Post-quantum security, in full

Cryptography, before and after Shor

What each lock is made of, which ones a quantum computer opens, and what replaces them.

Ten topics, from why a secret can be safe at all to how you move a real system. Every worked number is small enough to check by hand and has been recomputed by a script; every size comes from the standards' own tables. It teaches the ideas underneath the tools on the post-quantum page. It does not replace advice for a system you run.

Why this course exists, and what you need

The Bitcoin page and the post-quantum page tell you what to do. This course tells you why: what a key, a hash and a signature each are, which of them a quantum computer opens (three) and which it only dents (two), and what the replacements cost. You need arithmetic and nothing more. The one operation that appears everywhere is working modulo a number, a clock that wraps around, and the first time it appears it is explained on the spot.

Each topic has the same four parts as the others on this site: a picture, the intuition, the mathematics, and where it actually runs. Each ends with a question you answer, and a correct answer marks the topic done and counts toward your Security rank.

Your progress: 0 of 10 understood

SecretsThree topics: what keeps a secret, and what a quantum computer does to the cheap half

Before the part that breaks, the part that does not. A secret needs a key and an open design, a fingerprint needs a one-way function, and both of those, the symmetric cipher and the hash, meet nothing worse than a square root.

01What a secret needs to surviveIf the attacker knows everything except the key, can a message still be safe? 02Hashes, the fingerprints inside everythingHow can a function be one-way, and does a quantum computer undo it? 03Does a quantum computer break AES?What does a square-root speedup do to a key?

Public keysThree topics: the locks anyone can close, and the one weak point they share

Public-key cryptography is what lets strangers talk safely, and it is the half a quantum computer breaks. These topics show how each lock works and what it rests on, using numbers small enough to follow, so that topic 07 can say exactly what Shor's algorithm does to them.

04How two strangers agree on a secretHow can a secret be made in public, in front of a listener? 05RSA, and its one weak pointWhy does a lock that anyone can close need a factoring problem to stay open only for you? 06What a signature or a certificate provesWhy does a break of signatures matter later than a break of encryption?

After ShorFour topics: what falls, what replaces it, and how you move

What Shor's algorithm takes and what it leaves, the two families of replacement (lattices and hashes) and what they weigh, and the order in which a real system moves. This is the section the tools on the post-quantum page put into practice.

07What Shor takes, and what it leavesWhich of the locks from topics 01 to 06 does a quantum computer open? 08Why lattices resist, and what they costWhat does a quantum computer have no trick for, and what does the replacement weigh? 09Signatures made from hashes aloneCan you sign with nothing but a hash function, and what does it cost? 10Migrating without breaking everythingWhere do you start, and what changes on the wire?

Where to go with this

Run the ideas on your own material: the Quick Check reads a certificate or a domain, the Inventory reads your own keys, the Harvest Clock applies topic 06's rule with your numbers, and the Sequencer orders a migration. To play instead of read: Q-Day Command, Lattice Heist and Shor's Clockwork. The Secure hub collects all of it.