In this paper we present a novel method for obtaining fast software implementation of the Elliptic Curve Digital Signature Algorithm in the finite field GF(p) with an arbitrary prime modulus p of arbitrary length. The most important feature of the method is that it avoids bit-level operations which are slow on microprocessors and performs word-level operations which are significantly faster. The algorithms used in the implementation perform word-level operations, trading them off for bit-level operations and thus resulting in much higher speeds. We provide the timing results of our implementations on a 2.8 GHz Pentium 4 processor, supporting our claim that ECDSA is appropriate for constrained environments.