This paper presents an energy‐efficient (low power) prime‐field hyperelliptic curve cryptography (HECC) processor with uniform power draw. The HECC processor performs divisor scalar multiplication on the Jacobian of genus 2 hyperelliptic curves defined over prime fields for arbitrary field and curve parameters. It supports the most frequent case of divisor doubling and addition. The optimized implementation, which is synthesized in a 0.13 μm standard CMOS technology, performs an 81‐bit divisor multiplication in 503 ms consuming only 6.55 μJ of energy (average power consumption is 12.76 μW). In addition, we present a technique to make the power consumption of the HECC processor more uniform and lower the peaks of its power consumption.