Pseudorandom functions in $ \textit{TC}^{0} $ and cryptographic limitations to proving lower bounds

@article{Krause2001PseudorandomFI,
  title={Pseudorandom functions in \$ \textit\{TC\}^\{0\} \$ and cryptographic limitations to proving lower bounds},
  author={Matthias Krause and Stefan Lucks},
  journal={computational complexity},
  year={2001},
  volume={10},
  pages={297-313}
}
Abstract.This paper investigates which complexity classes inside NCcan contain pseudorandom function generators (PRFGs). Under the Decisional Diffie-Hellman assumption (a common cryptographic assumption) $ \textit{TC}^{0} $4 contains PRFGs. No lower complexity classes with this property are currently known. On the other hand, we use effective lower bound arguments to show that some complexity classes cannot contain PRFGs. This provides evidence for the following conjecture: Any effective lower… 

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