QA-NIZK Arguments in Asymmetric Groups: New Tools and New Constructions

Abstract. A sequence of recent works have constructed constant-size quasi-adaptive (QA) NIZK arguments of membership in linear subspaces of ˆGm , where ˆG is a group equipped with a bilinear map e : ˆG × ˇH → T. Although applicable to any bilinear group, these techniques are less useful in the asymmetric case. For example, Jutla and Roy (Crypto 2014) show how to do QA aggregation of GrothSahai proofs, but the types of equations which can be aggregated are more restricted in the asymmetric setting. Furthermore, there are natural statements which cannot be expressed as membership in linear subspaces, for example the satisfiability of quadratic equations. In this paper we develop specific techniques for asymmetric groups. We introduce a new computational assumption, under which we can recover all the aggregation results of Groth-Sahai proofs known in the symmetric setting. We adapt the arguments of membership in linear spaces of ˆGm to linear subspaces of ˆGm × ˇHn . In parti...

• Type: Journal
• Year: 2015
• Where: ASIACRYPT
• Authors: Alonso González, Alejandro Hevia, Carla Ràfols
• Keywords: ASIACRYPT 2015, Cryptology