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Paper: Homomorphic Trapdoor Commitments to Group Elements

Authors:
Jens Groth
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URL: http://eprint.iacr.org/2009/007
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Abstract: We present a homomorphic trapdoor commitment to group elements. In contrast, previous homomorphic trapdoor commitment schemes only allow the messages to be exponents. Our commitment scheme is length-reducing, we can make a short commitment to many group elements at once, and it is perfectly hiding and computationally binding. The construction is based on groups with a bilinear map and the binding property follows from the simultaneous triple pairing assumption. While the simultaneous triple pairing assumption is new, we demonstrate that it is implied by the well-known decision linear assumption.
BibTeX
@misc{eprint-2009-18284,
  title={Homomorphic Trapdoor Commitments to Group Elements},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / homomorphic trapdoor commitment, bilinear groups, simultaneous triple pairing assumption},
  url={http://eprint.iacr.org/2009/007},
  note={ j.groth@ucl.ac.uk 14247 received 3 Jan 2009},
  author={Jens Groth},
  year=2009
}