We define a new type of mix network that offers a reduced form of robustness: the mixnet can prove that every message it outputs corresponds to an input submitted by a player without revealing which input (for honest players). We call mixnets with this property reputable mixnets. Reputable mixnets are not fully robust, because they offer no guarantee that distinct outputs correspond to distinct inputs. In particular, a reputable mix may duplicate or erase messages. A reputable mixnet, however, can defend itself against charges of having authored the output messages it produces. This ability is very useful in practice, as it shields the mixnet from liability in the event that an output message is objectionable or illegal.
We propose three very efficient protocols for reputable mixnets, all asynchronous. The first protocol is based on blind signatures. It works both with Chaumian decryption mixnets or ElGamal-based re-encryption mixnets, but guarantees a slightly weaker form of reputability which we call near-reputability. The other two protocols are based on ElGamal re-encryption over a composite group and offer true reputability. One requires interaction between the mixnet and the players before players submit their inputs. The other assumes no interaction prior to input submission.