So many times he has to ask for students to be quiet. His students should appreciate this subject, he's really good. We don't even have this subject in my alma mater.
That's simply not true. I don't even know why you'd think that. He has better English than some foreign professors, but not American professors. That's simply because English is very common in Germany.
@@chrism7574 He's not talking about the Quality of the English, but about the coherency of it. You can have excellent well spoken english but still fail at actually teaching with it.
dunno if anyone gives a shit but if you are stoned like me atm you can stream all of the new series on instaflixxer. Have been streaming with my gf during the lockdown =)
If only i could've studied in your university. Im pretty sure all professors are absolutely top notch. Having to tell people to not talk during the lecture is .... just... i don't even know. Lecture is so so interesting, so brilliant, would've been drowning myself in coffee and listening with both my ears. Much thanks for your work professor.
Prof. Paar NOTHING boring about your class. You are a great and excellent teacher. THANK YOU for all the videos of your class It has sparked my interest and passion for cryptography. Best wishes for you and family. You don't have to worry about me sleeping in your class. I'm ALWAYS AWAKE!
It was the opposite for me: I came here to learn about Galois fields, and I learnt how the AES internals really work as a bonus :) (to this day, I only knew how to do the computations by using precalculated "multiplication tables" - now I can conjure up those tables myself :) )
Thank you Prof Paar for making a whole lecture series on cryptography. Your explanation is super clear and easy to understand. This is saving me a lot of hours reading my textbook.
This was an absolutely brilliant lecture. I had been trying to understand the galois theory used in AES for a while and this lecture just saved me. Thank you so much.
this is not galois theory. galois theory is a different beast and a branch of maths. what he did is presenting the basic arithmetic properties of GF(2^m), which are sometimes called Galois fields
Thank you so much for putting your course online, Prof. Paar. You are an outstanding teacher. I just ordered your book and eagerly waiting for it to be delivered.
Thank you, this lecture was really helpful. I am giving a short presentation in class on Reed Solomon codes, but didn't fully understand Galois fields, and this helped tremendously!
Such an interesting lecture. Came here to get a basic idea on finite field, but stayed on till the end. It is almost the end of my Semester at Unimleb (Course: Crypto) and I have an exam next week but it was only until today that I was really able to understand a lot more than what I wanted to know. Thanks, Professor Paar (many thumbs up).
A brilliant brilliant explanation ....thank you so much. Teachers like you are the reason why education is so much fun and interesting. Otherwise the teachers in universities like mumbai university make the students hate the subject so that they have to put less efforts in classrooms .
ich moeche darauf hinweisen, dass ich, waehrend der youtube-lektion, wirklich nicht geredet habe! :-) Aber ernsthaft: wie viele anderen hier kommentierten, haben Sie auch mich endlich ueber das Mysterium Galois Fields verklaert. Vielen Dank, Herr Paar! Sie verdeinen Respekt!
Wow.. it's really amazing as well as interesting Introduction to Galois Fields (which was helpful to understand mathematics involved behind RAID 6 as well.)
Good lecturer. Well organized presentation. Good video production. Good audio. Easy to read the chalk board. I wish all the class room videos could be this good. This should be the example of the industry standard for filming a classroom lecture. I have watched the entire series and I am pleased that the mystery of encryption is gone from my mind. I've tried to watch other lecture series but disappointed that the production was not as good as this one.
Excellent lecture ! Just what I needed to fill in the missing gaps in my understanding of AES. Tried to understand the material from several sources, but nowhere was it as clear as the professor explains in this video. Worth the 90 minutes spent.
Fun fact: this can also help you understand CRC (Cyclic Redundancy Check) checksums as a bonus :) (AES could be thought of as a glorified version of a CRC)
My current professor has great understanding, but lacks the ability to communicate the concepts well. Thank you so much for laying out these tough topics in a way that is easy to understand!
Man today I just chosed my subject for my presentation about different algorithms and I drawn "finite fields and it's appliance in cryptography" and since 4 hours I am sitting listening and reading about them and I was so angry at the beginning that I had such hard topic but now I feel really entertained lol I wish I had a teacher like you in my univeristy. Greets
Thank you Dr. Parr, I'm not joking when I say you saved my buttocks. I am using the same book in my Crypto course but was baffled by how exactly reduction takes place after my professor's explanation. I watched your course from start to finish, took notes, and now I understand. Thank you! Now, on to the Extended Euclidean Algorithm. Thank you again Dr. Pharr, this was an excellent lecture.
Also, not all lecturers are as good as the ones found on RUclips. There are lectures by legends in some fields (think Reinforcement Learning by Dr. David Silver)
The video was really very helpful. We would love to listen about the irreducible polynomials p(x) from you immediately after the term is introduced in lecture-4 as primitive polynomial
Thank you for a good and interesting lecture. One suggestion and one question. Suggestion: when discussing Galois say from the beginning that the definition is applicable to modular math. It feels like a cheap-shot to just bring it up at the end, with the buildup having viewer puzzled how the fields could possibly work in non-modular math. The question is this: in modular math with numbers the size of the set was used for modulation (mod2 for 0 and 1; modP for 0,1,2...P-1) What is the justification to be using a prime polynomial rather that a set size with polynomial modulation? Or perhaps the Largest polynomial+1, so for 3-bit case would be X^2+X+1+1=X^2+X? Thanks again for interesting lecture.
I loved your lecture ,sir ,Thanks a lot. I am trying to guess the words in German would be "Don't speak for the video" or similar ,Also you made me enjoy cryptography a lot,once again Thanks Prof.Paar :D .
Thank you so much for the lecture. I have one question please. How can compute the coefficients from GF(2^8) and compute the inverse of the coefficient?
When you draw the diagram of the structures in the beginning, you should draw the groups as the largest circle, and as you add structure/operations it makes the set of elements smaller and smaller i.e. all fields are rings and all rings are groups. The way you draw it makes it seems like all groups and rings are fields, which is nonsense. Very interesting though:)
I see your point and that could actually help some students. On the other hand, I always pictured the structured as follows: every ring contains a group and every field contains a ring and groups. Thus, I am not sure what the best approach is pedagogically speaking. Thanks for your thoughts, though. christof
If that was the case, then the diagram should have contained two instances of the group ;) (one for addition, the other one for multiplication), pretty much sharing the common set (except 0 being excluded from the multiplicative group's set). Another possible way to draw it that could be more intuitive to IT engineers could be to use an inheritance diagram similar to those used in programming languages like C++ or Java ;)
@@introductiontocryptography4223 , in addition to your point, making the group the largest circle might also defy the fact that the group is defined by only one operation. Because you will end up having all the other operations contained in the bigger circle which represents a group. I therefore agree more with your own structure. Thanks a lot for this brilliant lecture.
Excellent lecture! You even get help to develop an intuition for finite fields. Only someone with deep knowledge can make something this difficult seem simple. Recommend watching the lecture in x1.5 speed.
Such shame he has to tell his students to be quiet and pay attention. This lecturer is brilliant! 10x better than ours.
Yeah... here where I live he could simply smack them through their heads or kick off the classroom :q
Yeah, the students are fucking dickheads
Had I had a teacher like Prof. Paar, I would have absolutely devoted to my study.
Normally it's really quiet compared to other lectures, however sometimes a few people talk and he will immediately call them out.
students are propably also discussing the course material.It happens
So many times he has to ask for students to be quiet.
His students should appreciate this subject, he's really good. We don't even have this subject in my alma mater.
4:45 Intro to Finite Fields (Galois Field)
29:20 Prime Fields (GF(p))
44:20 Extension Fields (GF(p^m))
Thank you!,!
thank you
At 17:00 "Don't work through chapter four by yourself". Wiser words never, ever spoken.
This Prof who I suspect has a native language of German is more coherent than most native English Profs in the USA. Excellent course
That's simply not true. I don't even know why you'd think that.
He has better English than some foreign professors, but not American professors. That's simply because English is very common in Germany.
@@chrism7574 He's not talking about the Quality of the English, but about the coherency of it. You can have excellent well spoken english but still fail at actually teaching with it.
This guy is unable to make two sentences together without throwing in a word in German
dunno if anyone gives a shit but if you are stoned like me atm you can stream all of the new series on instaflixxer. Have been streaming with my gf during the lockdown =)
@Major Malachi Yup, have been watching on InstaFlixxer for since december myself =)
If only i could've studied in your university. Im pretty sure all professors are absolutely top notch. Having to tell people to not talk during the lecture is .... just... i don't even know. Lecture is so so interesting, so brilliant, would've been drowning myself in coffee and listening with both my ears. Much thanks for your work professor.
Prof. Paar NOTHING boring about your class. You are a great and excellent teacher. THANK YOU for all the videos of your class It has sparked my interest and passion for cryptography. Best wishes for you and family. You don't have to worry about me sleeping in your class. I'm ALWAYS AWAKE!
Came here to learn about AES, and learned a lot of Math. Not disappointed :). Thumbs up for your lecture.
It was the opposite for me: I came here to learn about Galois fields, and I learnt how the AES internals really work as a bonus :) (to this day, I only knew how to do the computations by using precalculated "multiplication tables" - now I can conjure up those tables myself :) )
Thank you Prof Paar for making a whole lecture series on cryptography. Your explanation is super clear and easy to understand. This is saving me a lot of hours reading my textbook.
This was an absolutely brilliant lecture. I had been trying to understand the galois theory used in AES for a while and this lecture just saved me. Thank you so much.
this is not galois theory. galois theory is a different beast and a branch of maths. what he did is presenting the basic arithmetic properties of GF(2^m), which are sometimes called Galois fields
Thank you so much for putting your course online, Prof. Paar. You are an outstanding teacher. I just ordered your book and eagerly waiting for it to be delivered.
Best(easiest) explanation for fields I have ever heard! Thanks!
Much better than my professor. Going to continue watching the series Prof. Paar. Thanks for uploading.
Extraordinary! A very complex theory handled in a very logical way in just 90 minutes. Thank you 🙏
Thank you, this lecture was really helpful. I am giving a short presentation in class on Reed Solomon codes, but didn't fully understand Galois fields, and this helped tremendously!
Really good supplement to my course at school that uses your book. Thank you for making these videos.
Such an interesting lecture. Came here to get a basic idea on finite field, but stayed on till the end. It is almost the end of my Semester at Unimleb (Course: Crypto) and I have an exam next week but it was only until today that I was really able to understand a lot more than what I wanted to know. Thanks, Professor Paar (many thumbs up).
Excellent explanation of GF, groups and rings. And I finally understand the reason for the "AES polynomial".
thank you very much. Clear presentation . I always look for clear explanations to watch and your presentation is very clear .
A brilliant brilliant explanation ....thank you so much. Teachers like you are the reason why education is so much fun and interesting. Otherwise the teachers in universities like mumbai university make the students hate the subject so that they have to put less efforts in classrooms .
This guy is awesome. Wish all my lecturers were like this guy.
Very good lecture. I don't get how someone would fall asleep by hearing about Galois Fields for the first time, it's so fascinating.
Excellent lecture. Highly proficient lecturer. Would recommend this lecture series to almost anyone.
Motivation AES 2:00
intro FF 5:00
prime field arithmetic 30:00
extension field arithmetic 45:00
ich moeche darauf hinweisen, dass ich, waehrend der youtube-lektion, wirklich nicht geredet habe! :-) Aber ernsthaft: wie viele anderen hier kommentierten, haben Sie auch mich endlich ueber das Mysterium Galois Fields verklaert. Vielen Dank, Herr Paar! Sie verdeinen Respekt!
Good explanations ! I liked the way you teach, looking forward to your other videos.
This material is exceptional and has helped me study for a undergrad fourth year course in cryptography.
Great teacher. I'd get a PhD if this guy was my advisor.
Great course, very well explained, a lot of useful info. Thanks a lot!
Wow.. it's really amazing as well as interesting Introduction to Galois Fields (which was helpful to understand mathematics involved behind RAID 6 as well.)
Wow - i am so glad i found this lecture. Danke Professor Paar!
Good lecturer. Well organized presentation. Good video production. Good audio.
Easy to read the chalk board.
I wish all the class room videos could be this good.
This should be the example of the industry standard for filming a classroom lecture.
I have watched the entire series and I am pleased that the mystery of encryption is gone from my mind.
I've tried to watch other lecture series but disappointed that the production was not as good as this one.
Awwww I want to learn about division! Damn lazy stupid undergrads! You guys were lucky to have this professor.
Thank you so much your a life saver. I really enjoyed your lecture, it helped me allot in understanding the mix columns step in AES
Legendary resource on RUclips, Thanks Prof!
Enjoyed the lesson. Excellent work. Thanks Prof. Paar
Excellent lecture !
Just what I needed to fill in the missing gaps in my understanding of AES.
Tried to understand the material from several sources, but nowhere was it as clear as the professor explains in this video.
Worth the 90 minutes spent.
Fun fact: this can also help you understand CRC (Cyclic Redundancy Check) checksums as a bonus :)
(AES could be thought of as a glorified version of a CRC)
My current professor has great understanding, but lacks the ability to communicate the concepts well. Thank you so much for laying out these tough topics in a way that is easy to understand!
That board cleaning was relaxing.
Superb explanation.. will follow for the full semester !!
Thank you so much. Your lecture helped me a lot to my final exam in next week :D
Thanks all the way from Cambridge University. I missed my last lecture but this definitely makes up for it!
had a tough time understanding....but wow this lecture is so good...now my concepts are crystal clear ...i have exams next week thanks sir...respect
thank you so much ....you finished one of my chapters in 90 minutes
Interesting lecture. Prof Paar did a lot of work in there! Thank you
Man today I just chosed my subject for my presentation about different algorithms and I drawn "finite fields and it's appliance in cryptography" and since 4 hours I am sitting listening and reading about them and I was so angry at the beginning that I had such hard topic but now I feel really entertained lol I wish I had a teacher like you in my univeristy. Greets
I would hit "thumb up" 1000 times if I could. Thank you very much, it was very helpful!
Such a great lecture. Thank you very much for uploading
Thank you Prof! Thank you very much for your brilliant lecture! :)
Can't believe this is a uni lecture. Last time I heard ''be quiet'' and 'dont fall asleep 'was in high school😵💫
I'm in high school and I find these fascinating such a shame that he has to ask his students to shut up
Thank you for this wonderful lecture, Mr. Paar.
Thank you! Wonderful teaching!
Thank you Dr. Parr, I'm not joking when I say you saved my buttocks. I am using the same book in my Crypto course but was baffled by how exactly reduction takes place after my professor's explanation. I watched your course from start to finish, took notes, and now I understand. Thank you! Now, on to the Extended Euclidean Algorithm. Thank you again Dr. Pharr, this was an excellent lecture.
Very helpful course! Big thanks for sharing.
This man is an American hero
Awesome lecture. Students are gifted
Excelent!! Thank you profesor.
Hello... Dr. Christof Paar ...Thank you so much i leaston you lucture on the You Tube its very Good..
Ironic that I skip all my actual classes but then spend hours watching stuff like this at home. Thank you for this and great job.
I do this too. i actually feel like i can learn better in my comfortable home space. What do you think is the reason why you do that?
Also, not all lecturers are as good as the ones found on RUclips. There are lectures by legends in some fields (think Reinforcement Learning by Dr. David Silver)
lol @ those two students fighting when he's cleaning the board
When was that?
At around 59:00
Thanks prof. paar for the lecture :)
The video was really very helpful. We would love to listen about the irreducible polynomials p(x) from you immediately after the term is introduced in lecture-4 as primitive polynomial
Thank you for the book and the lectures!
Fantastic lecture, thanks very much.
Way better than my professor...!
Amazing that junior undergrads get to learn this. So jealous of these kids!
Excellent course, thanks.
great great great explanation. Thank you
This REALLY helped. thank you so much
Really helped a lot.thanks professor...
A pleasure to watch, ty.
Love it when he talks about his past :D
cleared all my doubts about finite fields . danke
Thanks professor for this amazing lecture !
Thank you prof, learnt tons!
Wonderful lecture. Thank you.
Wow. Thank you so much. You just helped me to connect the dots :D
Best lesson on encryption ever.
Thank you sir ....great lecture
Thank you for a good and interesting lecture. One suggestion and one question. Suggestion: when discussing Galois say from the beginning that the definition is applicable to modular math. It feels like a cheap-shot to just bring it up at the end, with the buildup having viewer puzzled how the fields could possibly work in non-modular math. The question is this: in modular math with numbers the size of the set was used for modulation (mod2 for 0 and 1; modP for 0,1,2...P-1) What is the justification to be using a prime polynomial rather that a set size with polynomial modulation? Or perhaps the Largest polynomial+1, so for 3-bit case would be X^2+X+1+1=X^2+X? Thanks again for interesting lecture.
Such an amazing explanation, in india professor makes things complicated
Thank you for the super video.
Thanks.
perfect teacher
Thank you, so much!
very clear, thank you so much
Thank u so much prof for lecture, it was really amazing
Perfect . you helped me so much...
I loved your lecture ,sir ,Thanks a lot. I am trying to guess the words in German would be "Don't speak for the video" or similar ,Also you made me enjoy cryptography a lot,once again Thanks Prof.Paar :D .
Thank you professor!
Thank you so much for the lecture. I have one question please. How can compute the coefficients from GF(2^8) and compute the inverse of the coefficient?
Started with 8 and now going to learn about this Galois magic.
same, just finished this one but I think I'm off to Lec. 11 now, down the rabbit hole we go!
Wonderful explanation of GF(p^n), thank you
Thanks for the great explanation since I am looking for the answer about AES GCM message authentication ❤
When you draw the diagram of the structures in the beginning, you should draw the groups as the largest circle, and as you add structure/operations it makes the set of elements smaller and smaller i.e. all fields are rings and all rings are groups. The way you draw it makes it seems like all groups and rings are fields, which is nonsense. Very interesting though:)
I see your point and that could actually help some students. On the other hand, I always pictured the structured as follows: every ring contains a group and every field contains a ring and groups. Thus, I am not sure what the best approach is pedagogically speaking. Thanks for your thoughts, though. christof
If that was the case, then the diagram should have contained two instances of the group ;) (one for addition, the other one for multiplication), pretty much sharing the common set (except 0 being excluded from the multiplicative group's set).
Another possible way to draw it that could be more intuitive to IT engineers could be to use an inheritance diagram similar to those used in programming languages like C++ or Java ;)
Totally agree!
@@introductiontocryptography4223 , in addition to your point, making the group the largest circle might also defy the fact that the group is defined by only one operation. Because you will end up having all the other operations contained in the bigger circle which represents a group. I therefore agree more with your own structure. Thanks a lot for this brilliant lecture.
Thank you very much Professor..
Thank you for the lecture
Excellent lecture! You even get help to develop an intuition for finite fields. Only someone with deep knowledge can make something this difficult seem simple. Recommend watching the lecture in x1.5 speed.
Sir it's excellent explanation. Can you share how to find multiplicative inverse of a number in GF2,8
Thank you so much !!!