Constrained Pseudorandom Functions from Homomorphic Secret Sharing

Geoffroy Couteau (1) , Pierre Meyer , Alain Passelègue (2, 3, 4) , Mahshid Riahinia (4)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 ARIC - Arithmétiques des ordinateurs, méthodes formelles, génération de code
3 Inria Lyon
4 LIP - Laboratoire de l'Informatique du Parallélisme

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 innerproduct 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.

Domains: Computer Science [cs]

Geoffroy Couteau, Pierre Meyer, Alain Passelègue, Mahshid Riahinia. Constrained Pseudorandom Functions from Homomorphic Secret Sharing. 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques,EUROCRYPT 2023, Apr 2023, Lyon, France. pp.194-224, ⟨10.1007/978-3-031-30620-4_7⟩. ⟨hal-04265643⟩