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Abstract

A highly efficient mix network for small numbers of inputs is provided. Four data messages would be a typical number of inputs. The structure of sorting/permutation networks is used to permute the input. This is done in a way that changes the position of pairs of items. A mix network is provided which is highly efficient on small input batches and is robust and private in the face of collusion by any minority set of mix servers. Additionally, the mix network method and apparatus has the feature of being publicly verifiable because the mixing method yields a transcript of results that can demonstrate to a third party that the mix proceeded correctly. An apparatus comprised of a plurality of mix servers is provided. Each mix server includes a randomizer network. Each randomizer network receives a plurality of input data messages and performs re-encryption and permutation operations on the plurality of input data messages to form a plurality of output data messages. The randomizer networks of the plurality of mix servers are arranged in a chain so that the first randomizer network of the first mix server in the chain receives its plurality of input data messages and provides its plurality of output data messages to the next randomizer network of the following mix server in the chain. Each randomizer network is comprised of a plurality of randomizers, wherein each randomizer receives first and second input data messages and produces first and second output data messages, wherein the first output data message is a re-encryption of either the first or the second input data message and the second output data message is a re-encryption of the other input data message. A bulletin board having computer memory may be provided, to which each mix server produces proof that each randomizer of each randomizer network has re-encrypted and permuted in a proper manner.

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