Hey guys, there’s been a ton of news the past week about a vulnerability in the WPA2 protocol that protects our Wi-Fi networks, and since we say that AES is secure in this video, we thought it would be helpful to explain how it all relates. In October of 2017, researchers released a viable hack against WPA2, known as KRACK Attack, which uses AES to ensure secure communication between computers and network routers. The problem isn't with AES, which is provably secure, but with the communication protocol between router and computer. In order to set up secure communication, the computer and router have to agree through what's called a "handshake". If this handshake is interrupted in just the right way, an attacker can cause the handshake to fault to an insecure state and reveal critical information which makes the connection insecure. As is often the case with these situations, the problem is with an implementation, not the secure algorithm itself. Our friends over at Computerphile have a great video on the topic: ruclips.net/video/mYtvjijATa4/видео.html
You can slow the playback down, can't you? It's not too fast for me. But I have heard others mentioning changing the speed of playback of youtube videos in general.
This is probably one of the best Crash course videos ever made. Really great explanation and somehow more detailed than other ones while still explaining the concepts easily. This videos deserves praise.
I look forward to watching this every week. You guys at crash course are keen on the idea of the feynman technique. Making things as simple as possible. I find these videos on computers to be basically an overview of all the things I've studied over the years. It's a very complete and timely piece. Perhaps you guys may choose to go into more depth on some of these topics in the future. Anyway, these are a great introductory learning tool for those who are interested. Power to male and female programmers and tech nerds! While we ride the wave of the future.
i've been cracking my head open to understand how keys function for the past few weeks since uni started and you just explained it all very clearly with some paint.....insane and amazing, i thank you ALSO finally understanding the math that's behind these encryption techniques thank you so much
Actually, the most devastating quantum attack (Shor) only breaks asymmetric encryption (RSA, DH key exchange). Grover can weaken AES, but that isn't nearly as bad (speedup by at most the square root). Other algorithms, including some asymmetric ones, might not be affected at all. djb & Tanja Lange have a 32C3 talk ruclips.net/video/-LlkJZJ5DMQ/видео.html and a mostly readable 2017 paper, "Post-quantum cryptography".
It is uncanny how much this series is aligning with what I'm learning in my Defense Against the Dark Arts class haha! Sharing all of these with my professor! Keep 'em coming!
I think it would be a great idea to make a second video where you talk about vulnerabilities of cryptography! For example, Diffie-Hellman is only secure against passive attacks; however you can fool both sides into thinking that a secure connection is established by a man-in-the-middle attack. There are different ways to eliminate this problem. Also public keys need to be stored in a secure source. If an attacker is able to distribute his own public key, it will lead to problems. There are many more examples, which could easily fill another video. I loved this one, it was a great introduction, but I wish you would go into more detail, especially since it might give the impression that these algorithms have no flaws :)
I love this course, and I'd like to add a little more information (due to the fact that CC cannot cover everything in just 15 minutes). First, when Carrie Ann says that one-way functions are "easy to do in one direction, but hard to reverse", "easy" and "hard" refer to computational complexity, specifically polynomial time problems. This means that the time needed to apply a one-way function must be small (a polynomial in the length of the argument of the function), but the time needed to reverse the computation must be awfully big. Second, the existence of one-way functions is an open problem in computer science. Modular exponentiation is a candidate for being a one-way function: indeed, computing the function is easy, even for huge numbers, but the reverse (the modular discrete logarithm) is believed to be difficult (but it has not been proved!).
Ignacio Correa NSA (no such agency) spends serious taxpayer money to preserve email encryption/decryption using the Cypher Chip ( ironically, iirc, proposed by Bill & Hillary Clinton while in White House to preserve emails securely ) Sharing Key Info with NSA (WTF?)
"For a 128-bit keys, you'd need trillions of years to try every combination, even if you used every single computer on the planet today. So you better get started" XD
This was such an amazing explanation. Perfectly paced, great graphics, fun analogies, easy to understand, and very well spoken. Thank you so much for this!
When I read that in my brain, I suddenly realized Carrie Anne does sound like carry on, if you live in the north as I do...soooo Minnesotan, dontcha know eh?!
In practical modular exponantiation you don't calculate the B^n before taking mod m since this number would be stupidly big and probably wont fit into memory. Instead you divide it into a series of taking power 2. If n = 2k is even, then B^n = (B^2)^k. If n = 2k+1 is odd, then B^n = B(B^2)^k. If B^2 > m, let C = B^2 mod m, then and (B^2)^k mod m = (B^2 mod m)^k = C^k (Also B(B^2)^k mod m = B(B^2 mod m)^k = BC^k). It is quite easy to code this if you want to give it a try.
I have learnt more from a few Crash course videos than I did my entire XX years spent at school. Just goes to show education is not education its just there to make you pass tests, not to learn. Thanks CC. Thanks Alan Turing
It's not that simple. Sure, this is explained in an easy way, but our brains aren't capable of storing this information in a way that you can remember it easily in the future. These videos should in my opinion instead be seen as a support for the subject which you then learn through a more conventional way.
The videos give you a taste of these subjects, just a scratch on the surface. You need education to learn how to study properly and get as much knowledge as you need. Don't hate school, it's normal to feel that way, but it's a lot more important than you think :)
Fantastic Video. I finally understand how key exchange works. i always wondered how it can be secure if the keys need to be known to both parties. Now i know that! Thank you Carie-Anne!
I did a course on Cryptography and Information Security in my degree. I remember we touched upon DES and AES, and other advanced topics such as elliptic curves.
An interesting addition: The first version of Enigma, the one which had only 3 rotors has been cracked even before the beginning of WWII by 3 Polish mathematicians. Unfortunately their methods became obsolete the moment the 2 additional rotors have been added to the machine, making it again impossible do decipher Enigma until the Turing's breakthrough. (A commemorative memorial of the Polish input was placed in 2002 at Bletchley Park).
"so now you know all the _key_ parts of modern cryptography" , this woman makes me crease omg im dying thanks cryptography for bringing this woman to me the puns are fantastic
Well a brute force attack will get you divorced I think so I don't recommend that! How about taking her on a phishing trip with you- If you promise to cook the catch and clean the dishes afterwards you may net that critical algorithm!
B^Y mod M to the X is not equivelent to B^X mod M to the Y. You have to take the modulo afterwards, and it only works for very specific bases and modulos.
ive watched a GAZILLION videos on cryptography... and i always had the sensation that some part was missing, that it didnt make total sense.. i thought i was just dumb, but FINALLY someone explained it completely and clearly! best explanation EVER. all other videos forget to tell the public key is used in conjunction to the private to create something new. thats key! (pun intended) awesome job! this crash course is truly a masterpiece
9:43 That is not mathematically equivalent... See for example: b = 4, x = 3, y = 7, m = 18 You need to take the modulo M of the result to get the same key. In the wikipedia article about that topic they say, that b needs to be a generator of the group of m , but I haven't tried it out yet.
Something you should have mentioned is that cryptography is only perfectly secure in theory - in the real world there are side channel attacks. Id explain it but I think that people who read this comment will have more fun researching this themselves ;)
thanks for the awesome videos. this is one of my favourite channels on youtube. can you please do a series on Criminology and also Linguistics? thanks :)
With the modular exponent example if somebody in the middle intercepts both sides of the communication they get the same value for the shared key - i'm sure the NSA is already doing this, they already compromised RSA security and functions with backdoors to decrypt without using brute force.
I'm pretty bad at math and could understand this , well done. Although it does beg the question of why people consider math a requirement when the principles have more to do with logic than mathematics.
Hot oil in the medieval ages wasn't used like you see it in Hollywood. Oil was an expensive resources so what they would actually do is pour boiling water or extremely hot sand. Yes there was some occasions where it happened but that's an exception not the norm as it's portrayed.
If my understanding is correct, it is crucial to the color-analogy that even if an eavesdropper has the shared color, and could theoretically "subtract" it from the two transmitted mixed colors to get the two secret colors, this subtraction-process is what would be prohibitively cumbersome?
hey carrie (or anyone else if you would like to help) , I wanted to understand that private key sharing( at 10:00) , so i thought of making myself a simple practical example out of it, but my calculations say your equation from 10:00 is not correct . can you please have a look? So If i have to transmit character '"P' (ascii 80 )from Boy A to B: >> I assumed x=2 would be private key of A and y=3 would be private key of B) >> I assumed my public key function as cipher(x,y)= (3^x % 7)^y Thus: - A would first Transfer cipher_a = 3^2%7 = 2 to B - B would first Transfer cipher_ a= 3^3%7 = 6 to A >> I assumed my publically available encryptor function as encrypted_text = cipher(B) ^x + ascii(character) - Thus, A would transfer the encrypted character 'P' to be as e_t = (6)^2+80 = 106 >> I assumed my publically available decryptor function as ascii(character) = encrypted_text - cipher(A) ^y - Thus, B would recieve the value as val = 106- (2)^3 = 97 , which is not equal to our original value of 80 Thus (B^y mod M)^x != (B^x mod M)^y != (B^xy mod M) But rather (B^yx mod M^x) == (B^xy mod M^y) but != B^xy %M Is this right?
You have very good videos, however i suggest you either decrease the amount or info or make a longer video. It’s a bit difficult following you with normal playback speed
Amazing video! Can you also make a video on modern cryptography, focusing more on all the cool things not directly related to encryption? Hardly anyone knows there's so much more to cryptography than that. Only one minor objection: please don't reiterate the myth of million-year cryptoanalysis. Assuming Moore's law to continue, even the strongest encryptions in use today can be broken within decades.
The first person to break the enigma code was Marian Rejewski and his colleagues, Polish mathematician, and he did it in 1932 ! Before outbreak of WW2 and certainly before Alan Turing. That's sad you don't mention it.
Guys, at 0:35 you used the picture of the monument dedicated to the 3 Polish mathematicians who first broke the Enigma cipher in 1932, making it possible for Turing et al. at Bletchley Park to proceed. Yet you didn't breathe a word of their contribution, nor did you even credit the photo (here it is on Wikipedia, recognizable by the digit order at the top: commons.wikimedia.org/wiki/File:Polish_cryptologists_breaking_Enigma_ciphers_monument_01.JPG ). I can understand that the English speaking world may be unwilling to break their tongues on names such as Różycki, but the complete erasure of the Polish contribution in ANY account of the Enigma-breaking is more than a little unfair.
Hey guys, there’s been a ton of news the past week about a vulnerability in the WPA2 protocol that protects our Wi-Fi networks, and since we say that AES is secure in this video, we thought it would be helpful to explain how it all relates. In October of 2017, researchers released a viable hack against WPA2, known as KRACK Attack, which uses AES to ensure secure communication between computers and network routers. The problem isn't with AES, which is provably secure, but with the communication protocol between router and computer. In order to set up secure communication, the computer and router have to agree through what's called a "handshake". If this handshake is interrupted in just the right way, an attacker can cause the handshake to fault to an insecure state and reveal critical information which makes the connection insecure. As is often the case with these situations, the problem is with an implementation, not the secure algorithm itself. Our friends over at Computerphile have a great video on the topic: ruclips.net/video/mYtvjijATa4/видео.html
I very much appreciate that posted this update; it again demonstrates that you're more into education than simply getting clicks.
Those expression should really have another "mod M".
+Axyron That was a typo, it should have been "(B^Y mod M)^X mod M" it was missing the second modulus.
Useless? How so?
You can slow the playback down, can't you? It's not too fast for me. But I have heard others mentioning changing the speed of playback of youtube videos in general.
As a total n00b in programming or encryption for some reason I understood the Debbie Hellman explanation over the paint trading analogy. Thanks.
I was confused due to being color blind and had to re watch that part, lol.
Comrade Dyatlov hows it going so far
This is probably one of the best Crash course videos ever made. Really great explanation and somehow more detailed than other ones while still explaining the concepts easily. This videos deserves praise.
The "Thanks cryptography" 👍👍 at the end was pure gold.
*_COME ON BRAIN!!!!_*
_404 Page not found_
Overload!.... HAHAHAHA!!!
I look forward to watching this every week. You guys at crash course are keen on the idea of the feynman technique. Making things as simple as possible. I find these videos on computers to be basically an overview of all the things I've studied over the years. It's a very complete and timely piece. Perhaps you guys may choose to go into more depth on some of these topics in the future. Anyway, these are a great introductory learning tool for those who are interested. Power to male and female programmers and tech nerds! While we ride the wave of the future.
Wow, this was actually the exact right speed to follow, awesome graphics and amazing good comparisons. I'm actually a little happier now!
i've been cracking my head open to understand how keys function for the past few weeks since uni started and you just explained it all very clearly with some paint.....insane and amazing, i thank you ALSO finally understanding the math that's behind these encryption techniques thank you so much
This is the best asymmetrical cryptography analogy I've seen so far! It makes so much sense to me. Thanks CC!
"Adding another level of... complexity" #trolled
I fell for it too
Tbh that whole intro and stuff is from complexity ssooo COPYRIGHT
I did not realize there was so much to a secure connection... Amazing! Thanks for the explanation!
Just waiting for that quantum computer to mess all of our encryption up.
We have to invent quantum cryptography then :D
Actually, we already did a long time ago.^^
en.wikipedia.org/wiki/Quantum_cryptography
Actually, the most devastating quantum attack (Shor) only breaks asymmetric encryption (RSA, DH key exchange). Grover can weaken AES, but that isn't nearly as bad (speedup by at most the square root). Other algorithms, including some asymmetric ones, might not be affected at all.
djb & Tanja Lange have a 32C3 talk ruclips.net/video/-LlkJZJ5DMQ/видео.html and a mostly readable 2017 paper, "Post-quantum cryptography".
No it won't
If quantum computer come to existence, then One-time Pad will be feasible to use
Your Public/Private key explanation was the best I have ever seen, now I understand it! Thank you so much.
It is uncanny how much this series is aligning with what I'm learning in my Defense Against the Dark Arts class haha! Sharing all of these with my professor! Keep 'em coming!
I think it would be a great idea to make a second video where you talk about vulnerabilities of cryptography!
For example, Diffie-Hellman is only secure against passive attacks; however you can fool both sides into thinking that a secure connection is established by a man-in-the-middle attack. There are different ways to eliminate this problem.
Also public keys need to be stored in a secure source. If an attacker is able to distribute his own public key, it will lead to problems.
There are many more examples, which could easily fill another video.
I loved this one, it was a great introduction, but I wish you would go into more detail, especially since it might give the impression that these algorithms have no flaws :)
Xappreviews yeah they didn't cover a really important part, the man in the middle attack, they should've mentioned certificates
I love this course, and I'd like to add a little more information (due to the fact that CC cannot cover everything in just 15 minutes).
First, when Carrie Ann says that one-way functions are "easy to do in one direction, but hard to reverse", "easy" and "hard" refer to computational complexity, specifically polynomial time problems. This means that the time needed to apply a one-way function must be small (a polynomial in the length of the argument of the function), but the time needed to reverse the computation must be awfully big.
Second, the existence of one-way functions is an open problem in computer science. Modular exponentiation is a candidate for being a one-way function: indeed, computing the function is easy, even for huge numbers, but the reverse (the modular discrete logarithm) is believed to be difficult (but it has not been proved!).
Ignacio Correa there is error in video
Ignacio Correa
NSA (no such agency) spends serious taxpayer money to preserve email
encryption/decryption using
the Cypher Chip ( ironically, iirc, proposed by Bill & Hillary
Clinton while in White House to preserve emails securely )
Sharing Key Info with NSA (WTF?)
"For a 128-bit keys, you'd need trillions of years to try every combination, even if you used every single computer on the planet today. So you better get started" XD
This was such an amazing explanation. Perfectly paced, great graphics, fun analogies, easy to understand, and very well spoken. Thank you so much for this!
That's by far the best explanation of asymmetric encryption (in particular, Diffie-Hellman key exchange) I've come across.
I'm taking a software engineering technical interview and wanted to brush up quickly on this stuff, thanks Crash Course 👍
Having a blue day? Keep Calm and Carrie Anne!
Seriously, she always cheers me up
They should sell this on a T-shirt.
When I read that in my brain, I suddenly realized Carrie Anne does sound like carry on, if you live in the north as I do...soooo Minnesotan, dontcha know eh?!
Banderi - OK OK you get a big ughhhhh ! for that...
In practical modular exponantiation you don't calculate the B^n before taking mod m since this number would be stupidly big and probably wont fit into memory. Instead you divide it into a series of taking power 2.
If n = 2k is even, then B^n = (B^2)^k.
If n = 2k+1 is odd, then B^n = B(B^2)^k.
If B^2 > m, let C = B^2 mod m, then and (B^2)^k mod m = (B^2 mod m)^k = C^k (Also B(B^2)^k mod m = B(B^2 mod m)^k = BC^k). It is quite easy to code this if you want to give it a try.
I have learnt more from a few Crash course videos than I did my entire XX years spent at school. Just goes to show education is not education its just there to make you pass tests, not to learn. Thanks CC. Thanks Alan Turing
It's not that simple. Sure, this is explained in an easy way, but our brains aren't capable of storing this information in a way that you can remember it easily in the future. These videos should in my opinion instead be seen as a support for the subject which you then learn through a more conventional way.
ratgreen no, you just don't recognise the skills you learnt in school
The videos give you a taste of these subjects, just a scratch on the surface. You need education to learn how to study properly and get as much knowledge as you need. Don't hate school, it's normal to feel that way, but it's a lot more important than you think :)
Hands down the best video on cryptography on RUclips. 12 minutes for expert level 😀
I love the flying toasters! Obscure reference that brings me back to the 90s PC computing world!
Really good explanation of how the fact that no secret key needs to be exchanged!
I've always thought there was something shifty about that Hank guy.
wow this is the first time I got my head around how public keys work, please do more videos on the subject!
Finally I understand the key exchange, thanks to your color explanation. Very nice :)
Wow, I knew a few basics of encryption but was always quite hazy on the details. This was so informative! Thanks! :D
Finally! An understandable explanation how prime numbers work in cryptography with color metaphor.
Very informative video!
Fantastic Video. I finally understand how key exchange works. i always wondered how it can be secure if the keys need to be known to both parties. Now i know that! Thank you Carie-Anne!
I did a course on Cryptography and Information Security in my degree. I remember we touched upon DES and AES, and other advanced topics such as elliptic curves.
An interesting addition:
The first version of Enigma, the one which had only 3 rotors has been cracked even before the beginning of WWII by 3 Polish mathematicians. Unfortunately their methods became obsolete the moment the 2 additional rotors have been added to the machine, making it again impossible do decipher Enigma until the Turing's breakthrough. (A commemorative memorial of the Polish input was placed in 2002 at Bletchley Park).
"so now you know all the _key_ parts of modern cryptography" , this woman makes me crease omg im dying thanks cryptography for bringing this woman to me the puns are fantastic
I just love the way you explain everything!! Amazing course.
the wife has got the best cryptography, I dont understand her at all!
don't they all?
The real question is, who is she encrypting it for? 😏😏😏
She is hashing, not encrypting
Well a brute force attack will get you divorced I think so I don't recommend that!
How about taking her on a phishing trip with you- If you promise to cook the catch and clean the dishes afterwards you may net that critical algorithm!
Boomer humor
B^Y mod M to the X is not equivelent to B^X mod M to the Y. You have to take the modulo afterwards, and it only works for very specific bases and modulos.
We can more appreciate this by citing non-electronic ciphering/deciphering.. Good job mentioning Ceasar and Columnar
I love this channel! Awesome videos
I really liked both the video's content and the narrator - She's great! Good job! :)
ive watched a GAZILLION videos on cryptography... and i always had the sensation that some part was missing, that it didnt make total sense.. i thought i was just dumb, but FINALLY someone explained it completely and clearly! best explanation EVER. all other videos forget to tell the public key is used in conjunction to the private to create something new. thats key! (pun intended)
awesome job! this crash course is truly a masterpiece
The paint analogy was very useful
The bit about key exchange was very informational.
9:43 That is not mathematically equivalent... See for example: b = 4, x = 3, y = 7, m = 18
You need to take the modulo M of the result to get the same key. In the wikipedia article about that topic they say, that b needs to be a generator of the group of m , but I haven't tried it out yet.
Something you should have mentioned is that cryptography is only perfectly secure in theory - in the real world there are side channel attacks. Id explain it but I think that people who read this comment will have more fun researching this themselves ;)
Yep and side channel attacks are the only crypanalysis attacks out there. There isn't a single other more common attack.
thanks for the awesome videos. this is one of my favourite channels on youtube.
can you please do a series on Criminology and also Linguistics? thanks :)
I love simple explanations of complicated things, awesome video
This series is so awesome!
Tip: if you want to learn something, change the speed to .75
With the modular exponent example if somebody in the middle intercepts both sides of the communication they get the same value for the shared key - i'm sure the NSA is already doing this, they already compromised RSA security and functions with backdoors to decrypt without using brute force.
I fall in love at the end of the video~
Awesome video, thank you!
I can finally understand a little bit of cryptography.
I'm pretty bad at math and could understand this , well done. Although it does beg the question of why people consider math a requirement when the principles have more to do with logic than mathematics.
The amount of times hank has been attacked lmao
Hey may need to go to -Hotel- Healthcare Trivago.
Hot oil in the medieval ages wasn't used like you see it in Hollywood.
Oil was an expensive resources so what they would actually do is pour boiling water or extremely hot sand. Yes there was some occasions where it happened but that's an exception not the norm as it's portrayed.
Thanks, this episode really helped me.
Love these videos!
Have a good day everyone!
If my understanding is correct, it is crucial to the color-analogy that even if an eavesdropper has the shared color, and could theoretically "subtract" it from the two transmitted mixed colors to get the two secret colors, this subtraction-process is what would be prohibitively cumbersome?
I have this same question in mind. It seems simple enough to solve. Let me know if you find the answer to your question.
Perfect description
This nice explanation you have given. Hope all needs to watch it.
OK, managing to get the Wilhelm Scream into a cryptography is an accomplishment in itself… \o/
Great episode!
so proud when turing came up :)
Cracking open the code book with the bois
You forgot to show the part where John has to call Daniel Biss and ask what an exponent is.
Now that's *harsh* LMAO
Alan Turing blinking on the bug of engima was hilarious
Nice Code Club shout-out - Claire and Linda will be happy :-).
3:20, nueral network 😅
hey carrie (or anyone else if you would like to help) , I wanted to understand that private key sharing( at 10:00) , so i thought of making myself a simple practical example out of it, but my calculations say your equation from 10:00 is not correct . can you please have a look?
So If i have to transmit character '"P' (ascii 80 )from Boy A to B:
>> I assumed x=2 would be private key of A and y=3 would be private key of B)
>> I assumed my public key function as cipher(x,y)= (3^x % 7)^y
Thus:
- A would first Transfer cipher_a = 3^2%7 = 2 to B
- B would first Transfer cipher_ a= 3^3%7 = 6 to A
>> I assumed my publically available encryptor function as encrypted_text = cipher(B) ^x
+ ascii(character)
- Thus, A would transfer the encrypted character 'P' to be as e_t = (6)^2+80 = 106
>> I assumed my publically available decryptor function as ascii(character) = encrypted_text - cipher(A) ^y
- Thus, B would recieve the value as val = 106- (2)^3 = 97 , which is not equal to our original value of 80
Thus (B^y mod M)^x != (B^x mod M)^y != (B^xy mod M)
But rather
(B^yx mod M^x) == (B^xy mod M^y) but != B^xy %M
Is this right?
She forgot to add a extra mod on both sides 🙄
You have very good videos, however i suggest you either decrease the amount or info or make a longer video. It’s a bit difficult following you with normal playback speed
Amazing video!
Can you also make a video on modern cryptography, focusing more on all the cool things not directly related to encryption? Hardly anyone knows there's so much more to cryptography than that.
Only one minor objection: please don't reiterate the myth of million-year cryptoanalysis. Assuming Moore's law to continue, even the strongest encryptions in use today can be broken within decades.
Thank you very very very much for this great video. It helped me a lot for understanding the fundamentals and history of Cryptography. :)
Nice video, I was really hoping for an illustration of one time pads though.
This is so interesting, wow!
great video!
you can check the color(private key) on the apps code maybe?
0:30 Wilhelm scream!
This is a great video!
I like how Hank is the bad guy here 😂
big fans of this series of videos, currently pursuing a diploma in IT.
'd to know if there is any plan for making a video about quantum computing?
Great video guys!
The first person to break the enigma code was Marian Rejewski and his colleagues, Polish mathematician, and he did it in 1932 ! Before outbreak of WW2 and certainly before Alan Turing. That's sad you don't mention it.
So well explained ! Thanks a lot !
Episode on blockchain pretty please?
I was hoping you'd touch on PFS.
Love the Shirts
very informative . Good job!
There should be one more modulas after the results in getting key.
Guys, at 0:35 you used the picture of the monument dedicated to the 3 Polish mathematicians who first broke the Enigma cipher in 1932, making it possible for Turing et al. at Bletchley Park to proceed. Yet you didn't breathe a word of their contribution, nor did you even credit the photo (here it is on Wikipedia, recognizable by the digit order at the top: commons.wikimedia.org/wiki/File:Polish_cryptologists_breaking_Enigma_ciphers_monument_01.JPG ). I can understand that the English speaking world may be unwilling to break their tongues on names such as Różycki, but the complete erasure of the Polish contribution in ANY account of the Enigma-breaking is more than a little unfair.
Do you have any plans to do a future of computing video . Maybe have something about AI?
Way to go Carrie Anne!
at 4:20 how do we know for sure a letter can not repeat itself? Is there a proof or is it just experimental?
it was already complex topic and then you gave it to a woman to present that, God bless i could not get it at all.
Thank you for making me understand
EXCELLENT . Nawar
Amazing animations
I love this!