Quantum lifting theorems for random permutations and ideal ciphers convert quantum attacks into few-query classical attacks, giving tight double-sided search bounds and new post-quantum security for sponge and Davies-Meyer.
Then, according to the induction hypothesis applied to πβ² and (π* 2,...,π * π), a tuple of length πβ 1, we have πβ²[π₯* 2βπ¦* 2]
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Quantum Lifting for Invertible Permutations and Ideal Ciphers
Quantum lifting theorems for random permutations and ideal ciphers convert quantum attacks into few-query classical attacks, giving tight double-sided search bounds and new post-quantum security for sponge and Davies-Meyer.