Public-Key Cryptography on the Top of a Needle

This work describes the smallest known hardware implementation for Elliptic/Hyperelliptic Curve Cryptography (ECC/HECC). We propose two solutions for Public-key Cryptography (PKC), which are based on arithmetic on elliptic/hyperelliptic curves. One solution relies on ECC over binary fields 𝔽 2𝓃 where 𝓃 is a composite number of the form 2𝑝(𝑝 is a prime) and another on HECC on curves of genus 2 over 𝔽 2𝑝 . This implies the same arithmetic unit for both cases which supports arithmetic in a field 𝔽 2𝑝 . Our best solution that still results in a feasible performance features less than 5 kgates with an average power consumption smaller than 10 μ W.