A Random Number Generator Based on Elliptic Curve Operations

A random number generator based on the addition of points on an elliptic curve over finite fields is proposed. By using the proposed generator together with the elliptic curve cryptography (ECC) algorithm, we can save hardware and software components. For hardware implementation, the proposed generator can be implemented using the existing ECC arithmetic processor. Up to 29% of gate counts can be saved when compared to the case of implementing a random number generator separately. Theoretical analyses show that periods of the proposed random number generator are sufficiently long. Moreover, the generated sequences have passed the FIPS 140-2 statistical tests. As a result, the proposed generator is suitable to be a reliable and efficient random number generator in ECC systems. © 2004 Elsevier Ltd. All rights reserved.