As an increasing number of Internet hosts are wireless handheld devices with small memory and strict CPU-latency constraints, the performance of cryptography methods has become critical for high transaction throughput. Elliptic Curve Cryptography (ECC) is emerging as an attractive public-key system for constrained environments, because of the small key sizes and computational efficiency, while preserving the same security level as the standard methods. The memory performance of ECC algorithms was scarcely investigated. We have developed a set of kernel benchmarks to examine performance of standard and corresponding elliptic curve public-key methods. In this paper, we characterize the operations and their memory impact on performance in Diffie-Hellman key exchange, digital signature algorithm, El-Gamal and RSA public-key cryptosystem as well as elliptic curve Diffie-Hellman key exchange, elliptic curve digital signature algorithm and elliptic curve El-Gamal algorithm. We modeled a typical mobile device based on the Intel XScale architecture, which utilizes an ARM processor core and studied the benchmark set on that target. Different possible variations for the memory hierarchy of such basic architecture were considered. We compared our benchmarks with MiBench Security, another widely accepted benchmark set, in order to provide a reference for our evaluation.