A question I get asked frequently is, “How did you learn cryptography?”
I could certainly tell everyone my history as a self-taught programmer who discovered cryptography when, after my website for my indie game projects kept getting hacked, I was introduced to cryptographic hash functions… but I suspect the question folks want answered is, “How would you recommend I learn cryptography?” rather than my cautionary tale about poorly-implemented password hash being a gateway bug.
The Traditional Ways to Learn
There are two traditional ways to learn cryptography.
If you want a book to augment your journey in either traditional path, I recommend Serious Cryptography by Jean-Philippe Aumasson.
The traditional academic way to learn cryptography involves a lot of self-study about number theory, linear algebra, discrete mathematics, probability, permutations, and field theory.
You’d typically start off with classical ciphers (Caesar, etc.) then work your way through the history of ciphers until you finally reach an introduction to the math underpinning RSA and Diffie-Hellman, and maybe taught about Schneier’s Law and cautioned to only use AES and SHA-2… and then you’re left to your own devices unless you pursue a degree in cryptography.
The end result of people carelessly exploring this path is a lot of designs like Telegram’s MTProto that do stupid things with exotic block cipher modes and misusing vanilla cryptographic hash functions as message authentication codes; often with textbook a.k.a. unpadded RSA, AES in ECB, CBC, or some rarely-used mode that the author had to write custom code to handle (using ECB mode under the hood), and (until recently) SHA-1.
People who decide to pursue cryptography as a serious academic discipline will not make these mistakes. They’re far too apt for the common mistakes. Instead, they run the risk of spending years involved in esoteric research about homomorphic encryption, cryptographic pairings, and other cool stuff that might not see real world deployment (outside of novel cryptocurrency hobby projects) for five or more years.
That is to say: Academia is a valid path to pursue, but it’s not for everyone.
If you want to explore this path, Cryptography I by Dan Boneh is a great starting point.
Security Industry-Driven Cryptography
The other traditional way to learn cryptography is to break existing cryptography implementations. This isn’t always as difficult as it may sound: Reverse engineering video games to defeat anti-cheat protections has led several of my friends into learning about cryptography.
There are also plenty of CTF events all year around, but they’re rarely a good cryptography learning exercise above what CryptoPals offers. (Though there are notable exceptions.)
A Practical Approach to Learning Cryptography
If you’re coming from a computer programming background and want to learn cryptography, the traditional approaches carry the risk of Reasoning By Lego.
Instead, the approach I recommend is to start gaining experience with the safest, highest-level libraries and then slowly working your way down into the details.
This approach has two benefits:
- If you have to implement something while you’re still learning, your knowledge and experience is stilted towards “use something safe and secure” not “hack together something with Blowfish in ECB mode and MD5 because they’re familiar”.
- You can let your own curiosity guide your education rather than follow someone else’s study guide.
Super Easy Mode: DholeCrypto
Disclaimer: This is my project.
I designed Dhole Crypto for securing my own projects without increasing the cognitive load of anyone reviewing my code.
If you’re an experienced programmer, you should be able to successfully use Dhole Crypto in a Node.js/PHP project. If it does not come easy, that is a bug that should be fixed immediately.
Easy Mode: Libsodium
Using libsodium is slightly more involved than Dhole Crypto: Now you have to know what a nonce is, and take care to manage them carefully.
Advantage: Your code will be faster than if you used Dhole Crypto.
Libsodium is still pretty easy. If you use this cheat sheet, you can implement something secure without much effort. If you deviate from the cheat sheet, pay careful attention to the documentation.
If you’re writing system software (i.e. programming in C), libsodium is an incredibly easy-to-use library.
Moderate Difficulty: Implementing Protocols
Since you have trusted implementations to test your construction against, this should be a comparatively low-risk effort (assuming the primitive implementations are also secure), but it’s not one that should be undertaken without all of the prior experience.
Note: At this stage you are not implementing the primitives, just using them.
Hard Difficulty: Designing Protocols and Constructions
To distinguish: TLS and Noise are protocols. AES-GCM and XChaCha20-Poly1305 are constructions.
Once you’ve implemented protocols and constructions, the next step in your self-education is to design new ones.
Maybe you want to combine XChaCha20 with a MAC based on the BLAKE3 hash function, with some sort of SIV to make the whole shebang nonce-misuse resistant?
You wouldn’t want to dive headfirst into cryptography protocol/construction design without all of the prior experience.
Very Hard Mode: Implementing Cryptographic Primitives
It’s not so much that cryptography primitives are hard to implement. You could fit RC4 in a tweet before they raised the character limit to 280. (Don’t use RC4 though!)
The hard part is that they’re hard to implement securely. See also: LadderLeak.
Usually when you get to this stage in your education, you will have also picked up one or both of the traditional paths to augment your understanding. If not, you really should.
Nightmare Mode: Designing Cryptography Primitives
A lot of people like to dive straight into this stage early in their education. This usually ends in tears.
If you’ve mastered every step in my prescribed outline and pursued both of the traditional paths to the point that you have a novel published attack in a peer-reviewed journal (and mirrored on ePrint), then you’re probably ready for this stage.
Bonus: If you’re a furry and you become a cryptography expert, you can call yourself a cryptografur. If you had no other reason to learn cryptography, do it just for pun!
Header art by circuitslime.