How to Remove the Exponent GCD in HK09

摘要

To improve the decapsulation efficiency of HK09 (proposed by Hofheinz and Kiltz in Eurocrypt 2009), we propose a new skill to remove the exponent GCD operation. In the proposed scheme, the decapsulation efficiency is improved by 38.9% (instantiated over the semi-smooth subgroup) and the efficiency of encapsulation is dropped by 5.7%.