Elliptic curves

a smooth projective curve of genus 1 equipped with a rational basepoint

positive integer that is the area of a right triangle with three rational number sides

In cryptography, Curve25519 is an elliptic curve used in elliptic-curve cryptography (ECC) offering 128 bits of security (256-bit key size) and designed for use with the Elliptic-curve Diffie–Hellman (ECDH) key agreement scheme, first described and implemented by Daniel J. Bernstein. It is one of the fastest curves in ECC, and is not covered by any known patents. The reference implementation is public domain software.

theorem of 2D geometry

theorem

special point on an algebraic curve

type of elliptic curve

form of elliptic curve

efficient algorithm to count points on elliptic curves

family of elliptic curves of the form 𝑥²+𝑦²=1+𝑑𝑥²𝑦²