This paper presents a technique to speed up the computation of inversion of NIST recommended elliptic curve with modulus p 521 -1. The property of multiplicative inverse between pair of numbers over Meresenne"s prime is used to reduce the number of iterations in the Binary Inversion Algorithm in GF(p). This increases the speed requirement for point operations applicable to Elliptic Curve Cryptography. This paper proposes an model of the architecture to achieve the above objective which uses parallelism in multiplicative inversion arithmetic block to speed up the computation.