The Mathematics of Cryptography 

Hope you guys enjoy! And here's part 2: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-xmwxDHX6xUc.html

Khoor friends

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.

This is one of the coolest math RU-vid videos that I'v seen.

Dude, you smart. More power to you.

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

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 RU-vid on such a level.

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

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

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!

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

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

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

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 😁😁😁

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.

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

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

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

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

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.

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

Information from your channel is so valuable

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

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

BEST VIDEO THAT EXPLAINED THIS MATH PROPERLY

Clear explanation, thank you

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

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

Definitely earned a sub. You really helped me.

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.

Very impressive presentation and explanations.

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

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

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

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

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 😌

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?

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

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!

That was amazing🤗🤗

8:42 fermat reference right here

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

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

Imitation Game is the best movie on this topic till now

I like your channel :-)

Thanks

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

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.

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.

I LIKE YOUR VIDEOS THEY ARE AMAZING LOVE FROM INDIA

Can we have some more videos on cryptography

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

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

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)

So cool.

Awesome

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...

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

An eighth grader learning cryptography.... Juuuuuust great

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

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.

Can we say relatively prime numbers as coprime numbers?

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

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

Dude i love u

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

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"!

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)

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?

You needed to get nord von to sponsor this omg

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

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

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

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

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

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

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) .

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'

What is the message length of the universe ?

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.

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?

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

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

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

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.

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

Farm fresh to you.

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.

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

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

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

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

That eulers thing is cool and confusing

cool

DOUBT PLEASE CLARIFY But 28 is congruent to 4 modulo 6 holds true when divided by 4. This should have been false since greatest common divisor of 4 and 6 is 2 not 1.. Please clarify!

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

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...

Okay i got lost when he started mentioning mod x 🤣

3rd ??

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