How the RSA algorithm works, including how to select d, e, n, p, q, and φ (phi)

Could not get the answer for p=23, q=19, and e=283 with the steps. Can someone try n lmk?

π

A simple trick to get the d as well: d = e-1 mod φ(n). Let's take the example in the video:

e = 7
φ(n) = 40

7^-1 mod 40 = 23

and that's how you can get it without going through the steps of the Extended Euclidean Algorithm

How to choose e, just a small prime that doesn't share a factor with φ(n) ?

I would make a big distinction in RSA between asymmetric encryption and public-key encryption. If you use a well-known and small 'e', you have public key, but can't support 'asymmetric' key encryption. With 'asymmetric' key encryption, 'e' and 'd' have the same properties; and are equally secret.

I use it to make digitally signed tokens such that you don't know the plaintext until you produce a witness that you performed verify to extract a secret to decrypt the signed claims. That way, the signer distribute the verify key to those who are allowed to VERIFY. It's not totally public, because it's (n,e), but signer has (n,d,e). This allows tokens to be passed around so that man-in-the middle can't decode the claims, and the verifier can only extract verified claims. ie: the current way of checking signatures (plaintext,Sign(H(plaintexty))=sig) has security problems. The main one being that you allow people to not verify the signatures; something that is very common in the hands of web developers. And the other is in leaking the tokens to intermediate proxies.

thats fun stuff

I have used your way finding D but I ended up with zero instead of 1. my number was p=5 and q=13 and e=35 I was not able to get a correct answer, I don't know why?

Thank you for making this easy to understand! I am no good with math but I like to be able to use it from time to time! 😀

For MOD-Inverse - Use pow() the built-in function in Python3.8 - e.g. d = pow(e, -1, (p-1)*(q-1) )

Thanks for this.

Thank you this was very helpful

Thank you, I got stuck implementing the RSA in Python at "d". your calculation path was easy to implement.

Best explanation ever.. Thank you.
Can I get the video for Elliptic Curve Cryptography, from you, please?

Stellar video

Thank the lords for this video!

This has to be one of the best if not the very best explanation of the RSA algorithm that i've come across, Thank you!

tnkz bud

OMG! so I am being taught Maths in uni and its basically everything in this getting me ready for next year. I find it hard to follow the lecturer sometimes and this is amazing! I need to also program a crypto algorithm and this gives me a good base! THANK YOU!

Amazing

Thank you

how is 40 ÷ 7 = 5? my calculator and my brain says it's 5,714....

what if i have something like phi- 24 and e- 11??

what is mod!??!

This is hands down the best RSA video out there. Too bad it took me so long to find it >.<

Allez Adams

Je t'aime

Thanks for this terrific explanation.

so great, very well explained, thank you so much.

You're the best!

this video is PERFECTION

Very well explained

i love u man

Best explanation 👍

Good explanation, but is important to point that e must be coprime with phi and N. With small numbers, it's relatively easy to pick a value for e, but if p and q have 30 digits each...

Now if someone would just do a video of how to use this on a message of arbitrary length in C or Python that was easy to follow for someone learning to code.

Simply Superb Job.... Want to give 1K likes

u made my day & saved my time & I love you
not rly but great video & u explained everything so well & simply that even I could follow & now I wrote a working python script & I'm happy ^^

Interresting content but boring presentation.

I've knocked together a primitive Python implementation of this and I've got two problems so far. One is that the algorithm to derive d occasionally results in a divide-by-zero error, which I've solved simply by scrapping it and starting over with a new value of e. It's still quick but there must be a more elegant solution to avoid the error in the first place?

The second problem is that, for anything more than three-digit values for p and q, the actual encryption and decryption is incredibly slow. For four-digit values it clocks in at almost a minute and a half. Why is it so slow when this process happens routinely for much larger primes than anything I'm using?

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Can somebody please explain to me how the message doesn't lose information when you calculate modulo n? As modulo is not an injective function?

thank you, your explanation was just great.

you are amazing!!! good work, you got a new sub