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The paper presents a system-on-a-chip (SoC) architecture, which targets reconfigurable hardware, for elliptic curve cryptosystems (ECC). A four-level partitioning scheme is described for exploring the area and speed tradeoffs. A design generator is used to generate parameterisable building blocks for the configurable SoC architecture. A secure Web server, which runs on a reconfigurable soft-processor and an embedded hard-processor, shows over 2000 times speedup when computationally-intensive operations run on the customised building blocks. The embedded on-chip timer block gives accurate performance information. The design factors of configurable SoC architectures are also discussed and evaluated.