Cryptography from the Ground Up

“One of the most interesting and useful things computers can do for us is cryptography. We can hide messages, validate identities, and even build entire trustless distributed systems. Cryptography not only defines our modern world, but is a big part of how we will build the world of the future.

However, unless you want to dedicate years and a PhD to studying the subject, the actual workings of cryptography can be hard to learn. It can involve a lot of pitfalls and if you dare build from scratch, you are bound to make a fool of yourself. Why?

In my opinion, it comes down to history. Cryptography has had centuries of methods that have been made, broken, and remade again. Most tutorials on cryptography focus on the what: do this, don’t do that, follow the rules. But they skip over the why: why do we do the things we do? What are we trying to avoid?

To understand the why, we need to understand how we got here in the first place. And to do that, let’s set computers to the side for the moment and delve into the world of classical cryptography.”

Math: Ambiguity & Order of Operations

“The real answer, the one I believe any mathematician, physicist, engineer, other number-cruncher would tell you is to make sure your
expressions aren’t ambiguous. There’s no extra charge for another set of parentheses. Just toss them in. If you want the answer to be 16, write (8÷2)(2+2). If you want it to be 1, write 8÷(2(2+2)). Problem solved.”

—Evelyn Lamb, “The Only Way to Win Is Not to Play the Game.” Scientific American. August 3, 2019.

Quantumcomputing For The Very Curious

“This essay explains how quantum computers work. It’s not a survey essay, or a popularization based on hand-wavy analogies. We’re going to dig down deep so you understand the details of quantum computing. Along the way, we’ll also learn the basic principles of quantum mechanics, since those are required to understand quantum computation.

Learning this material is challenging. Quantum computing and quantum mechanics are famously ‘hard’ subjects, often presented as mysterious and forbidding. If this were a conventional essay, chances are that you’d rapidly forget the material. But the essay is also an experiment in the essay form. As I’ll explain in detail below the essay incorporates new user interface ideas to help you remember what you read. That may sound surprising, but uses a well-validated idea from cognitive science known as spaced-repetition testing. More detail on how it works below. The upshot is that anyone who is curious and determined can understand quantum computing deeply and for the long term.”

Andy Matuschak and Michael Nielsen. “Quantumcomputing For The Very Curious.” March 18, 2019.

Looks like I’m going to have to brush up on my math.

Greg Egan and the Permutation Problem

“Then on September 26 of this year, the mathematician John Baez of the University of California, Riverside, posted on Twitter about Houston’s 2014 finding, as part of a series of tweets about apparent mathematical patterns that fail. His tweet caught the eye of Egan, who was a mathematics major decades ago, before he launched an award-winning career as a science fiction novelist (his breakthrough 1994 novel, in a happy coincidence, was called Permutation City). “I’ve never stopped being interested in ,” Egan wrote by email.

Egan wondered if it was possible to construct superpermutations even shorter than Houston’s. He scoured the literature for papers on how to construct short paths through permutation networks, and after a few weeks found exactly what he needed. Within a day or two, he had come up with a new upper bound on the length of the shortest superpermutation for n symbols: n! + (n-1)! + (n-2)! + (n-3)! + n-3. It’s similar to the old factorial formula, but with many terms removed.”

—Erica Klarreich. “Mystery Math Whiz and Novelist Advance Permutation Problem.” Quanta. November 5, 2018.

Greg Egan’s hard sci-fi novels are amazing. Axiomatic is a collection of short stories that can give you a sense of what to expect. Read Diaspora if you want to jump right into the deep end. Read Quarantine if you want to take on a series.