Primer

Volume VII · 00 · The lock

Volume VII · Crypto

One-way functions, RSA, the discrete log — and the stories Shor makes false.

Crypto is a one-way function plus a story about what is hard. RSA’s story is factoring. Diffie–Hellman’s is a discrete log. Shor is a machine that makes both stories false.

In English

Crypto is a one-way trick plus a story about what is hard. RSA’s story: factoring big numbers is hard. Diffie–Hellman’s: finding a hidden exponent is hard. Shor is a quantum machine that makes both stories false. AES and hashes get a haircut, not a funeral.

Try this
Start with the clock (Mod). Skip to RSA if you just want the lock. End at The threat for what still stands.
Keep this
Public-key crypto is “this math is hard.” Shor disputes some of those stories, not all of them.

The stack · click a layer

  1. 06The threat
  2. 05Hash
  3. 04RSA
  4. 03Discrete log
  5. 02One-way
  6. 01Mod

What this is

Tiny moduli you can factor by hand, a discrete-log hunt you can watch, RSA that opens, a hash that avalanches, and a stack of what Shor actually kills.

What this is not

Not OpenSSL and not a 2048-bit threat model. The numbers are toys so the algebra is visible. The claims (RSA is factoring, DH is a discrete log, Grover is only quadratic) are the real ones.

  1. 01 · The clockModAdd and multiply on a clock.mod n means “remainder after wrapping the clock.”
  2. 02 · The betOne-wayMultiply instantly. Count the trial divisions.One-way = cheap forward, expensive reverse — unless you know a secret.
  3. 03 · The betDiscrete logSet x. Hunt it the classical way.Discrete log: gˣ is easy, x is not. Diffie–Hellman is that fact as a handshake.
  4. 04 · A lockRSAEncrypt a number. Open it with d.Lock with e, open with d. d comes from the factors of n.
  5. 05 · No trapdoorHashChange one letter. Watch the bits.Hashes are one-way with no trapdoor. Grover nicks them; Shor does not.
  6. 06 · The systemThe threatWhat dies, what gets a haircut, what stands.Shor eats public-key periods. Grover nicks symmetric. Lattices stand. Harvest-now is why it matters now.