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Constrained PRFs for Unbounded Inputs with Short Keys

  • Hamza AbusalahEmail author
  • Georg Fuchsbauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9696)

Abstract

A constrained pseudorandom function (CPRF) \(F:\mathcal{K} \times \mathcal{X} \rightarrow \mathcal{Y}\) for a family \(\mathcal{T}\) of subsets of \(\mathcal X\) is a function where for any key \(k \in \mathcal{K}\) and set \(S\in \mathcal{T}\) one can efficiently compute a short constrained key \(k_S\), which allows to evaluate \(F(k,\cdot )\) on all inputs \(x\in S\), while the outputs on all inputs \(x \notin S\) 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.

Keywords

Constrained PRFs Unbounded inputs 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Science and Technology AustriaKlosterneuburgAustria
  2. 2.Inria, ENS, CNRS and PSL Research UniversityParisFrance

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