Homomorphic Trapdoor Commitments to Group Elements

Jens Groth

Paper 2009/007

Homomorphic Trapdoor Commitments to Group Elements

Jens Groth

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.

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: homomorphic trapdoor commitment bilinear groups simultaneous triple pairing assumption
Contact author(s): j groth @ ucl ac uk
History: 2009-01-04: received
Short URL: https://ia.cr/2009/007
License: CC BY

BibTeX

@misc{cryptoeprint:2009/007,
      author = {Jens Groth},
      title = {Homomorphic Trapdoor Commitments to Group Elements},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/007},
      year = {2009},
      url = {https://eprint.iacr.org/2009/007}
}