Efficient Implementation of AND, OR and NOT Operators for ABCs

In the last few years several practitioners have proposed different strategies for implementing Attribute-based credentials (ABCs) on smart cards [3, 4, 20–23]. ABCs allow citizens to prove certain properties about themselves without necessarily revealing their full identity. The Idemix ABC [10] is the most versatile ABC system proposed in the literature, supporting pseudonyms, equality proof of representation, verifiable encryption of attributes [12] and proving properties of attributes via the AND, NOT and OR operators as described in [8]. Vullers et al. and De La Piedra et al. addressed the implementation of the selective disclosure operations, pseudonyms and multi-credential proofs such as equality proofs of representation [21,23]. In this manuscript, we present implementation strategies for proving properties of user attributes via these operator and show how to combine them via external and internal commitment reordering.