Quantum Attacks on HCTR and Its Variants

Recently, in Asiacrypt 2019, Bonnetain
et al.
have shown attacks by quantum adversaries on FX construction and Even-Mansour Cipher without using superposition queries to the encryption oracle. In this article, we use a similar approach to mount new attacks on Hash-Counter (HCTR) and Hash-Counter-Hash (HCH) constructions. In addition, we mount attacks on HCTR, tweakable-HCTR, and HCH using the superposition queries to the encryption oracle using strategies proposed by Leander and May in Asiacrypt 2017 and Kaplan
et al.
in Crypto 2016.