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Constrained Pseudorandom Functions from Homomorphic Secret Sharing

Authors:
Geoffroy Couteau , Université Paris Cité, IRIF, CNRS
Pierre Meyer , Reichman University and Université Paris Cité, IRIF, CNRS
Alain Passelègue , Inria, France and ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, Inria, UCBL), France.
Mahshid Riahinia , ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, Inria, UCBL)
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DOI: 10.1007/978-3-031-30620-4_7 (login may be required)
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Presentation: Slides
Conference: EUROCRYPT 2023
Abstract: We propose and analyze a simple strategy for constructing 1-key constrained pseudorandom functions (CPRFs) from homomorphic secret sharing. In the process, we obtain the following contributions: first, we identify desirable properties for the underlying HSS scheme for our strategy to work. Second, we show that (most of) recent existing HSS schemes satisfy these properties, leading to instantiations of CPRFs for various constraints and from various assumptions. Notably, we obtain the first (1-key selectively secure, private) CPRFs for inner-product and (1-key selectively secure) CPRFs for NC 1 from the DCR assumption, and more. Last, we revisit two applications of HSS equipped with these additional properties to secure computation: we obtain secure computation in the silent preprocessing model with one party being able to precompute its whole preprocessing material before even knowing the other party, and we construct one-sided statistically secure computation with sublinear communication for restricted forms of computation.
BibTeX
@inproceedings{eurocrypt-2023-32995,
  title={Constrained Pseudorandom Functions from Homomorphic Secret Sharing},
  publisher={Springer-Verlag},
  doi={10.1007/978-3-031-30620-4_7},
  author={Geoffroy Couteau and Pierre Meyer and Alain Passelègue and Mahshid Riahinia},
  year=2023
}