Paper 2017/977

Cryptanalysis against Symmetric-Key Schemes with Online Classical Queries and Offline Quantum Computations

Akinori Hosoyamada and Yu Sasaki

Abstract

In this paper, quantum attacks against symmetric-key schemes are presented in which adversaries only make classical queries but use quantum computers for offline computations. Our attacks are not as efficient as polynomial-time attacks making quantum superposition queries, while our attacks use the realistic model and overwhelmingly improve the classical attacks. Our attacks convert a type of classical meet-in-the-middle attacks into quantum ones. The attack cost depends on the number of available qubits and the way to realize the quantum hardware. The tradeoff between data complexity $$ and time complexity $$ against the problem of cardinality $$ is $$ and $$ in the best and worst case scenarios to the adversary respectively, while the classic attack requires $$. This improvement is meaningful from an engineering aspect because several existing schemes claim beyond-birthday-bound security for $$ by limiting the maximum $$ to be below $$ according to the classical tradeoff $$. Those schemes are broken if quantum offline computations are performed by adversaries. The attack can be applied to many schemes such as a tweakable block-cipher construction TDR, a dedicated MAC scheme Chaskey, an on-line authenticated encryption scheme McOE-X, a hash function based MAC H$$-MAC and a permutation based MAC keyed-sponge. The idea is then applied to the FX-construction to discover new tradeoffs in the classical query model.