International Association
for Cryptologic Research

This paper introduces \"hyper-and-elliptic-curve cryptography\", in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (e.g., Diffie--Hellman shared-secret computation) and at the same time supports fast elliptic-curve formulas for fixed-base-point scalar multiplication (e.g., key generation) and multi-scalar multiplication (e.g., signature verification).