2010 | OriginalPaper | Buchkapitel
Structure-Preserving Signatures and Commitments to Group Elements
verfasst von : Masayuki Abe, Georg Fuchsbauer, Jens Groth, Kristiyan Haralambiev, Miyako Ohkubo
Erschienen in: Advances in Cryptology – CRYPTO 2010
Verlag: Springer Berlin Heidelberg
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A modular approach for cryptographic protocols leads to a simple design but often inefficient constructions. On the other hand, ad hoc constructions may yield efficient protocols at the cost of losing conceptual simplicity. We suggest
structure-preserving
commitments and signatures to overcome this dilemma and provide a way to construct modular protocols with reasonable efficiency, while retaining conceptual simplicity.
We focus on schemes in bilinear groups that preserve parts of the group structure, which makes it easy to combine them with other primitives such as non-interactive zero-knowledge proofs for bilinear groups.
We say that a signature scheme is
structure-preserving
if its verification keys, signatures, and messages are elements in a bilinear group, and the verification equation is a conjunction of pairing-product equations. If moreover the verification keys lie in the message space, we call them
automorphic
. We present several efficient instantiations of automorphic and structure-preserving signatures, enjoying various other additional properties, such as
simulatability
. Among many applications, we give three examples: adaptively secure round-optimal blind signature schemes, a group signature scheme with efficient concurrent join, and an efficient instantiation of anonymous proxy signatures.
A further contribution is
homomorphic trapdoor commitments to group elements
which are also length reducing. In contrast, the messages of previous homomorphic trapdoor commitment schemes are exponents.