Traditionally, cryptographic protocols are described in terms of a sequence of steps, each of which sees one principal sending a message to another principal. It is implicitly assumed that the fundamental communication primitive is necessarily one-to-one and protocols addressing anonymity tend to resort to a highly redundant composition of multiple elementary transmissions in order to frustrate traffic analysis. This talk, building on the case study of an anonymous auction between mistrustful principals with no trusted arbitrator, presents "anonymous broadcast" as a new protocol building block. This lower-level primitive is, in its class of cases, a more accurate model of what actually happens in local area networking and, with certain restrictions, can be used as a particularly efficient implementation technique for many anonymity-related protocols.