When a card number is compromised, an attacker may search for active numbers sharing its prefix. An issuer might respond by reissuing cards from heavily populated prefixes into less populated ones. We show that this intuitive count control can backfire. For fixed search regions, exposure weights, and total activity, we derive exactly when reducing the maximum prefix count increases the chance that a budgeted search finds an active number. In matched synthetic simulations over 50,000 candidates, targeted replacement meets the count limit in every run but raises supplied-12-digit-prefix discovery relative to equal-volume random replacement in three of twelve settings. Thus a lower prefix count does not by itself certify lower enumeration risk.

翻译：暂无翻译