Cryptography for Beginners

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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[philmts]

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.

[surrealistidealist]

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.

[drwhackadoodle]

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.

[juliancastrence]

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.

[TheInterceptGuy]

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.

[project-alc]

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!

[pilotpeego]

I appreciate math so much more because of you.

[nubius]

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."

[mistervacation]

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.

[Kimwilliams]

One nice introductory popular science book on cryptography is Simon Singh's 'The Code Book'

[LydellAaron]

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.

[RageRabbitGames]

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.

[billylee]

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.

[tbg-brawlstars]

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

[gmcenroe]

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.

[Douchemaster_McChest]

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.)

[SequinBrain]

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.

[RK_Stats]

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... )

[WitchidWitchid]

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.

[raxirex]

One of the most underrated areas of math!