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Hyper-Elliptic Curve Cryptosystem (HECC) is well suited for all kinds of embedded processor architectures, where resources such as storage, time, or power are constrained due to short operand sizes. The authors can construct genus 3 HECC on 54-bit finite fields in order to achieve the same security level as 160-bit ECC or 1024-bit RSA due to the algebraic structure of Hyper-Elliptic Curve. This paper explores various possible attacks to the discrete logarithm in the Jacobian of a Hyper-Elliptic Curve (HEC) and addition and doubling of the divisor using explicit formula to speed up the scalar multiplication.
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