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

[@gibsonman507]

This is the best RSA explanation I've seen

[@santaclaus897]

me too

[@fnamelname2445]

Better explained than my professor in college ... for which i pay hefty tuition fee each semester. lol

[@sharonomonua1747]

@@fnamelname2445the only thing i don't understand is mod how is it used and like what is it

[@fnamelname2445]

@@sharonomonua1747 Mod or modulo only returns the remainder of a division operation. For instance, if you divide 5 into 5, the result is 1. But if you divide 5 into 3, the remainder is 2. Therefore, we write 5 modulo 3 = 2. These videos might help: 1 - kzbin.info/www/bejne/bJW9faRtbMyGfbc 2 - kzbin.info/www/bejne/aqvEmamZf56aosk

[@lukacavara6254]

Cleanly explained without messy hand written scribbles many KZbin publishers practice

[@InshuMussu]

You spent your time to save our time, double likes from me

[@michaelschepens3750]

I was trying to understand the Wikipedia page on this topic with some difficulty. Your video did an excellent job of explaining it simply. Thanks a lot.

[@zx600e93]

Nice simple introduction and the slow transitioning of deeper and technical understanding with step by step interactivity in processing the RSA algorithm. Finally, ending with a real life example using Amazon's cart totally amazed me how it all works together. I'm sharing this with one of my Math Faculty members who teaches math for teachers, she'll be impressed to see how cryptography applies in real life and that most people don't know it. Thank you for taking the time out and scripting this too, good job, and an A+!

[@Blacktouch2000]

I spent my life searching for this video. I am eternally grateful.

[@chrominox]

The Extended Euclidean Algorithm method you've shown here was absolutely stellar. It made my job very easy. Thanks a ton, mate.

[@DutchlimitsDesign]

You have the best explanation from all the video's ive seen regarding RSA. Thanks so much!

[@thebestisyettocome7]

Very good explanation of the RSA algorithm, one of the best I've seen on KZbin.

[@ianfitchett2768]

I just wanted to say that the way you showed the extended Euclidean algorithm was not something I had seen before and it made my work SO much easier. You've more-than earned my like.

[@asfandalikhan6269]

extended euclidean algorithm is far easier than this technique and less time consuming. whereever you go there's just a matter of time and if you are slower then no one cares :)

[@usamaliberty]

This video was such a gem that it explained almost everything of the concept clearly in just a couple of minites Thanks mate, you made me very happy today

[@OldFilmCameras]

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!

[@samosapakora9086]

I really have to say that was top notch, clear, simple, articulate. Thank You!

[@TON-vz3pe]

Fantastic Job. Like others said , "By far the best Explanation of RSA Algorithm" after scraping the entire KZbin

[@MissNorington]

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! 😀

[@MustafaAlhadi]

Dude... you are a time saver, thank you very much for this great and clear video

[@hqiu6828]

Excellent explanation! You reveal the magic behind the RSA encryption-decryption algorithm!

[@cdemetriad]

Very well explained, it helped me a lot. Good, simple graphics and good, timed voice. THANKS!

[@EMate-vu3ku]

Thank you very much for this video! It is of excellent quality and I could understand it easily despite I'm only at secondary school. It is the best explanation I've come across both in print and on the internet. Many thanks!

[@freewheelburning8834]

what other reads have you found in print that's this intuitive? (just curious)

[@EMate-vu3ku]

@@freewheelburning8834 There was a section about this in Marcus du Sautoy's book, The Music of Primes. I recommend it, a fascinating read!:)

[@chrisweaver7989]

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!

[@dkarthiganesh]

This is great explanation. Helped me to solve d for (e,N)=(53,299) and encode(m)=171. Thanks a lot.

[@TechnikMeister2]

As Edward Snowdon said recently and as Gordon Welchman said 70 years ago, a computer generated algorithm thats creates a cypher can always be decrypted. The only true unbreakable encryption is a non computer generated one time pad. Its still used today. There is a guy in Switzerland who has a barrel with 50,000 dice and it spits out five dice in a row it then grabs them back and the next turn does the same. He will manually create one time pads for you at a cost of $500, good for 10,000 characters. No machine, not even a simple typewriter is used. They are written out by hand and you get both copies. He keeps no records of who buys them. Swiss banks now use them to protect their clients transactions after the US got a court order for computer records of US Taxpayers. Now not even the banks know.

[@unh0lys0da16]

Sure it can be decrypted, it just takes 1000 years

[@rickyc1991]

I'm very interested to learn more! Do you know what the non-computer generated method is called? I'm having trouble finding it.

[@markstephens8423]

There is an encryption program out there named Vial 7 - Only way to get a copy is if you know the person. Each copy is made to order and it will only work on the users computer. He hard codes the key into the program and puts the location of the file somewhere on the computer at the request of the client. When you try to use the program it looks for the key and if it's not found it will close the program, so everyone that wants to communicate with that program they have to have a custom made version to work on their computer. The encryption math is said to make RSA look like 1+1. If you are not government USA, you will never own it. After it locates the key to use it then the real encryption begins and if you use the same password every time, the encryption out put will always be different, that means there is no standard algorithm with the exception of unlocking the program for use. Estimated bit strength - Unknown because the more text there is the higher the bit strength gets.

[@Amazing._Games]

They can use cryptographic random number generators

[@BoleDaPole]

But it's never truly random, that's why it has to he done manually

[@suphasitthongniam9082]

Thank you so much. I have confused about RSA for a while , I just watched your video and now I clearly understand about RSA Algorithm. Thanks so much.

[@andrewlittle9569]

This video makes it much easier to understand. Thanks a lot!

[@caitancorreia8379]

thanks, the way to find 'd' using a short-cut version of the EEA is a life saver :)

[@gaastonsr]

Best explanation I could find on KZbin. Thanks!

[@anand.suralkar]

Best video on RSA mathematics..so far and finally i am able to get maths behind RSA

[@davidr.flores2043]

Anthony, great work sir. I appreciate your effort, very well done and you know the topic inside-out. Kudos to you man!

[@davidhedin-abreu4426]

Terrific video Anthony, I used it to teach the mathematics of RSA and to write an example Java program for encryption and decryption.

[@deepakrai6353]

Its very good description of RSA .I am became fan.................

[@iycgtptyarvg]

Thanks for the video. It helped that I already understood the process, but this is still useful. It would perhaps have been informative to explain to people why we use phi = (p-1)(q-1), but hopefully they will search the Internet to see why that is so.

[@muhammadlawal6719]

thank you very much . i was confuse before about how to get d bt i am now satisfied with explanation.

[@mariomax2960]

the best course I've ever seen about rsa !!!!

[@kirkouimet]

This is awesome Tony! Thanks for creating and sharing! Hope to see more like it :)

[@JWentu]

One of the best explanations that i found on the topic. thankx a lot

[@tehownerer1547]

Amazing video. TO ANYONE CONFUSED: LEARN ABOUT THE EUCLIDEAN ALGORITHM AND THEN STUDY THE EXTENDED EUCLIDEAN ALGORITHM INDEPENDENT OF RSA. That might help.

[@Ali-mi9up]

more importantly the eulers theorem

[@crypticnomad]

This is actually super useful for what I am currently working on. I'm attempting to generate rsa keys using a seeded rng which uses bitcoin's bip39 seed or "mnemonic phrase".

[@kf4426]

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

[@bennetbraune2513]

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

[@vishalmishra3046]

Use d = pow( e, -1, (p-1)*(q-1) ) in Python3.8 built in function (not math.pow).

[@marciocastro7101]

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...

[@nafiz1938]

no need to coprime with N, just coprime to phi

[@marciocastro7101]

@@nafiz1938 whatever, same problem because of big numbers.

[@kimkarlson7820]

@@marciocastro7101 Ever heard of Fermat primes? It shouldn't take you longer than a fraction of a millisecond to find a suitable e.

[@TheMrVogue]

Minor mistake at 6:28, you said the result is two thousand five hundred seven, and we can see it is 2557. Cheers though, this is the best RSA tutorial I've found to date.

[@cybotx3872]

That was Excellent, Anthony ! Great Work !

[@An.Individual]

Thanks for this terrific explanation.

[@Lucaemar]

Finally got it, now I can complete my math's paper. Hallelujah & thank you

[@raghuma1]

wow awesome video...i finally found short and clear cut explanation of algorithm to find d. thank u so much for this awesome video

[@ariayang2980]

My mind is blown, the shortcut method. Nice 👍

[@tomay3000]

Nice, this is a very nice and clear explanation. Well done (y)

[@Melrix]

Thank you very much! It was awesome. Nice and clear explanation.

[@Chaya-uv6oq]

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 ^^

[@Ha1ization]

Great work Anthony. Thank you kindly.

[@bharathnayakb]

Best explanation 👍

[@chaitanyavinnakota9909]

Thanks a ton. Immensely helpful explanation.

[@conanalbrecht5157]

Very descriptive of the mathematics. Awesome.

[@SkelleRok]

Thank you for this awesome and clear tutorial.

[@minomino200]

Thanx bro......it help me a lot

[@tiyasharma441]

So clear and crisp

[@karimbarakat7732]

thank you, your explanation was just great.

[@wabafethacker1552]

I really liked your explanation

[@finestinlondon8837]

Dude, this has helped amounts that you can't even imagine - thank you so much! 'Liked' the video too. I'm trying to write a bit of code to replicate RSA's encryption method, but was struggling to work out how to calculate 'd', and this worked wonders. Thank you again. Just a quick query though, how did you get -34 MOD 40 to equal 6? Mathematically, doesn't this equal -34? When I get a negative number, should I be adding the value of phi (until the value becomes positive) instead of MOD'ing the value by phi?

[@JimVekemans]

39 MOD 40 = 39 100 MOD 40 = 20 because there's 20 LEFT! after subtracting 40 two times. so, you don't try to see how much less -34 is than 0, you try to find out how much MORE -34 is than -40. Which is 6.

[@finestinlondon8837]

+Jim Vekemans ah, this makes complete sense. So you simply just take the absolute value - thank you for your help!

[@whythosenames]

3:27 did you mean d?

[@michaelmcgoldrick5241]

Thank you this was very helpful

[@AkumaRaion]

this is a great explanation of rsa. thanks a lot.

[@pobg807]

this video is PERFECTION

[@alvianibnuburhan2484]

You are the best brohh big thanks

[@wramarante]

Useful ^ 4096 = A better word to be used at the end of the video. Thanks for sharing.

[@fruney_x]

Thank you, that was clear and to the point.

[@abderrahmanghorfy3281]

Excellente video and explication, GREAT JOB!!!!

[@SANDEEPSINGH_9]

Good work Anthony...

[@Magicsquarepuzzles]

Very well explained

[@cycletechsa_dev]

Thanks,...... you are a life saver

[@ananamz]

Love you man! Thanks for the video.

[@Nada-yc8uo]

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

[@teus1500]

Hello, very nice explanation. Now, I read somewhere that if I want to have a 8bits key, my 'n' needs to be less than 2^(8), but I saw many resolutions where they use a 'n' that is > 2^(key lenght that they want). Could someone light me up?

[@glitchy_weasel]

Excellent video, I've read some resources about RSA but there is still something that confuses me: what do you all mean to "choose" e, can I choose any value for e? Which usually is 3 or 65537 on modern applications. I mean, is "3" always going to be coprime with any phi? Like in the example in 10:15 how did you found that e=7 ?

[@vishalmishra3046]

e can be any Prime, since primes are co-primes with any PHI. Should be large with very few 1 bits - so 0x10001 = 65537 is one of the best choice for fast encryption (during key exchange) and signature verification.

[@justincaseOne]

thank you very much...Very useful nd very clear

[@mekaramu]

Super Explanation!!!!! Great Thank you

[@madhabahlal-madinah4309]

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

[@avatekmuhammed5013]

Very very very nice. Thank you so much

[@navjotkaur4795]

thank you very much.. awsome work

[@christopherderrell8470]

@Anthony Vance Thank you very much for such a useful video.

[@mackomako]

Excellent video!

[@ajithkumar6787]

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

[@hutaospunchableface7381]

Thank the lords for this video!

[@davidmiranda3129]

Great video! Thanks!

[@atombomb58]

Thank you so much for the video

[@mahmoud-ibrahim]

great video. many thanks.

[@PragmaticWays]

So @11:40, what do you do when phi / e doesn't equal a whole number?

[@BrunoTarasco]

it wont ever be :) and that's the point. That's why you can do PHI/E then multiply it by E again and get a whole number. You just have to discard the decimal digits :)

[@benjadamore]

Fantastic!! Good job!

[@Tango_Alpha_Charlie]

Thank you ... this helped me a lot. :-)

[@duniajamma6031]

In the last example, if you calculate 3 * 6219 mod 2328 = 33 not 1

[@kolawoleolusola]

thanks this really helped me

[@راجيةرحمةالله-ز6م]

Thanks a lot, I have a question "Can I used same the way to generate the key to steganography for embedding data in an image?"

[@brandondupuis8243]

to find d : (k*PHI(N) + 1)/e. increment k by 1 until the answer is a round number. EX: ((1x1872) + 1 )/7 = 267.571... (not working, not a round number) ---> increment k by 1---> ((2x1872) + 1)/7 = 535 .... so d = 535 in that case. now you can build a simple program to find d , using this concept and loops

[@asddsaaassddd]

wouldnt this take very long if ur numbers are huge?

[@zayedzihan6594]

thank u, it helped...

[@vishalmishra3046]

Use Python3.8 built-in function d = pow(e, -1, phi) for mod inverse calculations if you don't want to implement on your own.

[@asdfasdfuhf]

11:30 *40 divided by 7 is not equal to 5!?* Do I have to floor the number if it is a decimal?

[@ItaiBarabi]

yes, when you divide in computers you floor the result

[@Patriciatrip6946]

Hey, great video but i got lost getting the e value. How did u get e to become 7?

[@bonuxxfull]

e you choose it yourself , the only condition is that e is an integer >2 and great common divisor ( e,φ ) = 1

[@TheDanishGamers0705]

e must be an integer, 1

[@anand.suralkar]

@@bonuxxfull smallest number not a coprime to phi

[@feliperodrigo7445]

Hi! I love your video and it is helping me a lot with my Internal Assessment from IB Maths HL. I really need to do something original with RSA encryption (or look at it at a different way), so I was wondering if you (or anyone reading this comment) could have any idea about an original idea or a further step to RSA encryption. Thanks ;)

[@BelievinSP]

clear and concise!

[@gibsonman507]

Why are you encrypting the Integer value 42 rather than the String "42" -> ASCII (5250) (6:24)

[@wompaper]

I guess I'm getting something wrong but 5:27 - you want to calculate x^2753 ?

[@tmdbah]

Thanks for this.

[@bish-jyag3371]

Great work