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Structure-preserving signatures are a quite recent but important building block for many cryptographic protocols. In this paper, we introduce a new type of structure-preserving signatures, which allows to sign group element vectors and to consistently randomize signatures and messages without knowledge of any secret. More precisely, we consider messages to be (representatives of) equivalence classes on vectors of group elements (coming from a single prime order group), which are determined by the mutual ratios of the discrete logarithms of the representative’s vector components. By multiplying each component with the same scalar, a different representative of the same equivalence class is obtained. We propose a definition of such a signature scheme, a security model and give an efficient construction, which is secure in the SXDH setting, where EUF-CMA security holds against generic forgers in the generic group model and the so called class hiding property holds under the DDH assumption.

Structure-Preserving Signatures on Equivalence Classes and Their Application to Anonymous Credentials