In this paper, a scalable VLSI multiplication architecture based on Montgomery multiplication (MM) algorithm for elliptic curve cryptography (ECC) over GF(pm), where p is a positive prime and m is the degree of extension of the base field GF(p), is presented. The elements of the GF(pm) are in polynomial basis (PB) representation. The coefficients of the polynomials are represented in Montgomery residue format to simplify the multiplications over GF(p). The proposed algorithm of MM over GF(pm) requires m(m+1) MMs and m2 additions over GF(p). However, the proposed architecture takes {m(m+1)Nmm+Nadd +1} cycles to compute MM over GF(pm), where Nmm > Nadd = 2, and Nmm and Nadd are the numbers of cycles to complete an MM and an addition over GF(p), respectively. The security of an ECC scheme depends on the number of elements in GF(pm). Hence, for a p with nominal bit length (p≫2), the value of m can be small, but the GF(pm) still contains almost equal number of elements to a GF(2k), where k is positive integer. The complexity of the MM architecture over GF(p) is reduced by using carry-save-adder (CSA) based implementation, where NPE is the depth of the CSA. Analysis shows that the area complexity of the proposed architecture is significantly less. Implementation in AMS-0.35um technology, with L=30 (for p=536872717), m=23 and NPE=8, yields a clock frequency of 20.885 MHz, throughput of 6243.68 multiplications per second and power consumption of 86.8 mW (at 20 MHz).