Editing Elliptic-curve cryptography (section)

{{Short description|Approach to public-key cryptography}} 

'''Elliptic-curve cryptography''' ('''ECC''') is an approach to [[public-key cryptography]] based on the [[algebraic structure]] of [[elliptic curve]]s over [[finite field]]s. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in [[Finite field|Galois fields]], such as the [[RSA (cryptosystem) | RSA cryptosystem]] and [[ElGamal encryption | ElGamal cryptosystem]].<ref name=":0"/>

Elliptic curves are applicable for [[key agreement]], [[digital signature]]s, [[Cryptographically secure pseudorandom number generator|pseudo-random generators]] and other tasks. Indirectly, they can be used for [[encryption]] by combining the key agreement with a [[Symmetric-key algorithm|symmetric encryption]] scheme. They are also used in several [[integer factorization]] [[algorithm]]s that have applications in cryptography, such as [[Lenstra elliptic-curve factorization]].