RSA is an extremely popular cryptosystem used to secure Internet communications today. In this video, John describes RSA encryption and shows a real example of how to encrypt and decrypt using RSA.
Hi, I was wondering how you get the value of d, ,when I do the calculations for d = 7^-1 mod (120) I get one as 120 = 7*17 +1 which to me indicates that the answer for d is 1? Thanks:)
@@amirsalarsalehi4968...great question! That's probably the hardest part of this entire system. It would take a lot to explain it here in these comments, but here's a great explanation of how to use the Extended Euclidean Algorithm to help find the value for "d" crypto.stackexchange.com/questions/5889/calculating-rsa-private-exponent-when-given-public-exponent-and-the-modulus-fact In the example at the link above, they don't use the exact same numbers that I did, but the concept is the same. I hope this helps!
That's probably the hardest part of this entire system. It would take a lot to explain it here in these comments, but here's a great explanation of how to use the Extended Euclidean Algorithm to help find the value for "d" crypto.stackexchange.com/questions/5889/calculating-rsa-private-exponent-when-given-public-exponent-and-the-modulus-fact In the example at the link above, they don't use the exact same numbers that I did, but the concept is the same. I hope this helps!
I also got stuck there but this helped. en.wikipedia.org/wiki/Modular_exponentiation Basically we are trying to replace the value 7 with a value that would make the following true. 7*X (mod 120) = 1 103 solves this equation: 7*103 = 721 721 mod 120 = 1
He wrote d = e^(-1) (mod ⏀(n)) but also he mentioned that GCD of e has to be 1: d = 1/e (mod 120) ≡ 1 (mod 120) d⋅e mod 120 = 1 d⋅7 mod 120 = 1 103⋅7 mod 120 = 1 d =103
This man really proves that university is a waste of money and time. I took 14 minutes of my life to understand the RSA than it took 3 hours of my lecturer going through it.
This video shows the core mechanics or RSA, which is okay, but it's also important to understand why RSA is secure, why it's hard to factor very large, why it's important that p and q be primes, etc. I don't know if your lecturer tried that, but even 3 hours is not enough to go over all of that, unless you already have a background with modular arithmetic and cryptography. It's one difference to have an idea what RSA is roughly about (perhaps that what's you were after), and another to understand the why and how.
That's a real possibility one day! In fact, that's the exact reason RSA bit strength keeps going up...to make it harder to factor out the prime numbers. If you have a larger number, then it's harder to factor it out correctly!
@@devcentral once somebody know how to calculate those without brute force, big big number won't matter anymore. Remember, our generation has a lot more population than last century. So there must be multiple number of Einstein-like people.
Great question! That's probably the hardest part of this entire system. It would take a lot to explain it here in these comments, but here's a great explanation of how to use the Extended Euclidean Algorithm to help find the value for "d" crypto.stackexchange.com/questions/5889/calculating-rsa-private-exponent-when-given-public-exponent-and-the-modulus-fact In the example at the link above, they don't use the exact same numbers that I did, but the concept is the same. I hope this helps!
Hi Pragati...great question! That's probably the hardest part of this entire system. It would take a lot to explain it here in these comments, but here's a great explanation of how to use the Extended Euclidean Algorithm to help find the value for "d" crypto.stackexchange.com/questions/5889/calculating-rsa-private-exponent-when-given-public-exponent-and-the-modulus-fact In the example at the link above, they don't use the exact same numbers that I did, but the concept is the same. I hope this helps!
The part where you said that most times the exponent "e" is same, and since an attacker would also will also get the "n". Would this not make him/her to find the privkey "d" using d=e^-1(mod phi(n)) ??? Unless you mean that the problem to find Euler's Totient "phi" is a bigger problem without knowing the actual 2 primes.
Hi nawnwa, great question! You are correct that the issue is finding Euler's Totient "phi". The attacker (or anyone else for that matter) would know the values for "e" and "n" but would have a mathematical problem in trying to figure out Euler's Totient or "p" or "q". Hope this helps!
The value of "e" is very important (as are all the values in the RSA algorithm) and it relates to the other numbers in a specific way. So, while it's true that the value of "e" needs to be between 1 and totient, it is also important that it is the correct value given the other values (p and q). So, in this specific case, "e" would need to be 7. I hope this helps...thanks!
@@uni1014 It's pretty easy to print a T-shirt backwards, easier than writing backwards. I haven't checked intensively but it looks to me as if there are a lot of left-handed presenters. Not conclusive of course, maybe people who can write backwards are predominantly left handed.
Hi Anthony...great question! Ultimately, all characters (numbers, letters, etc) can be converted to binary 1's and 0's (and then converted back once the operations are complete). This way, you can run the mathematical equations on everything. Thanks!
Hi from Argentina. It was one of the best explanation about RSA. Thank you for share with us. Only one question, the value "e" is a random value or derive from other calculation?.
That's probably the hardest part of this entire system. It would take a lot to explain it here in these comments, but here's a great explanation of how to use the Extended Euclidean Algorithm to help find the value for "d" crypto.stackexchange.com/questions/5889/calculating-rsa-private-exponent-when-given-public-exponent-and-the-modulus-fact In the example at the link above, they don't use the exact same numbers that I did, but the concept is the same. I hope this helps!
The private key isn't "n" it's p and q. Even though they equal "n" when multiplying together, you're losing the point that they are the private values.
Hi Jesse...thanks for the comment. As you said, p and q are private values that are multiplied together to get n. When referencing the private key, I'm referring to the actual private key that is the complement to the public key in a given RSA implementation. The public key is actually a key pair consisting of the values e and n. The private key is also a key pair...consisting of the values d and n. The public key is shared with everyone...the private key is kept secret on the server. Thanks again for the comment!
That's probably the hardest part of this entire system. It would take a lot to explain it here in these comments, but here's a great explanation of how to use the Extended Euclidean Algorithm to help find the value for "d" crypto.stackexchange.com/questions/5889/calculating-rsa-private-exponent-when-given-public-exponent-and-the-modulus-fact In the example at the link above, they don't use the exact same numbers that I did, but the concept is the same. I hope this helps!
Great question! The RSA encryption described in this video is the public key cryptosystem used for key exchange between browser and web server. This cryptosystem is not tied to one specific company or computer...it's used by millions of computers and web servers all over the world. On the other hand, there is a company named RSA (www.rsa.com) that specializes in all sorts of computer security solutions and technologies. The RSA keychain that you are asking about is a specific product that the RSA company offers to customers (community.rsa.com/docs/DOC-62315). This keychain provides authentication services to users and can also be used to do things like sign emails, encrypt files on your computer, etc. A user can input the number that is displayed on the keychain in order to gain access to the computer or application. The number on the keychain can be programmed to change every 30 seconds to make it very hard for attackers to break into the authentication session. I hope this helps clarify for you!
Hi Jason. This is a great catch! I ran several versions of numbers on my notes before I recorded the video. I was using several different combinations of the variables, and I must have mixed up one of the variable values...very sorry about that! Obviously, the formulas and the process for RSA still holds true, but I should have double checked these numbers before I used them in the example. Again, great catch, and sorry for the mistake!!
That's probably the hardest part of this entire system. It would take a lot to explain it here in these comments, but here's a great explanation of how to use the Extended Euclidean Algorithm to help find the value for "d" crypto.stackexchange.com/questions/5889/calculating-rsa-private-exponent-when-given-public-exponent-and-the-modulus-fact In the example at the link above, they don't use the exact same numbers that I did, but the concept is the same. I hope this helps!
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