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Structure-Preserving Signatures on Equivalence Classes and Constant-Size Anonymous Credentials
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| Abstract: | Structure-preserving signatures (SPS) are a powerful building block for cryptographic protocols. We introduce SPS on equivalence classes (SPS-EQ), which allow joint randomization of messages and signatures. Messages are projective equivalence classes defined on group-element vectors, so multiplying a vector by a scalar yields a different representative of the same class. Our scheme lets one adapt a signature for one representative to a signature for another representative without knowledge of any secret. Moreover, given a signature, an adapted signature for a different representative is indistinguishable from a fresh signature on a random message. We propose a definitional framework for SPS-EQ and an efficient construction in Type-3 bilinear groups, which we prove secure against generic forgers. We also introduce set-commitment schemes that let one open subsets of the committed set. From this and SPS-EQ, we then build an efficient multi-show attribute-based anonymous credential system for an arbitrary number of attributes. Our ABC system avoids costly zero-knowledge proofs and only requires a short interactive proof to thwart replay attacks. It is the first credential system whose bandwidth required for credential showing is independent of the number of its attributes, i.e., constant-size. We propose strengthened game-based security definitions for ABC and prove our scheme anonymous against malicious organizations in the standard model; finally, we discuss a concurrently secure variant in the CRS model. |
BibTeX
@article{jofc-2019-30142,
title={Structure-Preserving Signatures on Equivalence Classes and Constant-Size Anonymous Credentials},
journal={Journal of Cryptology},
publisher={Springer},
volume={32},
pages={498-546},
doi={10.1007/s00145-018-9281-4},
author={Georg Fuchsbauer and Christian Hanser and Daniel Slamanig},
year=2019
}