The Mathematics of Cryptography

[@zachstar]

Hope you guys enjoy! And here's part 2: kzbin.info/www/bejne/rp7aqXd-jZuri8U

[@PKPS01238]

MajorPrep Hey MajorPrep, thanks for creating these videos, I’m a freshman CS major and am interested in cryptography, so these videos really help!

[@dancepants3399]

i read a really good book called the code book all about cryptography. it also covers ciphers like rsa... you should read it

[@Boss-3guru]

Sir .. group theory in cryptography ma bi ya example LA saktay

[@chinmayrath8494]

We did, thanks a lot

[@johnsantavicca5016]

Do you get paid in cash to secretly do peoples homework? That is a tricky subject because I wouldn't learn. It's actually more like you get paid to tutor. Extra credit

[@dragonrykr]

Khoor friends

[@skylark.kraken]

iulhqgv*

[@kevin780313]

khoor zruog!

[@xofyu]

d564145aa1bae0255dc21dacfe33b258370b3c7cec44956af2d1366f5025a5ad

[@evm6177]

Scifi talks about transferring thoughts through something like brain waves. Crypto to me is a step in the direction of future communication as it evolves. 🍷👄💬

[@xxdxx3776]

@@xofyu "friend" in SHA256

[@channelofoxford2131]

This is one of the coolest math KZbin videos that I'v seen.

[@jordancarpenter676]

Simon Singh wrote a famous book detailing all of this in 1999 called “The Code Book”. With an impressive challenge of 10 ciphers to beat at the end that had a monetary prize. It was fascinating.

[@jasonbates9906]

Read The Code Book as a kid. Loved it.

[@jordancarpenter676]

@God Slayer I don’t know what this means. Sanskrit name so what?

[@jordancarpenter676]

@God Slayer that’s not even punny. You’ve spoke a lot without saying anything.

[@MrTokyo-wc6xr]

I was half way through then I released I hadn't yet subscribed, my bad dude. Love your channel

[@Engel-ol5rm]

Your channel was one of the factors in me wanting to study mathematics

[@pravatyadav3623]

Ur content are always original and exciting....makes me want to rewatch it time and again

[@zachstar]

Thank you!

[@haseebtubing]

Dude, you smart. More power to you.

[@theulmitter5725]

That's what I think in most of these videos, I keep watching even if I don't understand anything

[@mk_4567]

@Benjamin 😭😭 please don't say that, I can't understand. Can you help me?

[@mk_4567]

@Benjamin after the mod part it is complicated for me

[@sahilkthakur]

Because of you I'm learning mathematics with curiosity and meaning.👍👍👍

[@majaano]

Perfect in terms of detail, depth and presentation, thank you. On a level that I can just about grasp most of it, but not all of it without stopping and perhaps writting stuff down. I wish more topics were covered on KZbin on such a level.

[@behnamasid]

You explaining things could not get any simpler. I'm really happy to be a subscriber to your channel

[@loserkingclinton9244]

100 youtube tutorials later I finally understood modulo arithmetic!Dude you a genius.

[@computeon727]

You ever think about changing the name of your channel? You are doing lots of new amazing videos that are more geared towards the applications of mathematics to STEM fields, as opposed to talking about college majors as you did more frequently in the past. I like this transition of content in your channel as it attracts a wider audience instead of just college students. You could grow huge if your channel focused on these types of videos. Your college major videos were great and informative in the past, don't get me wrong, but now you've established a theme of mathematical applications that make your channel really unique and interesting!

[@zachstar]

I have been thinking about this! I haven't really thought about changing the name because there are still majors I want to talk about but I have really enjoyed showing these applications of math to STEM fields and they seem to be received pretty well. I think I'm still just playing around with what people enjoy and what I like making so we will see what happens moving forward. Definitely a positive that these apply to a wider audience though which is something I have to think about. Thanks for the comment though and hope you continue to watch!

[@jackmaison4209]

Look how times have changed.

[@iampaapa]

Now, I really want to know what his old name was 😂😂😂

[@bigbrothersinnerparty297]

Paapa Kwesi Quansah it is in his channel description

[@bigbrothersinnerparty297]

Paapa Kwesi Quansah it’s MajorPrep

[@ilyaaslunat8382]

This is a really good video. I’m doing coding and cryptography as a module in my final year maths, and your covering the main points 😁😁😁

[@enjoyablehistory5958]

Is enjoyable to study cryptography

[@oyaoya2468]

I'm currently studying abstract algrebra (group theory,ring theory,...) anh yeah, it along with number theory are really useful stuff for cryptography

[@Bill_W_Cipher]

1:29 What if the other person thinks you are trying to say, "You can't rust me" instead of "You can trust me"?

[@sharathkumar8422]

I'm about to go to sleep and this is the perfect way to start a good night's sleep. Very good presentation. Keep it up.

[@NovaAnimations]

Honestly I really don't like doing math but this was so much fun to learn

[@arunmalik790]

BEST VIDEO THAT EXPLAINED THIS MATH PROPERLY

[@perx5171]

Best video I have come across so far. Thank you for sharing!

[@Nocbsocbsox]

Today I learned that literally every number you can possibly think of had at least one thing in common. Relatively prime.

[@91722854]

I would like to recommend "The code book" written by Simon Singh

[@glokta1]

+1. Amazing book

[@chinmayrath8494]

thank you, i finally understand what congruence is about now ! The video until the end, absolutely great !!

[@simonmultiverse6349]

The problem of passing notes in class is NOT ONLY that of secrecy. If someone knows that you have passed a note, even if they don't know what's in the note, you are STILL in trouble. Therefore, you have to (1) conceal the _contents_ of the note; (2) conceal the very _existence_ of the note.

[@turtlemun]

The beginning, one after the caesar cipher, is actually called the Vigenerre cipher! It's much easier to decode with an alphabet grid- you use one side as the ciphertext letters, and the other for the Key phrase. Match each letter in the ciphertext to its key counterpart and bam. Same deal for encryption.

[@0ijm3409fiwrekj]

Cryptography was my second favourite module in my Maths degree.... only behind Number Theory ;)

[@johnadriandodge]

Shalom Your clones caught me off guard. Your explanations are splendid. Thank you for sharing.

[@mancillagarfiasabraham8392]

Hackers: WRITE THAT DOWN!! WRITE THAT DOWN!!

[@gnt10]

They know that stuff alredy😅 That is if they actually are hackers😑

[@worldedit8784]

Thanks for this video. I wanted to learn more about this before desided to do it in university.

[@purnendushukla8463]

It seems like you are highly interested in cryptography as i can see an elelment of it in every of you video. Btw well laid and explained 😌

[@leosacademy]

Wow!!! very good video. I have learned many things. Thank you Zach Star

[@JarppaGuru]

2:12 no need calculate just make 2 rings bigger and smaller with A-Z then turn smaller ring what key is to A first would be C under A now you look whats under Y yes there is B. no need calculate. same thing with long strip paper A-Z and A-ZA-Z "smaller is 2x longer" so its easy. was that so hard move key letter under A then look whats under letter you try encode that cipher letter. same it works backward move current key under A then look cipher letter then look whats is it decoded

[@vlhz69420]

Imitation Game is the best movie on this topic till now

[@elsie1379]

This will help me with my cryptology paper for my number theory class! Thanks!

[@johnadriandodge]

If you have not seen these movies, you might want to look into them! A Beautiful Mind, Good Will Hunting, The Imitation Game, Stand and Deliver and The Theory of Everything

[@dannys2817]

Clear explanation, thank you

[@moustafaabousalem1411]

Definitely earned a sub. You really helped me.

[@vadimneonov6172]

I don't think at 9:47 'x' is any integer, because it doesn't work for 'x' that is divisible by 5. Please correct if i am mistaken.

[@ericj4094]

More common (civilians) AES-128 symmetric key encryption with RSA-2048 as key exchange mechanism (military) AES-192 or AES-256 symmetric key encryption with RSA-4096 as key exchange mechanism

[@vinnaroonie]

Great vid! Can you make a video on combinatorics? Taking it rn in undergrad and it’s chipping way at my life🙃😂

[@raulmogos1282]

I really enjoy your videos! Please make a video on computational science and engineering (master specialisation). :)

[@alperenorsdemir4164]

I didn't know this guy is actually teaching technical stuff.

[@aiden359]

Information from your channel is so valuable

[@AjayKumar-fd9mv]

It's super easy to understand when you explain to us, Thanks , but how someone had to think about it and invent it for first time?

[@HandsomEnchilada]

never knew this existed .But im glad i found it .

[@nitamishra9645]

But at 7:11 shouldnt you also divide the mod4 by 2 which would equal to 5 = 3(mod 2) which would be correct

[@souling8773]

I don't understand euler's theorem at 11:45 . Can someone please explain or give me the name of the theorem?

[@Gekreuzigt]

That's Euler's totient theorem

[@sidstam]

Very impressive presentation and explanations.

[@SAM-ft9jd]

Your videos are truly stunning. The production is top tier considering the content you're putting out there. If anything you truly deserve more subs. Hopefully I can gain you a few by sharing your content on reddit? Eitherway just want to say keep this up, hope you don't ever doubt yourself or your content.

[@zachstar]

Thanks so much! And yes please share the videos wherever you can, really appreciate it.

[@SAM-ft9jd]

@@zachstar Btw think it's possible you could do a few videos on information technology and mechatronics?

[@zachstar]

Mechatronics is definitely one I still need to get which I've been really slow to do. But I promise I will!

[@tuesdaymartesvr1942]

You needed to get nord von to sponsor this omg

[@cubicardi8011]

8:42 fermat reference right here

[@78anurag]

Shoutout to those Chads writing programs and doing lots of math just so that I can text 'Haha big chungus so funny'

[@zajec11]

Understanding 7:25 is the most important part, and without understanding that, you won't fully understand the rest

[@giladlad]

Great video, but I think you made a small mistake. at 9:40 you are reffering to Fermat's little theorem , but in order to use the equation you used you need an integer x which is not divisable by p, and not just any integer you would like. for example if you use: x=4 & p=2 4^(2-1) != 1 mod(2) .

[@zachstar]

Thanks! And yes definitely right, forgot to mention that part.

[@99bits46]

giladlad Khoor nerd

[@awkweird_panda]

At 10:46 You should have said "how many positive integers....". You got me guessing infinity😂😂

[@zachstar]

haha my bad! I did so many takes where I said 'numbers' instead of 'integers' and I was so focused on not messing that up.

[@awkweird_panda]

@@zachstar Haha. I really appreciate the Hardwork you put in.

[@kittymeow3298]

An eighth grader learning cryptography.... Juuuuuust great

[@purityvsprofanity2962]

Still doing my IGCSEs and this isn't part of the syllabus, but why not learn it anyway??!! thanks for the video

[@jaspaw.5473]

Hey, could you please do a video on Computational mathematics? Am taking it I would really appreciate if I could get your point of view about the program. Thank you in advance!

[@sidneylc281]

Are there some books you can recommend about the math in cryptography? I know the basic stuff like theory and application by using libraries but I want to understand it deeply. Do you have a series or books ordered by difficulty? I know a book can't explain all about cryptography but you that explains must know a path I can take to master the math in cryptography. And also, awesome video, nir easy nir hard.

[@zachstar]

'The code book' is a really good one to get started with cryptography. Then I personally haven't gone through a specific cryptography textbook before but this reddit post should help. From a mathematics side number theory is definitely a good place to start though. www.reddit.com/r/crypto/comments/287y7j/best_intro_book_to_cryptography/

[@abdullahalmalki2464]

hey, at 7:55, aren't 72 and 15 both divisible by 3 so they aren't relatively prime and this still works, or did i get it wrong?

[@Plundarr]

The divisor and the modulus, or the 2 and the 15, must be relatively prime.

[@aanya7607]

I LIKE YOUR VIDEOS THEY ARE AMAZING LOVE FROM INDIA

[@anuragpandey8996]

what if 10 ≡ 6 mod 4 devided by 2 equals 5 ≡ 3 mod 2?? check video at 6:18

[@samuelfey4924]

I love computer security I wish I was a super hacker but I ended working as a game developer I hope some day I get into computer security

[@brandonfox9618]

10 congruent to 6 mod 4 isn't really the best way to put it because it contradicts part of the "Division Algorithm". Specifically, the part where it states that integer remainder "r" is greater than or equal 0 and less than integer "n" (0 < or = 6 not < 4). THIS IS JUST WHAT I HAD LEARNED FROM CONGRUENCE MODULO "n"!

[@catherine_404]

If we decided to pass notes in the class so that no one could decipher them if caught, the best method is us speaking some exotic language. Chinese or Japanese would be sufficient. There are many small living languages which do not have translator in Google.

[@MatiGebreyehans]

What if we use algebric equation like y=4x+4 0r y=4y+4 is it too easy for computers to crack

[@uchicha666]

11:23 the formula makes no sense at all... fi(p) = p-1, so fi(15) should be 14 right? And just above it there is equation where fi(15) = 8...

[@zachstar]

15 isn’t prime

[@johnohm8067]

you have to intialize a handshake and an ever changing multi algorithm encryption

[@ravirajsinhzala9535]

That was amazing🤗🤗

[@AkashDeep-bu9fu]

Can we say relatively prime numbers as coprime numbers?

[@richkillertsm6664]

Two big mistakes: 1. Vigenère and not vigener 2. You don't need many messages to decipher Vigenère when the key is short, you can decode fairly short messages with other analysis methods. The only problem comes when the key is in the same length as the message (or close to it) and the key is random, which basically turns the cipher into One-Time-Pad.

[@zachstar]

Thanks for the corrections. And I’m assuming you mean the cipher becomes more secure when it essentially turns into the one time pad? (Assuming one time use).

[@richkillertsm6664]

Yeah, it's perfectly secure when we're using a random key in the same length as the message ONCE (hence the name One-Time-Pad). When used that way it is mathematically impossible to know the plaintext without the key.

[@zachstar]

Okay yeah that makes sense. I was actually going to include a one time pad example using xor operations but didn’t have time.

[@richkillertsm6664]

You can define OTP (One-Time-Pad) under with any modulo as long as the key is random. XOR is addition under modulo 2. When working with letters in Vigenère we work under modulo 26, and can be turned into OTP as described. Besides that there's no difference, and they both result in perfect security.

[@JarppaGuru]

4:25 yes yes yes but your encoded E is splitted many other letters and also other letter change same ammount to others you cant see whats E. its only work if your cipher is subtition means ABCDEFGHIJLKMNOPQRSTUVWXYZ MRHOPKVNEWBGTAZSQDLUCIJFYX then we could analyze that P could be E if it apper most but its not allways but if you shift that lower part every letter VOLA that P not occur anymore most lol

[@YoshikaKehelpannala]

10:51, the primes under 10 should be 2,3,5,7. Nine is not a prime and 1 cannot be counted in.

[@petern.j.4121]

How Is 1 not prime?

[@lucioleepileptique9195]

What is the message length of the universe ?

[@clayz1]

Frank HEUSER 42

[@elibenaron]

Message: You can trust me Me reading it: You cant rust me

[@kd8691]

In the example at 7 minutes 10=6 (mod 4) >> 5=3(mod 4) why would you not perform the same operation on the mod? If you did would it not be correct? 5=3(mod 2)

[@henribebo]

Dude i love u

[@SBVCP]

I laughed because the first time i tried to make a cesa cipher i ended up doing a variation of vigenere lol (it has a few complicatiosn but not that many)

[@diegovergaracampos2325]

Hi Im doing an essay of the topic, does anyone knows any bibliography of it ?

[@starshinesun738]

If use x=6 and p=3, that formula doesn't hold. Right?

[@SubduedRadical]

a =- b (mod c) means "a has a remainder of b when divided by c", then? Seems that'd be an easier way to say it...

[@hklausen]

I like your channel :-)

[@hannahtang5018]

LOVE your videos!!! Numberphile is too hard for a nub like me

[@RickyPisano]

What about a cipher and key with letters, numbers and symbols as follows: TR#DUTR#DU6J23DAXX3 using key = 1#L-H1#L-HBEQ9-WNN9 This is only a portion of it. Thanks.

[@W1LDGAMING.]

Can we have some more videos on cryptography

[@alleygh0st]

can't I just find a common factor and see if the results can be divided by the modular?

[@jonelong4020]

I have one idk what it is called IETRNCUOTOMOHSEM So, count all the letters which is 16. Square root of 16 is 4. Write the letters in a square form I E T R N C U O T O MO H S E M Read it downwards 'In the costume room'

[@xavierlondres6519]

hi mate its called ceazar's box. Correct me if im wrong mate.

[@HandsomEnchilada]

so written in asian scrolls style?

[@SunSunSunn]

@@HandsomEnchilada Why did you refer to scrolls from Asia? All scrolls work that way??

[@HandsomEnchilada]

@@SunSunSunn sorry don't even understand what i typed .I guess I was watching KZbin during my KZbin rabbit hole journey and forgot . I possibly was referring to "Asian scrolls "because from what I've seen in movies, scrolls often appear to be written verticaly

[@RifqiPriyo]

It looks like columnar transposition cipher.

[@bolivianoman1831]

Me who just finished my first chapter of cryptography and I see this video: YAMETE KUDASAI

[@brendawilliams8062]

Nice I guess it is a math that some people really like.

[@neelamsuryawanshi1137]

How do you explain someone that cryptography is use of mathematics majorprep?

[@TooManyEditsProductions]

Broke: You can trust me Woke: You cant rust me

[@SevenDeMagnus]

So cool.

[@guillermoflores5511]

Farm fresh to you.

[@mohammedaasri2774]

Thanks

[@danielpetrov3023]

I have a question. I tried it and saw that this works, but why when we subtract 1 from 3^8 the number isn't divisible by 15?

[@zachstar]

Good question and I only mentioned this briefly but at 11:54 I say that x and n have to be relatively prime which 3 and 15 are not. Try it with 4, 7, 11, 13, 14, etc instead of 3 and it'll work.

[@bardhokajvazi2726]

Is not 10=2 mod(4) ? Or i am missing something ?

[@pawanghimirey2195]

is x^(p-1)=1(mod p), true for any number? or are there any exception?

[@dallasfaircloth8040]

Yes any number x, and prime p

[@sab2597]

Ø(7)=6x1 then how come its relative prime numbers include 1

[@ahamadxaveel1383]

Awesome

[@eve.m1026]

Okay i got lost when he started mentioning mod x 🤣

[@houssaineidrissi7106]

fun fact : arabs were the most people gone really deep into cryptography and create most of these cryptos