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Predicate Encryption from Bilinear Maps and One-Sided Probabilistic Rank

Authors:
Josh Alman
Robin Hui
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DOI: 10.1007/978-3-030-36030-6_7
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Abstract: In predicate encryption for a function f, an authority can create ciphertexts and secret keys which are associated with ‘attributes’. A user with decryption key $$K_y$$ corresponding to attribute y can decrypt a ciphertext $$CT_x$$ corresponding to a message m and attribute x if and only if $$f(x,y)=0$$. Furthermore, the attribute x remains hidden to the user if $$f(x,y) \ne 0$$.We construct predicate encryption from assumptions on bilinear maps for a large class of new functions, including sparse set disjointness, Hamming distance at most k, inner product mod 2, and any function with an efficient Arthur-Merlin communication protocol. Our construction uses a new probabilistic representation of Boolean functions we call ‘one-sided probabilistic rank,’ and combines it with known constructions of inner product encryption in a novel way.
BibTeX
@article{tcc-2019-29971,
  title={Predicate Encryption from Bilinear Maps and One-Sided Probabilistic Rank},
  booktitle={Theory of Cryptography},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={11891},
  pages={151-173},
  doi={10.1007/978-3-030-36030-6_7},
  author={Josh Alman and Robin Hui},
  year=2019
}