Generation and Implementation of Cryptographically Strong Elliptic Curves.

Elliptic curves over finite fields are an essential part of public key cryptography. The security of cryptosystems with elliptic curves is based on the computational intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). The paper presents requirements which cryptographically secure elliptic curves have to satisfy, together with their justification and some relevant examples of elliptic curves. We implemented modular arithmetic in a finite field, the operations on an elliptic curve and the basic cryptographic protocols.