Paper 2023/387

Constrained Pseudorandom Functions from Homomorphic Secret Sharing

Geoffroy Couteau, Université Paris Cité, CNRS, IRIF, Paris, France.
Pierre Meyer, Université Paris Cité, CNRS, IRIF, Paris, France., Reichman University, Herzliya, Israel.
Alain Passelègue, Inria, France, 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), France.

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) 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. Lastly, 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.

Available format(s)
Public-key cryptography
Publication info
A major revision of an IACR publication in EUROCRYPT 2023
Homomorphic Secret SharingConstrained Pseudorandom FunctionSublinear Secure Computation
Contact author(s)
couteau @ irif fr
pierre meyer @ irif fr
alain passelegue @ inria fr
mahshid riahinia @ ens-lyon fr
2023-03-24: approved
2023-03-17: received
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Creative Commons Attribution


      author = {Geoffroy Couteau and Pierre Meyer and Alain Passelègue and Mahshid Riahinia},
      title = {Constrained Pseudorandom Functions from Homomorphic Secret Sharing},
      howpublished = {Cryptology ePrint Archive, Paper 2023/387},
      year = {2023},
      note = {\url{}},
      url = {}
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