Efficiently computable endomorphism for genus 3 hyperelliptic curve cryptosystems

• GLS and LYʼs idea is extended to genus 3 hyperelliptic curves over a finite field of even characteristic.
• The explicit formulae for the computable endomorphism are proposed.
• That the endomorphism leads to 2-dimension GLV method is demonstrated.
• Our method is 49.9% faster than the previous best methods.

Scalar multiplication methods using efficiently computable endomorphism are known for efficient methods to speed up (hyper)elliptic curve cryptosystems. In this paper we extend the results of Galbraith et al. (2009, 2011) [13] and [14] and Li et al. (2011) [16] to any genus 3 hyperelliptic curves over a finite field of even characteristic. For the quadratic twist of a genus 3 hyperelliptic curve, we give the explicit formulae for the efficiently computable endomorphism on the Jacobian and demonstrate that the endomorphism leads to 2-dimension GLV method. Our method is 49.9% faster than the previous best methods for the 128-bits point multiplication of genus 3 hyperelliptic curves.