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.
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