RSA -- The Math

Explaining the elegant and simple math that opened the door for modern online cryptography. RSA defends its users with a math problem that frustrated mathematicians for centuries -- when they tried to solve it for fun. Now major hacking organizations attack the same problem for profit, big profit -- how long will RSA survive? Edward Snowden claims that the NSA did solve the RSA challenge to factor large numbers. Who else? Get the math here, and think for yourself!

[@vishalmishra7018]

I wish I could double like this video. All these years of trying to understand how RSA works and it is finally clear to me. Professor you have a gift of explaining things. Thanks for making this video.

[@DanielDa2]

You have provided an extremely elegant summary of the fundamental idea. It is usually lost in most material: in the sea of computations for some or in that of lemmas and proofs for others. Thank you.

[@karthikkrishnan6026]

The a-ha moment when the math suddenly clicks and you appreciate how beautiful it is, is priceless. Thank you for this video!

[@AdrianVrabie]

great video! i like how u delve into the concepts of the theory and not on the algorithm of solving 2+2

[@GideonTheTeacher]

Adrian -- you got it, the concept stands on its own merit without the mathematical camouflage.

[@CamiloSanchez1979]

Thank you for these videos, they are so enlightening, you explain very well.

[@americaninseoul]

quantum computing: im boutta end this mans whole career

[@GideonTheTeacher]

Indeed, but we have a remedy: eprint.iacr.org/2021/1510

[@sputnickers]

I understood everything up until 10 minutes. The step at 10:00 was pretty big. Not sure I followed.

[@Marco-hw7nc]

For anyone still wondering, it is actually easy: you have _k Phi(n)+1 (mod Phi(n))_ just remove the +1 for a moment, obviously _k Phi(n) (mod Phi(n)) = 0_ for any integer _k_ adding back the +1 the result is of course 1, giving the equation _ke kd = 1 (mod Phi(n))_

[@ravel1]

@@Marco-hw7nc thanks

[@eng60340]

Thanks. Good explanation! Most ppl only explain the algo.

[@GideonTheTeacher]

glad you found it useful.

[@dannys2817]

Thanks for this video, you made RSA easier to understand

[@GideonTheTeacher]

thanks!

[@miguelsantos8972]

Very good video! Thank you!

[@yusefskaff2601]

you are a great prof !!

[@eggtimer2]

I think you are confusing congurnecr and equal signs.

[@mnazaal]

Most videos I saw just showed the algorithm then proved it, I like this one way better since you derived it from first principles. Thank you very much

[@eggtimer2]

This seems to miss the point that we need to exchange information about each other's keys ...

[@GideonTheTeacher]

We exchange public key, not the private key

[@eggtimer2]

@@GideonTheTeacher agree, so there are a few congruent signs missing plus that the maths you outlined would require the message to be coprime with your p*q=n.

[@Aetna1207]

to save time and board space, he did not write "mod n" for some equations. as long as message is not p or q (not likely, as both are big), message will be co-prime with n.

[@mostafaramezani8364]

Great! Thank you :)

[@VladimirDjokic]

Great!

[@Gattomorto12]

thanks. you're good

[@ikirstenHD]

Cool Stuff, Learning about PKI for the Network + Exam, how did I reach here lol

[@eggtimer2]

Dude, you have random mod n appearing and disappearing. Love the idea of the video but there are big gaps.

[@Ellenki_007]

I love cryptography