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A quantum lower bound for distinguishing random functions from random permutations

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 نشر من قبل Henry Yuen
 تاريخ النشر 2013
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 تأليف Henry Yuen




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The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problems hardness. We study the quantum query complexity of this problem, and show that any quantum algorithm that solves this problem with bounded error must make $Omega(N^{1/5}/log N)$ queries to the input function. Our lower bound proof uses a combination of the Collision Problem lower bound and Ambainiss adversary theorem.



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