Introduction to blockchains and cryptocurrencies for the mathematically mature.

Question

I have spent several days off and on looking for a good introduction to blockchains and cryptocurrencies for someone with mathematical background but no specific computer science or cryptography background. I've had no real luck. All of the books I find are either targeting investors, who don't care about the mechanics and just want to make money, or experts, whose language I am unfamiliar with.

For example, I don't really know what a hash function is, but I am totally comfortable with number theory, combinatorics, probability, etc.

What is a good introduction to blockchain and cryptocurrencies for someone with a reasonably strong math background, but no domain specific knowledge?

A hash function is just a map that is computationally hard to invert. What else do you want to know? How is your background in computer science? — Zhen Lin, Jan 25 '22 at 05:41
@ZhenLin Don't read too much into that one example--I only provided that as an example of the sort of language barrier that a mathematician (without a CS background) might have in approaching crypto. My CS background is a basic knowledge of coding (mostly for numerical PDE and ODE), but no knowledge of the theory, especially as it pertains to cryptography. — Yly, Jan 25 '22 at 05:45
You might get better responses/advice posting this on a blockchain / crypto investing/ computer science/… Q&A site or forum because that’s where the experts are. — Adam Rubinson, Jan 25 '22 at 05:57
Try 3Blue1Brown's "But how does bitcoin actually work", https://www.youtube.com/watch?v=bBC-nXj3Ng4 He gives you a mathematician's view of crytopgraphy, digital signatures, etc. — Greg Thatcher, Jan 26 '22 at 17:23
Yan X. Zhang wrote a good overview article of the Mathematics related to blockchain. It is not exactly an introductory article, but some topics there that are related to cryptocurrency could appeal to you (e.g. to analyze CFMMs such as Uniswap you can use tools from convex optimization and avoid most of the CS part related to cryptography). — shamisen, Jan 27 '22 at 04:25

score 3 · Answer 1 · answered Jan 26 '22 at 13:08

I'd change your search to be on cryptography, rather than blockchain, as the hash function is where all the interesting maths is. There seem to be quite a few online lectures searching for "mathematics of cryptography". Just browsing books, Applied Cryptography by Bruce Schneier gets high reviews, and is apparently quite mathematical (including reviews telling you not to be afraid of the maths).

The rest of blockchain designs are the practical issues with having a distributed database. That could potentially be a very long rabbit hole. Outside of the obvious suggestions of books and tutorials on YouTube, the Morning Paper blog covered quite a few papers in this area, as one of his main interests. But this is aimed at computer scientists.

score 3 · Answer 2 · edited Jul 22 '22 at 08:01

First, download the errata of any book that you are going to read and print it and place it inside the book. If possible, in one pass edit the book for the errata.

For block chain;

Mastering Bitcoin Andreas M. AntonopoulosSecond Ed is almost a good way to start to learn the blockchain. The errata is here. Why it is almost is due to some incorrect terminology on the Elliptic curve. They call elliptic curve scalar multiplication as point multiplication and this confused many and we can still find more on the internet.
After this one can read Build Your Own Blockchain (Management for Professionals) for some other aspects of blockchain. I haven't seen an errata for this book.

Of course, those books are not talking much into the mathematical side of the blockchain. One may need to look see Hash functions, Elliptic Curves, Digital signatures like ECDSA, and some introduction to Grover and Shor's quantum algorithms.

For the Cryptography/Mathematical side;

Serious Cryptography A Practical Introduction to Modern Encryption by Jean-Philippe Aumasson is a gentle introduction with errata.
Cryptography Engineering: Design Principles and Practical Applications is a good book on the side of engineering, Niels Ferguson, Bruce Schneier, Tadayoshi Kohno. I couldn't locate errata. This is the new book as the same approach with Applied Cryptography ( as mentioned in the other answer) and one should not read this one, it may misguide you and it is old.
A more mathematical/probabilistic introduction is Introduction to Modern Cryptography: Third Edition, Jonathan Katz, Yehuda Lindell with errata.

Introduction to blockchains and cryptocurrencies for the mathematically mature.

2 Answers2