Elliptic-curve cryptography: Difference between revisions

Public-key cryptography is based on the intractability of certain mathematical problems. Early public-key systems are secure assuming that it is difficult to factor a large integer composed of two or more large prime factors. For elliptic-curve-based protocols, it is assumed that finding the [[discrete logarithm]] of a random elliptic curve element with respect to a publicly-known base point is infeasible. The size of the elliptic curve determines the difficulty of the problem. The primary benefit promised by ECC is a smaller key size, reducing storage and transmission requirements -- ie, that an elliptic curve group could provide the same level of security afforded by an RSA-based system with a large modulus and correspondingly larger key.