Security Analysis and Key Modification for ZHFE

ZHFE, designed by Porras et al., is one of the few promising candidates for a multivariate public-key encryption algorithm. In this article we extend and expound upon the existing security analysis on this scheme. We prove security against differential adversaries, complementing a more accurate and robust discussion of resistance to rank and algebraic attacks. We further suggest a modification, $$ZHFE^-$$, a multivariate encryption scheme which retains the security and performance properties of ZHFE while optimizing key size in this theoretical framework.