Notes

A visual and mathematical path from real elliptic curves to finite-field point sets, groups, and the base-point subgroups used by cryptography.

From Caesar's cipher to threshold cryptography. Explore how encryption evolved from simple shifts to distributed systems where multiple parties must collaborate to decrypt secrets.

What are the differences between noise and jitter

Follow scalar multiples around a finite curve to distinguish curve order, point order, subgroups, base points, cofactors, and the base and scalar fields.

A high-level orientation to elliptic curves and the mathematical path from smooth real curves to finite-field point groups.

Build visual intuition for elliptic curves using real-number curves, Weierstrass form, smoothness, and curve points.

Learn the chord-and-tangent point addition rule, point doubling, inverse points, the point at infinity, and why curve points form a group.