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The performance analysis of Hyper Elliptic Curve Cryptosystems (HECC) over prime Fields (Fp) of genus 5 and 6 are discussed in this paper. The authors have implemented a HECC system of genus 5 and 6 in a Intel Pentium III Celeron processor at 933 MHz speed with 256 MB RAM in Java 1.5. They have also compared their efficiency on the parameters of time taken for divisor generation, key generation, encryption and decryption. Their results demonstrate that the performance of higher genus HECC system gets degraded in terms of divisor generation, key generation, and encryption and decryption process.