On the continuum between on-line and off-line E-cash systems — I

Abstract

Electronic cash systems for small transactions are discussed, with the functionality goal of minimizing involvement of third parties in transactions between users. To this end the potential role of randomized audit mechanisms is discussed. A continuum exists between the extremes of totally on-line and totally off-line payment systems, and there exist business motivations to establishing an intermediate “working point.” Our security goal is to protect the systems against economically motivated adversaries. Let the adversarial expenses (to interfere with normal operation of wallets) be Cb, and 1/d be the audit sampling rate, and for simplicity assume that each payment has a value of one unit. Then when the adversarial payer breaks even with her investment, Cb, the probability not to detect her is O(exp(-Cb/d)). A curious observation on the so called “after the fact double-spender exposure” mechanisms unexpectedly falls from the analysis of randomized audit mechanisms.