AUTHOR=Cai BinBin , Gao Fei , Leander Gregor 

TITLE=Quantum attacks on two-round even-mansour

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1028014

DOI=10.3389/fphy.2022.1028014

ISSN=2296-424X

ABSTRACT=Even-Mansour is one of the most important constructions in symmetric cryptography, both from a theoretical and practical perspective. With the rapid development of quantum computing, the security of Even-Mansour construction in quantum setting needs to be considered. For one round Even-Mansour construction, it is well settled by classical and quantum attacks. While for the iterated scheme, the situation is much more complex. In this paper, we study the next case in line in detail and depth: quantum attacks against two rounds case. We make an asymptotic comparison with existing classical and quantum attacks and present concrete resource estimation that allows to deduce the most efficient attacks in the case of round reduced LED cipher and $\mathrm{AES}^{2}$.