How to Construct Quantum Random Functions

By Mark Zhandry. IEEE Annual Symposium on Foundations of Computer Science, 2012

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Breaking Symmetric Cryptosystems Using Quantum Period Finding (2016, background): “More-over, any superposition x,y λ x,y | x i| y i is a valid input to the quantum oracle, who then returns x,y λ x,y | x i| y ⊕ O k ( x ) . attacks P P i In previous works, these attacks have been called superposition [19], quantum chosen message attacks [13] or quantum security [47].”
Pseudorandom Functions: Three Decades Later (2017, background): “As in the case of GGM, the NR construction is also secure against quantum distinguishers [139].”
Complexity-Theoretic Foundations of Quantum Supremacy Experiments (2016, methodology): “=n) seems to be needed. In Section 7, to prove that one-way functions imply the existence of an oracle A2P=poly such that PA6= BQPA, we adapt a construction that was independently proposed by Zhandry [Zha12] and by Servedio and Gortler [SG04]. In this construction, we ﬁrst use known reductions [HILL”