Cryptography for Beginners
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- Опубліковано 26 кві 2024
- This is a book which I used for a course long ago. It is a very good book and I think a beginner could use it to learn some Cryptography. It is called Introduction to Cryptography with Coding Theory and it was written by Trappe and Washington.
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Thank you:)
I think it's one of the hardest math subjects.
You really have to love it to get through.
Kudos for those who dedicate their lives for cryptography.
I really love Joshua Holden's The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption. It's not a textbook, but the conceptual explanations are great for an introduction.
Reading that right now. Been great
Cryptography is amazing, I am about to start a PhD in post quantum cryptography and I just finished a project building a library including Kyber and Dilithium as well as a full AES implementation, I wish more people would appreciate it for what it is and all the heavy lifting it is doing behind the scenes.
It's always great to see people discussing the topics they love. Cryptography, being the future, those who delve into this subject significantly increase their chances of success in life.
Arizona State University has an entire certificate for cryptography within the school of mathematical and statistical sciences. Requires two semesters of cryptography at the 400 level, abstract algebra, number theory, and a few electives in advanced linear, group theory, etc.
I took almost all the electives and abstract algebra but sadly i didn't get the chance to take number theory or either of the cryptography classes. Great stuff math sorcerer!
Thank you so much for your videos! I was so scared of mathematics in grammar school and that fear thwarted my career in astronomy. I’ve spent so many years mad at myself but since I started watching your videos and buying textbooks, I can’t believe the progress I am making!
This is a fantastic book that goes straight to the point. Obviously this is a beginner's text but still I kinda wish more of these topics were common knowledge for people that supposedly work in "crypto."
Thanks, Mr. Sorcerer. The third edition covers cryptocurrencies.
I had the pleasure of having Lawrence Washington for Cryptography at the University of Maryland. One of the best professors I ever had. You could really tell how passionate he was about Cryptography.
Oh wow! Thanks for sharing this!!
One of the most underrated areas of math!
Always love your videos! Your love for the subject is obviously genuine and infectious.
Took a grad-course in Cryptography looking at this very stuff last year and found the mathematics super interesting and neat. I'm a CS student but have been more on the theoretical side so the mathematics were not out of reach for me. Plus the course got me more familiar using mathematical libraries like Sage. On top of that looking at all of these cryptography systems has ended up being useful as I just started a job doing some systems admin work and cybersecurity is a huge component of my company's day to day tasks.
I appreciate math so much more because of you.
Oh the old Wellington Cipher. That hasn't been used in probably a hundred years. The Wellington Cipher, a lesser-known historical encryption method, was named after Arthur Wellesley, the 1st Duke of Wellington. Used in the early 19th century, this cipher was employed during the Napoleonic Wars for secure military communications. The cipher itself hasn't been in use for around 100 years, largely due to advancements in cryptographic techniques and technology.
I got this from your last video, totally worth the $$. I love how it shows you a converter program you can do w/ pencil and paper right off the bat. I never saw congruences before, modes yes, but we never spent much time on modes. I'm working on Finnegans Wake atm & my own book, but I'll get back to that later for sure.
Since you mentioned having a teacher, not many are able to self-teach as effectively as with a teacher. Teachers may or may not (usually not due to time constraints) go over every single detail in the book, but that's not sine qua non. A good teacher will give you footholds into key sections of the mountain of knowledge that comes with well-written books, even average books like the Zill DE. Once you have those and take good notes, you can use the answer key to pull up practically everything else you would need from the uncovered sections of the book. At least that's how I am, I just need anchor points, I can get the rest if I need it later once I have those footholds.
You were mentioning breaking bitcoin, I saw somewhere they're working on getting 256-bit encryption going where we currently use only 128, and that's gotten us this far. I doubt anything will break 256.
I watched the youtube lectures of a German professor (Christof Paar) on cryptology and also bought his book (Understanding Cryptography). He was fun to watch especially when he caught students sleeping during his lectures. Class was in English at some German University. The hardcore book on the subject is "Applied Cryptography" by Bruce Schneier.
One nice introductory popular science book on cryptography is Simon Singh's 'The Code Book'
Just started reading this the other day, definitely an enjoyable read
I have that book and I LOVE it!!!
An excellent read, though I think the book being reviewed here goes more deeply into the nuts and bolts of cryptography.
@@jimsimpson1006 You are right. I might see if I can obtain a copy somehow since I am struggling to understand the ins and outs of cybersecurity.
Elliptic curves look like third order systems, which can be expressed with an exponential-style of expression, and exponentials have sinusoidal properties, possibly making them susceptible to sinusoidal analog quantum computers.
I hate math but your videos causes a spark within my mind so hopefully the math spark can from into a math inferno
In every crypto course I ever studied the first thing they say is "never make your own" the short version they teach about crypto but then say only use the tried and true released versions.
I played around a bit with cryptography when I was taking a course in Number Theory. I had already studied linear and abstract algebra. Normally in my Mathematical endeavors I tend to avoid applications and focus on the "pure / abstract" math. However, Cryptography is one application that I would like to study in greater depth I am interested in taking an course (online or in-classroom) on Cryptography or else obtaining a good textbook and doing it as a self-study.
This is right up my alley thanks for the recommend!
Fundamentally, all cryptographic algorithms ( other than those based on elliptic curves ) are based on prime number theory.
The basic idea is that it's easy to multiply two large prime numbers and get a much larger number that has only two factors ( other than 1 ), but extremely hard to factorize the large number to get it's factors. If one of the factors is a public key, the other can be immediately verified to be a private key by mere division.
In elliptic curves, the interesting fact is that a line parallel to the y axis can intersect the elliptic curves in zero, one or Max two points. But a line not parallel to the y axis can intersect the curve in a maximum of three points.
Therefore, given a point on the elliptic curve, it's trivial to check whether another specified point could represent an intersecting line that also lies on the curve.
Here, one point could be a private key and the other point is the public key.
But if you only have the public key ( as is usually the case ! ), you need to try millions of points to see if it could represent the private key and that's a discrete log math problem... ( My two cents take... )
now you got me interested
After I got my graduate degree in Mathematics, I started on my graduate degree in Computer Science. In my final semester of my graduate work in Computer Science I took an elective course in Cryptography and we covered all those topics you pointed out. One thing I remember the most was the the factoring of huge numbers (product of 2 huge primes) via elliptic curve attacks. The professor was a professor of computer science at the university, but his PhD was in Mathematics and his field of study was Applied Number Theory and Cryptography. He was one bright person and was the textbook, stereotypical Math/Comp. Sci professor. Had glasses, had messy hair, was eccentric, wore button down shirts with a front shirt pocket and had a pocket protector while also keeping a couple pencils/pens in his shirt pocket. For the course, we didn't use a real textbook. We used the professor's own notes that were printed out and placed in a soft-bound binder. Essentially it was an unofficial book that the professor wrote but never bothered getting published. I still have it somewhere. That was in 1993 when I took that course. It was an elective computer science course and I think only 4 people took the course. I was the only one, out of the 4, who had a graduate degree in mathematics. So, I didn't struggle with the mathematics part of the course. Concurrently, during the same semester, I was taking a graduate Computer Networks Systems course that was taught by another professor and one of the topics in that course was Network Security and we were assigned a project that involved some cryptography. I remember I used some of the stuff I was learning in Cryptography and applied it to my Network Security project. It had to do with encrypting/decrypting messages via a Network System. IIRC, it involved 256-bit encryption techniques. Remember writing a program (in C) that did all the calculations for the encryption/decryption. The 30+ years since I took Cryptography, I know there have been more leaps made in the field and some of the encryption/decryption techniques that were considered secure back then are no longer considered secure now due to the speed of advanced hardware used in computers now (mostly the encryption/decryption key sizes affected by brute force attacks.)
With due respect, do you work in tech?
How can I contact you? I have a complex math problem.
Dang I see so one of the methods cryptography uses is matrices, hm. I'm used to matrix premultiplication of multiple matrices and taking the inverse to project onto a vector as the answer as well as getting the sandwich estimators from covariance diagonal matrices. But I know it's mainly abstract algebra and number theory.
Page 50: Enigma!
When worlds of quantum mechanics of a computable world collide with the world of relativity and its world of the space-time continuum.
I didn't searched for this, I was already subscribed to you from some time, I didn't even asked for this, and just today I was learning about cryptography on Google, this video came today
HOW IS EVERYTIME EVERYTHING HAPPENS RELATED TO MY LIFE ?
I AM SURE I AM IN A SIMULATION
you are the main character
Nah. Most probably just the recommending system doing its job.
Wake up. This isnt real. Look your hands
The Math Sorcerer heard that you were interested in cryptography today so he made this for you real quick
@@CategoryTheorist The math sorcerer read his mind through the internets on the youtubes and created this just for him.
Even worse they made a 3rd edition recently that I really want, but their publishers make it really super hard / expensive to just get the book. They really want you to "rent" it (wtf?) or get the ebook, they hardly want you to have the binding and paper -_- As a private hobbiest not in the US it makes no sense for me to rent the physical book from them.
I believe a lot of the new post-quantum crypto systems (which are still being finalized by NIST, hopefully without backdoors) are based on lattice systems. I don't know any more than those buzzwords lol
Sir could you please suggest math truoks to crack jee advanced (indias toughest exam)
How do you remember all that you have learned through the years, do you have use that knowledge a long the way?
It looks like a common book. Under $5 on Abe books, hardcover.
If you master the mathematics of cryptography, you master cybersecurity, well one side of computer science, then you have assembly language. I wonder if cryptography is discrete like number theory or like maybe even some of abstract algebra? Jk.
I learnt absolutely zero about "cryptography for beginners" from this video. The only information is that you had a really cool teacher and that you have a rather interesting textbook that is hard to get.
agreed, "my 1 course in crytogragraphy" better title
did you expect him to read the whole thing...?
@@coriollis Of course not. I just expected that the video content was in some way related to the title , which it clearly wasn't.
U have a whatapp group
Why do I know about cryptography? 🤨 I must of learnt it somewhere
✌🏻👼🏻🤟🏻
Cryptocurrency for Beginners: Get in First. Sell at the Top. If you want to buy back in at the Bottom, wait until Zero.
this is math, not digital currency trading stategies.
Buy high sell low
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Wizard, i think everyone should have Bitcoin and Etherum in there portfolio.
They said the Zodiac really liked cryptography.
Quantum computing is the future.
Matrices, my math education stopped at them 🧮