In this paper we compare the computational complexity of two parallel scalar multiplication methods used to speed up scalar multiplications for Elliptic Curve Cryptography applications. Pre-computations are advantageous only when the elliptic curve point is fixed. However, during secure communication sessions using either public keys or digital signatures, the elliptic curve point depends on the public key of the communicating entities and is therefore session dependent. Hence, a second method that replaces pre-computations with some post-computations, allows the pre-computation overhead to be distributed amongst parallel processors. Thus scalar multiplication can be computed more efficiently using the post-computation method in the more typical case where the elliptic curve point is variable.
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