A Stronger Definition for Anonymous Electronic Cash

We investigate definitions of security for previously proposed schemes for electronic cash and strengthen them so that the bank does need to be trusted to the same extent. We give an experiment-based definition for our stronger notion and show that they imply security in the framework for Universal Composability. Finally we propose a scheme secure under our definition in the common reference string (CRS) model under the assumption that trapdoor permutations exist. As a tool we define and prove the existence of simulation-sound non-interactive zeroknowledge proofs (NIZK-PK) in the CRS-model under the assumption that a family of trapdoor permutations exists.