We design the first collusion-resistant constrained PRFs (CPRFs) for a non-trivial and expressive class of constraints from standard LWE. The two predicate classes for which we design CPRFs are: compute-&-compare and predicated range constraints. We improve our CPRF for compute-&-compare predicates to also satisfy collusion-resistant constraint privacy. An additional feature of our CPRFs is that they also satisfy (almost-)key-homomorphic property. Prior to this work, we did not have any post-quantum collusion-resistant CPRF beyond prefixfixing constraints, and collusion-resistant CPRFs for expressive predicates relied on either code obfuscation or multilinear maps.
As an immediate application, we obtain a two-sided predicate encryption (PE) and functional encryption (FE) for the compute-&-compare class in the symmetric-key setting. Prior to this work, we did not have any post-quantum construction for 2-sided PE/FE beyond inner product predicates. An important contribution of this work is to introduce a new framework of purifying functionality. The main motivation behind our new framework is to systematically eliminate zeroizing attacks, which have been a highly successful cryptanalysis paradigm for breaking various candidates for advanced cryptographic objects.