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**2016/279**

**Title:**

Constrained PRFs for Unbounded Inputs with Short Keys

**Authors:**
Hamza Abusalah, Georg Fuchsbauer

**Abstract:**

A constrained pseudorandom function (CPRF) F \colon {\cal K} \times {\cal X} \to {\cal Y} for a family {\cal T} of subsets of \cal X is a function where for any key k \in {\cal K} and set S \in {\cal 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.

**ePrint:**
https://eprint.iacr.org/2016/279

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