Cryptography | The Mathematics of RSA and the Diffie-Hellman Protocol 

In case you missed part 1: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-uNzaMrcuTM0.html

Now I'm smarter than I ever intended to be. Thank You.

After trying to understand this algorithm for about 4 months, this single video has effectively set in motion the change of my life

Wtf i just randomly got the first part recommended, watched it and landed here 20 minutes after the upload xD So thats kinda creepy :D

I learned the Caesar Cipher and RSA Encryption in my Hardware Security class. It's honestly so cool.

The new thing in cryptography now is lattice cryptography. The idea is that you form a multidimensional lattice with vectors that are mostly orthogonal, read in your byte from your plaintext (ex: 'g'), find a lattice coordinate that is also 'g' (you associate L points with bytes), but instead of choosing the cardinal coordinate of that lattice point, you choose a point near it; that point is then written to your ciphertext. It is impossible for an attacker to read the point from the ciphertext and match it to the lattice to discover the byte it is because they do not have the lattice basis (vectors) to reconstruct the lattice. All they have is a random point in space. They cannot even reconstruct the lattice from many sample points because the points were not chosen at the exact lattice coordinate: they were only chosen near them. So the sample of all points is completely random. The math part of this comes in with cryptographers wanting to represent a string of vector coordinates as a polynomial. They are, as I understand it, able to write coordinates (4,7,3,5,etc) as a polynomial, then they appear to write the exponents of the polynomial + coefficient backwards and this is the final thing that is written to the ciphertext. Anyway, if you ever feel like exploring the polynomial aspect of it and doing a video about it, I would love that. It's cutting edge stuff, mainly because lattice encryption is resistant to quantum computing attacks so far.

Second here. U r such an underrated RU-vidr. Another great video again

you do an excellent job explaining things in your videos keep up the good work

Really good videos! I'm watching this to educate myself on what I want to major in and this by far has made computer science a really interesting and fun field.

Thank you so much! You explain it so simple and easy!

Omg, this is great. Keep posting such great videos.

After studying number theory in my math major classes I’m glad to know all its applications and how cool it actually is

The only explanation of correctness I found after 2 days internet search. Thank you very much.

Awesome thank you so much for the super clear explanation!

The proof for Euler's Theorem is so nice. You should do a video on that!

You actually saved my exam, I did not understand DH protocol at all. Thanks a lot!!

Mindboggling 🙄😮😮

You know a video is good when there are more then 9k views but 0 dislikes there is usually that 1 hater who dislikes and leave so good job.

First video I have ever seen with 0 dislikes despite having more than 10 k views

We want more!!!!!

Great videos on cryptography! How about maybe sometime doing a video on Nikola Tesla and his inventions, including some of the technical aspects? So fascinating and revolutionary.

Ur awesome man!!!

This is awesome

You’re awesome

Interesting video. I was just thinking that if the uncracked code was a string of letters, then I could enter that string into a computer programmed with the formula. Have the computer cycle through possible cypher numbers until a string of three letters to a viable word such as or and see if the rest of the cypher follows and translates.

at 7:23, shouldn’t x and n(so m and n in the demonstration) be coprime to apply euler’s formula? Great stuff btw

If you know e, but to find d.. d=1:while(d< some-number){if ((e*d) mod n)= 1){print d}:d++} it will show all the possible of d

You should maybe mention what is considered a "safe prime number" on the Diffie-Hellman.

I take Cryptography I at my university this semester :)

Hey I have a question. I noticed that there can be multiple values of d(private key) (e.g.- d=63 also works for the above example). But isn't the private key supposed to be unique?? How do you explain that??

So, the key is chosen by the Prime number and number on the Diffie-Hellman Protocol or is it random?

Thank you for the Video - im trying to get warm for potential studies next year and even for someone that didnt study much of anything durring the last decade it really gives some understanding in how these encryptions can work - so big credits for that. I actually have a hard time understanding why the mod(N) is not really "reflected" in the term m^ed at 6:39 if some smart people want to explain it to me :-)

Generally euler theorem is the fundamental of cryptography

Can you make a video on sha256?

Today I felt: Prime numbers r prime for many reasons. Salute to all prime numbers serving for humanity and cryptography

Interesting notion. Can one time pad work with end to end encryption to pass the secret key successfully without "Eve" detecting it?

Make video about architecture

How did you get to congruent to 8 in the first calculation?

Doesn't the entire security of RSA rely on the value m then? Since an eavesdropper knows e,n and the value of m^e mod n, couldn't they just brute-force to find the value of m?

why do the values you and your friend select for diffie hellman protocol have to be less than the mod divisor (in this case 23)?

5:00 Not explained how one chooses 7 and 23; is 23 easy to calculate knowing 7 and Fi(N)?

So what you are saying is p and g are the public key, a is my own private key and g^ab (mod p) is our secret key? Or am I missing something?

I realize this is an old video, with the most recent comment being several months old but I have a specific question on some confusion I have. First let me say I viewed part one and this video and I'm with it all except for a small part at the 1:30 -1:50 mark. As you summarize how it all works you say that what you and the friend did was: (g^b)^a (mod p) (g^a)^b (mod p) and that = g^(a*b) (mod p). But that's not what you actually did a little earlier. You did g^a (mod p) and sent THAT result to your friend, who then applied his secret key, b to it. And you did vice versa. Thus yielding your common secret key, or 2. With the notation (g^b)^a (mod p) are you saying 5^4^6 (mod p) ?? 5^4^6 is an enormous number. Shouldn't that notation read read: ((g^b) mod p)^a (mod p) = 2 the shared secret key. I only raise the issue because you talk about g^(ab) and I don't see you doing that exact calculation anywhere earlier. It could be I just don't understand mod notation. Zach or anyone else, help here would be appreciated. Big fan Zach, love your stuff.

when I divided the value of G to the power of A by the Value of P i got a remainder of 0. is that a problem?

That Stanford course is NOT for beginners, unless "beginners" means "advanced math students, who never used their advanced math for Cryptography specifically"!

2:27 ".. and this means they either need the value of a or b. Either one works because once they have it they can figure out what this entire value is." Um, what? Huh? Why? How? Thank you

why can't the eavesdropper solve the equation? e.g. 5^a mod 23 = 8 i.e. 5^a = 23n + 8 where n is an integer i.e. a = log(23n + 8, 5)

Is it Dan Boneh's course?

I have a question, what do e and d mean?

Great video! But please somebody help me out: at 6:32 you raise (m^e) to the power of d. But how? You don't know m^e, you just know (m^e MOD N). Shouldn't (m^e MOD N) be raised to d?

Make a video on blockchain also.

ok so do we use RSA OR DH? or are they used together? i know DH exchanges secret keys so why need RSA? I'm missing something there obviously.

I have just posted my new Zodiac Killer Z340 decryption. It is in a Billowy wave format not in the dreaded cryptographical grid beloved of some mathematical types! Please click on the round abstract humanoid profile icon to see. Thanks.

where is the link to the course ?!

turns out your professor may not care more about your grade than an youtuber.

How do you select e and d? It seems that you've picked them somewhat at random, but what are the rules for picking those numbers computationally?

Can someone explain how he got 5^6(mod23)=8, I saw his first video but I don’t understand the math behind this specific problem I’m lost

why is the 0 with a line in it 5?

WHAT IS YOUR DEGREE OR PROFESSION IN MY OPINION YOUR A ENGINEER

Only 44k made it .... Not-at-all-strange

Difficult

First again?

Mind your ps and qs :D

what's with the annoying background music ?

Your looks more like 5

Please we need more Electrical engineering videos, not CS stuff

Coursera is garbage, Udemy.com is way better.