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

Abstract

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. As a second contribution, we use the proposed signature scheme to build an efficient multi-show attribute-based anonymous credential (ABC) system that allows to encode an arbitrary number of attributes. This is – to the best of our knowledge – the first ABC system that provides constant-size credentials and constant-size showings. To allow an efficient construction in combination with the proposed signature scheme, we also introduce a new, efficient, randomizable polynomial commitment scheme. Aside from these two building blocks, the credential system requires a very short and constant-size proof of knowledge to provide freshness in the showing protocol.