Ilan Komargodski

Pseudorandom Functions in $\mathsf{NC}^1$ from LWE/LPN/CDH (Or: How to Build PRFs in $\mathsf{NC}^1$, Generically)

We present a new generic transformation from weak PRFs computable in depth $d(n) = \Omega(\log n)$ to strong PRFs computable in depth $O(d(n))$. This construction refines the classical tree-based paradigm of GGM by {tapering} the internal state so the per-level depth decreases geometrically. We complement the above wit...