 256 uh page? Okay. Check. Yes. Cool. So, um once we're doing hashes, it's using um ask as key values of uh letters. So, for this example, we have um uh we have a small h but if we change it to capital H, you see how dramatically the output changes.

Or if we have exclamation mark you can try it and play with it and uh that is something you can even change what kind of type of shai you're having and an MD and you will see you have all the the the the hashes here. So so you can play with it and see how it looks like. Ah, okay. Let's go back.

All right. I'll give you the ask key table. I'll give you the ask key table. All right. So I'll be sending you an asky table so that we can do um one exercise.

Let me just see where is Yeah. So here um for AS key values um I I have attached um I hope uh I hope probably

the the good ASI key table but um as per AS key table you will have um cats um as word uh turn to 67 + 65 + 84 which will uh turn into 216. And if we want to use the modules we have um we have uh learned last time uh we we could say it's 16. And um this will be a toy hash by hand uh for you guys. And uh we'll try to make uh we'll try we'll try to uh work with um two um

two words. One is a gentleman. The another one is elegant man. And please use notebook and pencil and calculate the same uh mod 100 um using as key letters. I'll write down about of uh words. So one is not capital letters, normal letters, no counting of space.

Okay. Um, it's not capital A as uh, yeah, I don't know. Okay, let's see. Text one. Okay, now it's much better.

Okay, please uh if you have any questions ask. And let's try creating a hash by hand. Yes. something we need to think of some

background music for exercises. >> Ah, yes. I don't know if I can put music. It's going to be the concentrate people. Yeah. How much time do they have?

Well, um until we hit collision. >> Okay. Okay. Okay. Uh, someone hit collision saying 52 and 52. Subhani. All right. So, what do we have here? Um

people um started having collisions um saying that uh we are having the same um yeah because they're anagrams. Uh we we should have the same uh the same uh um hashes to say so for uh for uh those um two um examples. Yeah, because they are the same charts, they will return the same results.

That's true. Bravo. Okay. Uh yeah. So we can have an exercise to create two different words with the same hash which would um showcase a smaller hash pool. Uh but unfortunately I don't think we would have the time. Uh but yeah let's uh try with um hashing hello versus hello with the uh with a capital letter.

uh that would um uh that would uh showcase drastically different um you can uh you can also use the same asy table that I have handed you and let's see what results we Okay, we started

having some results back uh that the first one is 32 and the other one is zero. Um so yeah that is um a clear showcase of avalanche uh where we do have uh one uh we we do have the same word just one has changed uh letter to a capital one. Cool. Um yeah uh we can take a look at uh Bitcoin uh mining difficulty uh at this website. I'll post it in the chat so that you can also join

and see it. See? Okay. So here uh we have um this is this is blockchain uh as we can um present it visually with a block announce and um well previous hash doesn't exist. So here in in the in the first one in the genesis one uh is is zero and uh the hash of it um is this one. And every time you want to change something uh or uh turn in some data you can see how hash is being changed and

also everyone every else uh block after it is being changed as well or we can change the nons to something else and still we won't be able to get um uh we won't be able to to get uh a proper proper hash let's say like this. Okay. So when we're mining uh blocks um we should have um zeros at the beginning and here like everything is taking part into calculating the hash of that specific block. So the block number the nons the

data that's being carried and the previous hash. So if anything is changed um um if anything has been changed in the previous uh blocks um even if it's one block um this new block needs to be remin um until uh something is changed as you have seen that it starts um going red u meaning that the hash is not proper. So yeah, you can uh play a bit with it and um we can um we can try guessing a word that would uh um hash that would turn this hash to zeros but I don't

think we will be in that kind of luck. You can try it, but I'm trying it. And so, so far or okay, there is a zero. We won't say anything much. Okay, another zero. Yeah, it won't mean much if we don't have um um as uh as many zeros as the consensus is asking for. Cool. You can you will um did I post it here? I think I did. I think I did. Yes, I did. So, you do have it uh here in the chat. Um try it out. It's fun.

Uh yeah. On to symmetric cryptography. Um why are we using symmetric cryptography? Well, it has been um since um since the beginning of uh people trying to um have some secrets and preserve them. uh we had symmetric cryptography. Um why is it called symmetric? Well, the same key is u um used for locking and the same key is also used to unlock um the same uh secret. Uh you can think of it as a key to your door and um then the same key is being used to unlock it as

well. um some of the algorithms um um is um advanced encryption standard um is still the current standard um I can uh share um something more about it in our group chat and um yeah we can u try it um it's this website I'll also share this in our chat Okay, here let's try it out.

Uh, we'll have um plain text to encrypt. Um, we can have a secret key and we can encrypt and we can decrypt text as well. So let's try um dev 3 back and the secret key would be zk math and let's encrypt it. All right. All right.

We didn't have enough of keys. Let's try with something else All right,

I'll check it for you guys. know if you still see it. I'm a bit lost in Zoom. Cool.

Let's see. Let's see where this zoom. Okay. Okay. Yeah. So for um uh uh for symmetric cryptography, what is the problem? Like I'll I'll send you uh more websites that you can use for um for trying out um advanced encryption standards. But um from um uh what you can see is that um using the same key

um is not practical anymore. And um why is it because of um distributing keys and if the key is lost um anyone can um um anyone can uh um open it and also like we will have a big key distribution problem. Um why is that? Because um how are you going to um distribute the key to um someone across the globe? um that is uh being um on on another side, right? Right. And you want to do it securely, it's going to be uh very very difficult. So um so for for it to be um

precisely um more secure, then we'll need to use some uh key exchange algorithms. But for a more uh modern um uh for a more modern uh encryption uh we'll uh try um using um asymmetric encryption and uh soon enough uh we'll uh see um how it looks like. Yes. See if there are any questions.

And then do you see my screen? Okay. Um, for some reason I'm not sharing. Let's see. So yeah, it's uh let's try three pack crypts. And this is your encrypted output. Um, and if we try, yeah, we can use the copy button and say this is an encrypted text.

And we're using the same um secret key and um input vector. Okay. What did we miss? What did we miss? parameters missing. Do we have everything right? I hope so. What kind of we can try also shot 256 as well.

Um that's encryption. This is a bit deprecated. Uh but still we can play with this as well. And um yeah that's um we also have initial vector. Someone asked um why are we using um um initial vector or padding scheme or cipher mode. So um for cipher mode you can think of for example like two blocks. Let's say that your secret is divided in two parts and then you are applying one function um let's say a hash function on one side

a hash function on other side or some addition function or um anything that you want to use um uh for example and then you are going to switch places and um and mix them and match them and um divide them again and uh um change places and apply some functions. You can apply and functions, store functions, um or functions and everything else so that we can make the life of uh hackers um um more interesting since uh they want to reveal our secrets and we want to keep our secrets and that's why we have

encryption standards. Super cool. Um let's see if if if there is uh how blocks are formed and and yeah it's the if for example we upload something in blockchain in crypto with advanced crypto standard but the key is in a server should be private but not symmetric. Correct.

Um for blockchain we're using a symmetric cryptography. Yeah. So let's see. Um as we said it's fast is efficient but we have problem with key distribution. So how to share secret key securely? uh we need to um we need to go usually through trusted sources. Um we need to use couriers that uh we know are going to um um transport our key uh without changing it and um

using some pre-shared secrets. uh modern solutions to it are defy helman um we'll see it in in an example as a key exchange and RSI um this is uh how we can imagine a symmetric cryptography with uh um key pairs uh public and private which the combination um is going to open and um see as shared secret.

Okay. And we have core algorithms RSA and elliptic curve cryptography which we'll see in um the following lessons. Um but not today. Um we need more um we need more uh topics to go through before we can understand it fully. And yeah, the applications are for digital signatures that uh we're having and we're using every day uh for blockchain and um usually you will have you can see it you can see digital signature of every website um that you're using if that one has a certificate.

Yeah. Pros and cons you cannot have everything right. So one is uh that it's definitely slower than a symmetric one and uh the another one that it's um um what it's solving the distribution problem. All right. Uh a bit more about defy helman. It's a very practical key exchange and you'll see how you can um exchange secrets as well. uh it's relying on discrete logarithm problem as many things are in cryptography and it's invented what like um well it's 50 years ago half a century and it's still it's

still a pillar of uh cryptography we don't need a safe channel if we're using the helman and um the security comes from um as we mentioned the discrete logarithm problem. Um how can we explain this crit logarithm is uh the problem of it is like if we are trying to um mix some colors because for me like I'm a visual being and uh when when they have been explaining it to me they use the color wheel. So maybe I can um maybe I can explain it uh the same way. So

yeah, we can have like a three main colors and we can have combinations and um once we start mixing and matching those colors, especially if they're not primary colors, but also the the derivative colors that we see here on the color wheel. um it would be um less and less likely that we can say um what colors took part in it and in which percentage. Um for some of them it's fairly easy to guess but it it would be usually um it would usually be a guesstimate.

Um so it's easy to go from uh primary colors to derivative derived colors but from derivative colors to go back to primary colors that is not um such an easy u problem to solve. um you will see it in uh uh in an example that we're going to um look at um how it looks in um how does it work with key exchange. So yeah, let's uh go through DA Helman key exchange protocol step by step.

We'll have uh public numbers. We'll have Alice and Bob as always in cryptography. Elvis will probably choose A and Bob would uh choose B. Uh well and uh we can compute A and B. We would exchange it and we can compute the shared secret. um the shared secrets would be known only to Alice and Bob but not to those parties who are trying to easedrop and um in in the cryptography that um eavesdropper is called Eve.

So for an example calculation uh this is what we are going to um use. Um so Alice and Bob are going to agree publicly on a prime modulus and u generator. So let's say 17 and and three and um Alice will select um so we'll use like um three modulus uh 17. So Alice will select a private random number 15. We'll calculate 3 to the power of 15 modulus 17 which will result in six. She will send six to Bob. Then Bob will select private random number 13. We'll

calculate 3 to the^ 13 module 17 which will result to 12. Send it he will send 12 to Alice. And then Alice will take Bob's public result 12 and her private key 15. And um she will calculate 12 to the^ of 15 modulus 17 which will result in 10. And the same thing uh just in reverse order but since it's reversible it would um um yield in the same result. Bob would take Alice's public result six and his private key 13 and calculate 6 to the^ 13 mod 17 which will end in 10 and then the shared secret would be um would be

10. Okay. Um so yeah let's um uh um uh let's um try uh computing uh some shared secret by hand. Just check. Yeah, let's um let's try working in pairs. So, Slingy told me there are 23 of us.

Right. Okay. I will leave this example calculation. Check. the chat. Seline, can we make um um pairs here or do you guys want to choose your own

pairs? Um yeah we are 28 so we can >> Okay. So except for me and you there 26. >> Yeah 26. Yeah. >> Okay. So um Eugenia. So the example calculation is being shared. I don't know um does everyone see it? Uh but this is how you guys are going to interact. You can use different numbers. But this is like a detailed calculation that you can use.

>> Do you want me to create uh breaking rooms too? >> Oh yeah, if you can that would be helpful. >> Okay, I can do that. Um, okay. So, you can go to a room. Oh, no. Assign manually. Maybe I will assign um manually room. Okay. Let me assign people then. Okay.

The same for three, four, uh, room five. Six, um, room seven. normally will be good.

I'm finishing assigning room. >> Okay. >> And there is still one more. Uh ah someone is left. So if you want to jump with me with someone. >> Oh, sure. You can again wait a sign. Yes. open all rooms. >> Mhm. >> Okay. Normally, you have been invited. >> Okay. If I if I um jump into a room, I won't be able to do screen sharing.

>> Ah, yeah. Okay. Okay. Okay. Um All right. >> That's why it says joining breakout room. Well, stop your screen share >> so I can I can see who uh join a room or who not actually. Uh yes, your your pair joins the room. So maybe move to Yeah, I will just check who is not coming. Okay, let me check.

Um Okay, I will move is good. Okay, tag. People are together. Um. Ah, just Maria. Okay. Move to I move you. Okay.

or the rise looks okay for others. Oh maybe. Okay. We still here.

Okay. Uh, could you join a room? Sorry those are join it like people that you can see as participant didn't join yet room just let know >> sorry what were you saying >> uh I was saying people who are um uh marked as participants like the seven people uh is people who are not yet into a room.

>> Oh, okay. Okay. So, I guess we need to wait for um people to come back from their rooms, right? Yep. there's equation.

Okay. So, you're supposed to calculate um your own shared secret using um slide that I have shared with you guys. Um, using your own parameters with your partner in a breakout room. >> Um, hi. How much time do we have for that?

>> Let's say five minutes. I think it would be okay. >> Okay. Thanks. And if you need to be assigned to a room, don't hesitate. Like I mean for example, room 11. Uh it's like Shu Bansi and Sinu. So you can you can go together. >> Yeah. Actually we both were there and we came back because we didn't know what to do. >> So we came to ask and yeah I we'll go back. Yeah. Thank you. >> No worries. Here for questions.

Jennifer Karam. Um, do you need a room or you are here just waiting? Yes, Karm. You can use uh this account

to connect with someone. Um Ramirez or Abin Boyer. Who else is here? Cilantro. Yes. Yes. Yes. Working on task together.

Oh, they scaram with alone into a room. So, let me just switch Jennifer with scaram. >> Mhm. Jennifer, room five. S think >> see the weather good maybe for others.

We can give like two three minutes left. >> Yes. Yes. >> Okay. So like Oh, maybe. Yes, that's in 2 minutes. I I send a notification to come back in

60 minutes 60 seconds. >> Okay. Welcome back.

Yay. Is everyone back in the room with us now? >> Yes. >> Okay, perfect. Uh, did you uh were you able to calculate the shared secret? How many of you guys have succeeded in it? Okay. Some people say that both of them

had the same result, which is um the the goal uh for having a shared secret um that no one can eaves drop on. Cool. Um yeah. Um we can continue that in our group chats as well um to to find people to calculate shared secret width. I hope you guys had fun.

Uh yeah so we have computed um the shared key. Uh yeah. Now um uh now for a bit of uh the discussion uh we have this uh small kitten here. Uh why cannot eaves drop or compute secret? Uh what happens if the p is too small? Um yeah so this is for a for a quick summary for you guys.

Uh what did we go through for uh every part uh of uh of this u of today's lesson? Uh were we using hashes? um uh for uh the integrity and security of protocols. um uh water symmetric and asymmetric cryptography and we had um one um example an exercise with Dy Helman uh for a secure key exchange and um yeah so what do you guys think um uh is why why did no one was no one able to eavesdrop uh on your shared secret

anyone or is it just too much for today? I mean I understand. >> Yeah. So why was um uh on once you calculated the shared secret, why was no one else um able to calculate it even if they were eavesdropping on your uh exchange data? What do you think? >> Because they don't have the secret key and I'm sharing the the key. So in that sense

uh is losing information. >> Yeah. Yeah. Yeah. We can we can say we can say it uh that way. But uh the thing is um that it is very difficult to reconstruct from um uh from the information you have exchanged and um the parameters you had. It is very difficult to reconstruct what the original secret was on both sides. And since uh both of you have exchanged the derivatives of um your own secrets and um then used it to um uh to calculate uh a common secret, a shared secret um then

uh it's um it's practically impossible to calculate that back if you don't know even if you know all the parameters and you're eavesdropping on exchange info. If the person is protecting uh um the number they have randomly um uh picked uh for for for this um shared secret challenge um then um it is practically impossible uh to uh to recreate the shared secret out of it.

I have a question that's related to the logarithmic problem, correct? Because you have a raise to the power of something and you have to do the inverse operations. So to find that inverse operation is very costly. >> Yes, exactly. That's that's right, Sebastian. You got it right. It's due to discrete logarithm problem. That is that is the key. That is the key and that's what I wanted to hear. Yeah, guys. Um I don't know if you have any questions you can

um you can ask. Uh but yeah, I know it's a bit too much, but >> this lesson is always too much, Seline. I know it's >> all right. Um, so yeah, don't hesitate if you have any question for me, of course. And even like on on Telegram, don't be shy to be honest, like very open-minded. All good.

>> Yeah, Seline and I know each other very well. We know we're both open-minded. So, shoot your shot. Here we are, >> sir. All right. So I will put the recording on YouTube as usual. Um also normally you already receive the recording of the last session uh today on Google classroom but also on the newsletters. Uh so we'll do the same for um this one too. So yeah >> sure thing I will share my slides as well for Google classroom.

>> Perfecto. Okay. So see you uh on Tuesday motivated as usual and take care enjoy your weekend too. >> See you guys and thank you for attending. >> Byebye. >> Just >> I had a question actually. Is it okay if I ask? >> Yes, we can. Yeah. >> Yeah. Uh actually so me and um the I I think I was with um my me and my partner we had the same like we had different random number but we generated the same public secret key um and since the public secret key was was same therefore the secret code was

also um same. So is that is that normal or because in the example I remember we had like different public uh number generated >> you you're thinking about the first step uh once you're generating uh um right when you when you're putting up uh when you when you're sharing your derivative secret to each other then you got the same numbers right? >> Yes. >> Yeah. Yeah. It happens. um uh it happens because we're using for examples we're using normally smaller numbers so it's a smaller batch and things like that um it can happen right

uh but yeah like um even though you have um the same number um it doesn't mean that it's the the original number is is the same as well. So it can because we're using modulus and since we're within um certain field um the chances are that we'll have the same number. So that's that's not an issue. I mean it would um it would uh for for um for defy helman as a protocol uh it would uh we would use some much bigger primes and uh and um there would be u stricter rules to it but for this one it's just an

example that um you can use and play around it just to see how you can have uh the shared secret in the end. Okay, thank you. Thank you for the class. All right, some are speaking Spanish, but anyway. So, yeah, see you on Tuesday then. To just >> see you and thank you everyone. Bye bye.

>> Bye bye.