He's the best

"...nothing on 2...nothing on 3...click on 4."

xD

🤣🤣🤣

Glad to see an LPL fan here

+Shawn Smith i tried to stole your account and it didn't work :/

+Shawn Smith Excellent choice! That will confound all those dictionary attacks of all words known to mankind.

+Shawn Smith hahahahaaaaaaaaaaaaaaa :)

+Shawn Smith That's the stupidest combination I ever heard in my life! That's the kind of thing an idiot would have on his luggage!

some babies were dropped and some were clearly thrown at walls.

Why does all of that work? And how is it linked to p|X^p-X?

@@qwertz12345654321 At night, tony will still toss and turn 'tween his sheets, wondering why the algorithm is solid.

What is the "small" number?

@@sarveshp1727 a number that fits the requirement stated. (no shared factors with X) 2, 4, and 8 are the smallest numbers that *do not* fit the criteria for X = 4

Red Salmon and make it a ringtone

I want you to repeat it

i approve your profile pic

As in the words of Red Salmon, I want you to repeat it

Don't worry Google upgraded to 2048bit (just like NatWest) shortly after this videos release.

that was reason why Hillary emails were haked.

@@muhumedmohamud2356 No, that was due to a spear-fishing attack.

but could they have done the other way because of the lower Bits

quantum cryptography

Tell me about it it's so weird!!!

That's because these are made for entertainment, so generally are about relatively entertaining mathematical principles. Where are lectures in class are about vital mathematical principles which are often not entertaining at all... and that you have to learn completely, not just vaguely understand from a video. There, problem solved.

Its easier as you think. :)

That's probably for the same reason that I like to see work of art, rather than learning about them in class.

Well, I was an EXCELLENT Math student, at least in high school, and I ALSO find these videos better then class lectures.

1 like in a decade???

first like and reply in seven years

Second like and reply in seven years

twenty second like and third reply in seven years

Didn't he do that Einstein joke? What do you call a bird that doesn't eat? A polynomial! ... Polly...No Meal

Andriy Shevchenko Hey does whatsapp and facebook vedio calls are safe and secure

Thats what makes RSA safe, because when you have difficults to follow a formular then imagine how hard it is to follow a coded forumlar. :)

G4mm4G0bl1n not useful for explanations though.

Dilip Tien The most guys here didnt know how a current becomes a Bit. So why they watching this? Its not possible to solve RSA with barehand and this has device specified reasons.

G4mm4G0bl1n they're watching this to learn. You don't need to know about how current becomes a bit. They didn't need to use three twice.

Dilip Tien Ohms Law, whats "U"? Whats 1 Tesla? Whats the Invention which Tesla makes important? Whats the "Tesla Integral" and how to calculate it? :)

Try try try

He explained right after: you need to factorize the number used for encoding: 10 in this case. The factorization is obvious, it's 2 and 5. It is not that obvious when the number is 657 digits long (2048 bits).

@@jide7765 ok, forgive me here because I'm lacking understanding in this as well. The secret number or what would be the private key in this case is 3. How does the prime factors of 10, being 2 and 5 have anything to do with 3?

@@quplet the formula for the private key is: d = (k x (p-1) x (q-1) + 1 ) / e, where p and q are the prime numbers, in this case, p = 2 and q = 5, e is 3 (as shared publicly) and k could be any integer, here I think they have used k = 2 There could be another way, but this is how they generally do it.

@@AnuragSingh-rh8li How does one find k = 2? Is this just a number the user decides, if not, how is it calculated?

Mining Forge Little late but if you're still curious... The secret number can be determined mathematically, it just needs the original primes first. Once you have the two primes, in this case 2 and 5, you can, somewhat quickly, determine the "secret" number. Without boring you with the actual proof, the secret number is the smallest number that can be multiplied by our first small number (3 in the video), have 1 subtracted from it, and then have (2-1)*(5-1) be a factor. In the video's case, 2-1 * 5-1 is 4, so we need 3*X-1=4. The first integer for which that works is X=3, so 3 is the secret number. So essentially, if we have publicly available number Z, and we find the two factors of the other publicly available number (p and q), then we can solve Z*X - 1 = (p-1)(q-1) until we find an integer solution for X, and that is the secret number (calculation is more commonly expressed as Z*x mod [(p-1)(q-1)]=1). That calculation is not very taxing on computers at all, so if you can get the 2 primes you can get the secret number pretty easily.

I want that shirt encrypted so that only I could read it!

to find out, click the lock by the https, click connection, certificate information, "Google Internet Authority G2", and under the details you'll see that the bit size (short answer yes). However, technically that's not what happens, if I remember correctly that's only used to sign the certificate that is actually used (a DSA, not RSA, totally different based on different math) to exchange the session key (which is just random, and used for a symmetric cipher for the duration of the secure connection)

I still don't understand one thing: If supercomputers are capable of finding primes MUCH bigger than those used in cryptography why would be difficult for those computers to find the primes of a 1024 bits key? For example: in 2013 was found that 2^57885161-1 is prime and that number is huge (17,425,170 digits), much bigger than the primes used in cryptography, which are about 2^1024. ("only" 308 digits). I am confused.

a personal computer can find a random prime of that magnitude pretty quickly... the problem is finding the right ones, there are very many of them

1) I thought that finding a random prime implies that you actually proved that the number is prime by FACTORING IT. 2) I thought that the only way to broke a key would be FACTORING IT. So shouldn't "1" and "2" take similar computer effort? If so, why "1" is easy (every now and then gigantic primes are found) and "2" is difficult (even for small keys like a 1024 bit key, generated with two 512 bit primes)?

I did some research, got some help (inStar-chan !) and I think I got the answer to why 2^57885161-1 is "easily" proved prime while smaller primes still too difficult to be factored. Because 1024 bit RSA numbers are completely general; the algorithms that create keys have been built to avoid kinds of numbers that are computationally easier to factor. Mersenne primes (like 2^57885161-1) can be found with a fast algorithm designed specifically for those kinds of numbers (search for Lucas-Lehmer primality test) and the formula for the algorithm is specifically why all largest prime numbers have been Mersenne primes since; it's ridiculously easier to prove a Mersenne number prime than any other kind of number known by the mathematical community today. Mersenne primes are found using the following theorem (Lucas-Lehmer Test): For p an odd prime, the Mersenne number 2p-1 is prime if and only if 2p-1 divides S(p-1) where S(n+1) = S(n)2-2, and S(1) = 4. Testing the Lucas-Lehmer Test is MUCH easier than factoring the number, but it has the downside of ignoring lots of legit primes on the list. Since the primes on a cryptography key have nothing to do with Mersenne numbers the Lucas-Lehmer Test does not help it in any way. The security of a 1024 bit key relies on the hope that there are no KNOWN tests that can work as an alternative to the boring and computational expensive factorization process.

Take a look at Pohlig-Hellman cipher which is a 'simpler' version of RSA if you are interested in this topic. It's hard to answer your question without solid understanding of modular arithmetic, Euler's totient, etc.

e*s = 1 mod (p-1)(q-1) (in other words: the remainder of (e*s) / (p-1)(q-1) = 1) e: the public number(3) p,q: the two primes (2 and 5) s: the secret number With the numbers in the video it would be: 3 * s = 1 mod (2-1)(5-1) 3 * s = 1 mod 4 s = 3 mod 4 s = 3

nope the way it works is encryption key is prime x prime = encryption key

I don't understand. What do you mean?

p4ch1n0 The RSA is more like: You take modulus n = p*q, where p and q are primes, and then you need 2 numbers, e and d which will have the following function: Encryption: Coded_Message = Message^e mod n Decryption: Message = Coded_Message^d mod n The 2 public ones are "e" and "n", and the private one is "d" That is why RSA is, in fact, a method of asymmetric key cryptography. I praise my textbooks.

Yeah, I think the way he did this encryption was weird. True RSA requires you to put all of the A1Z26 numbers together, and when you decrypt the code, it'll have all of the numbers put together. For example, if you get back a small number, let's say 1234, it could represent "A Y D" or "L C D" of just plain "A B C D".

Its drewmo! you are still my favorite flash animator :D

This would probably answer your question as best as it could be answered: en.wikipedia.org/wiki/Shor%27s_algorithm

Currently, real life quantum computers do not perform tasks as fast classical computers; but theoretically you are correct. Eventually our understanding of building quantum computers will catch up to classical computers and cracking the RSA key encryption will be trivial.

Don't think of it just in terms of speed of calculation. A Quantum machine can exploit properties of physics that a classical computer can not. That is what makes Shor's algorithm work. Shor's algorithm itself is faster because it has a better runtime complexity than all other algorithms that are designed to find prime factors of large composite numbers.

65537 is 10000000000000001 in binary en.wikipedia.org/wiki/Fermat_number it's apparently a fermat number, im guessing it has something to do with how the cpu calculates the modulo operation... i'll investigate further lol.

If I understand RSA correctly, and for the example given: Start with 2 = p and 5 = q (prime numbers that multiply to make n=10), multiply (p-1)×(q-1) = (2-1)×(5-1) = 4 = z, then pick a prime number k that is both smaller than, and does not divide into z. In this case, k=3. n and k are the public keys. That is, 10 and 3. The secret key is a number j such that (k × j) MOD z = 1 or (3 × j) MOD 4 = 1. j = 3 because (3×3)/4 = 2 remainder 1 and we only need to make sure we have a remainder of 1. The public keys are n = 10 and k = 3, and the secret key is j=3. If I had a huge piece of craft paper, I could draw the math out easier.

+Jeff Harris thanks

It's Me Why don't you read the description?

It's Me He did not explain it because it needs some advanced mathematical knowledge which would steal the video's purpose. The secret number is the inverse of e(the number 3 he picked) mod phi(n) where phi(n) is Euler's function

8 bit

It would have to be disgustingly massive I'm afraid. GG banks indeed :(

***** That's super interesting. Cheers for sharing!

Information-theoretically secure numbers

Well, we are at the 2 Kbits, (1 Kilo bit = 1024 bits) and if the 512-bit quantum pc can break it in a short period of time, i think that we will slowly go to greater multiples of 2, like the Mbit for these numbers

+Barraco Barner Yes, every time I see this explained (on KZfaq anyway), the lecturer is so concerned about making the maths easy, they forget that people might want to quickly test what they learned by encoding their own random messages. And they use tiny moduli which don't even allow for more than half the alphabet! I find it a little annoying.

1024* Just look it up

I can only assume that Americans can only count up to one, and that's why they call it 'Math'? :o

@@cleverbobby Canadians call it "math" as well. 🍁

+Szymon Bartosiewicz (Simon) Facebook encryption in a nutshell.

really? does facebook use my type of encryption?

n = 1

or p = 0

Well, your sarcasm was helpful. I did not know that "J" is backward 10 seconds, and "L" is forward 10 seconds (both in lower case)

And right and left arrow are 5 seconds.

:p

+omegadan Theoretically, yes, but the method is not practical.

+omegadan And it's not hack into banks, it's hack into other people's bank account.

+omegadan , true: the message is, perfect prime number factorization. That's how you hack into banks. Presently, that's thought to be infeasible with 2048-bit keys.

+omegadan No, he just told the internet why it is impossible to hack the banks.

+YiFei Yang Actually yes. If you can factorize that giant number that James showed in the beginning, then you can break the security of the bank. The entire bank. Not just individual people.