PPP-Completeness with Connections to Cryptography

@article{Sotiraki2018PPPCompletenessWC,
  title={PPP-Completeness with Connections to Cryptography},
  author={Katerina Sotiraki and Manolis Zampetakis and Giorgos Zirdelis},
  journal={2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2018},
  pages={148-158}
}
Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound connections to the complexity of the fundamental cryptographic primitives: collision-resistant hash functions and one-way permutations. In contrast to most of the other subclasses of TFNP, no complete problem is known for PPP. Our work identifies the first PPP-complete problem without any circuit or Turing Machine given explicitly in the input, and thus we answer a longstanding open question from… 
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