Clock Arithmetic
ℤₙ · Extended Euclid · Euler φ · Cyclic Groups · CRT · Montgomery REDC
Work through the arithmetic underneath RSA and Diffie–Hellman — inverses, φ, cycles, generators, the Chinese remainder theorem and repeated modular multiplication — and watch each one fail when its precondition does.
Exact, small-number teaching experiments. No production cryptography or secret-key generation.
Where this lesson stops
- Primality testing: Prime Witness.
- RSA and fast exponentiation traces: Educational RSA.
- Discrete-log algorithms and Pohlig–Hellman: Log Forge.
- Quadratic residues and Jacobi symbols: Residue Gate.
- Full-group versus subgroup message encoding: ElGamal Plain.
- Polynomial arithmetic in GF(2⁸): AES Anatomy.
- Elliptic-curve groups: Point Arithmetic.