Elliptic-curve cryptography

Elliptic-curve cryptography is public-key cryptography built from group operations on elliptic curves over finite fields. Its security relies on the difficulty of recovering a scalar from a known point multiple.

Elliptic-curve group: A finite abelian group formed by the points of an elliptic curve over a finite field, together with a point at infinity. Its group law makes repeated point addition the operation behind public-key generation.
Elliptic Curve Diffie–Hellman: A key-agreement method in which parties derive a shared secret using elliptic-curve public keys. It uses scalar multiplication to let two parties establish a shared key over a public channel.
RSA: A public-key cryptosystem whose security is based on the difficulty of factoring large integers. RSA offers a different mathematical basis and generally needs larger keys for comparable classical security.
Group theory: The study of sets equipped with operations satisfying rules such as associativity, identity, and inverses. Elliptic-curve points form groups, making group theory the algebraic foundation of the construction.
Neal Koblitz: An American mathematician who independently proposed elliptic-curve cryptography in 1987. His proposal established one of the two independent introductions of elliptic curves to public-key cryptography.
Elliptic-curve scalar multiplication: The operation of adding an elliptic-curve point to itself a specified number of times. Public keys are computed by multiplying a public point by a secret scalar.
Elliptic Curve Digital Signature Algorithm: A digital-signature scheme that adapts the Digital Signature Algorithm to elliptic-curve groups. It uses elliptic-curve private keys to sign messages and public keys to verify them.
Finite-field Diffie–Hellman: A key-agreement method based on discrete logarithms in the multiplicative group of a finite field. It provides a comparable key-agreement role using a different group and typically larger parameters.
Weierstrass equation: An equation of the form y² = x³ + ax + b used to define many elliptic curves. It is a standard coordinate description for curves used in elliptic-curve cryptography.
Victor S. Miller: An American computer scientist who independently proposed elliptic-curve cryptography in 1985. His proposal introduced elliptic-curve groups as a basis for public-key cryptography.

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