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Paper: Verifiable Random Functions with Optimal Tightness

Authors:
David Niehues
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Abstract: Verifiable random functions (VRFs), introduced by Micali, Rabin and Vadhan (FOCS’99), are the public-key equivalent of pseudo- random functions. A public verification key and proofs accompanying the output enable all parties to verify the correctness of the output. How- ever, all known standard model VRFs have a reduction loss that is much worse than what one would expect from known optimal constructions of closely related primitives like unique signatures. We show that: 1. Every security proof for a VRF has to lose a factor of Q, where Q is the number of adversarial queries. To that end, we extend the meta- reduction technique of Bader et al. (EUROCRYPT’16) to also cover VRFs. 2. This raises the question: Is this bound optimal? We answer this question in the affirmative by presenting the first VRF that achieves this tightness. We thus paint a complete picture of the achievability of tight verifiable random functions: We show that a security loss of Q is unavoidable and present the first construction that achieves this bound.
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BibTeX
@article{pkc-2021-31000,
  title={Verifiable Random Functions with Optimal Tightness},
  booktitle={Public-Key Cryptography - PKC 2021},
  publisher={Springer},
  author={David Niehues},
  year=2021
}