A Fast Java Implementation of a Provably Secure Pseudo Random Bit Generator Based on the Elliptic Curve Discrete Logarithm Problem

We present a pseudo random bit generator whose security is based on the intractability of the discrete logarithm problem in the group E(Fp) of rational points on an elliptic curve over a finite prime field Fp. The bit generator is implemented within the framework of the Java Cryptography Architecture (JCA). It uses an elliptic curve E chosen such that both E(Fp) and its twist E (Fp) are of prime order and cryptographically strong. We show how to efficiently find such curves. As attacking the bit generator is at least as difficult as the elliptic curve discrete logarithm problem we propose to use it for generating key pairs for elliptic curve cryptography.