Risk Management for E-Cash Systems with Partial Real-Time Audit

Abstract

We analyze “coin-wallet” and “balance-wallet” under partial real-time audit, and compute upper bounds on theft due to the fact that not all the transactions are audited in real time, assuming that everything else is perfect. In particular, we assume that the audit regime holds for innocent payees. Let v be the maximum allowed balance in a wallet, and 0≤μ≤1 be the fraction of transactions that are audited in real time in an audit round. Assume one unit transactions. We show that the upper bound on expected theft for coin-wallet is lim μ→0μ−2, while for plausible (similar) parameter choice the bound for a balance-wallet is O(exp (mvμ)), where 1<m. The former is nicely bounded for small transactions, however, the bound for balance-wallet can become huge in those cases where we require very small false alarm probability. We conclude that partial audit, may be suitable for coin-wallets with low denomination coins, and possibly for balance-wallet, when we may tolerate a relatively high false alarm rate, but it may be too risky for balance-wallet, where very low false alarm rate is required.