For the two last decades, people have tried to provide practical electronic cash schemes, with more or less success. Indeed, the most secure ones generally suffer from inefficiency, largely due to the use of restrictive blind signatures, on the other hand efficient schemes often suffer from serious security drawbacks. In this paper, we propose both a new tool providing scalable anonymity at a low cost, and a new Internet business: "Anonymity Providers". Those "Anonymity Providers" certify re-encrypted data after having been convinced of the validity of the content, but without knowing anything about this latter. It is a very useful third party in many applications (e.g. for revocable anonymous electronic cash, where a coin would be a certified encryption of the user's identity, such that a Revocation Center, and only it, can recover this identity, if needed). With this new tool, each user can get the required anonymity level, depending on the available time, computation and/or money amounts. Furthermore, the "Anonymity Provider" may be a new type of business over the Internet, profitable for everybody: 1. from the provider point of view as he can charge the service; 2. from the user point of view as he can obtain a high level of anonymity at low computational cost. Moreover, a user who does not require anonymity has no extra computation to perform. This technique is quite efficient because of its "optimistic" orientation: in case of honest use, everything is very efficient. Some slightly more heavy processes have to be performed in case of fraud detection, but with overwhelming tracing success.
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