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Constrained PRFs for Unbounded Inputs with Short Keys

Hamza Abusalah 1 Georg Fuchsbauer 2 
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : A constrained pseudorandom function (CPRF) F:K×X→Y for a family T of subsets of X is a function where for any key k∈K and set S∈T one can efficiently compute a short constrained key k_S, which allows to evaluate F(k,⋅) on all inputs x∈S, while the outputs on all inputs x∉S look random even given k_S. Abusalah et al. recently constructed the first constrained PRF for inputs of arbitrary length whose sets S are decided by Turing machines. They use their CPRF to build broadcast encryption and the first ID-based non-interactive key exchange for an unbounded number of users. Their constrained keys are obfuscated circuits and are therefore large. In this work we drastically reduce the key size and define a constrained key for a Turing machine M as a short signature on M. For this, we introduce a new signature primitive with constrained signing keys that let one only sign certain messages, while forging a signature on others is hard even when knowing the coins for key generation.
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Submitted on : Wednesday, October 19, 2016 - 5:49:55 PM
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Hamza Abusalah, Georg Fuchsbauer. Constrained PRFs for Unbounded Inputs with Short Keys. Applied Cryptography and Network Security - 14th International Conference, ACNS 2016, Jun 2016, Guildford, United Kingdom. ⟨10.1007/978-3-319-39555-5_24⟩. ⟨hal-01384375⟩



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