Precomputed and transactional mixing

A cryptographic apparatus comprising:

• a plurality of cryptographic node devices, each node device at a substantially different fixed location, and each node a separately-secured device, and each node securing plural substantially different symmetric cryptographic keys;
• a plurality of mobile cryptographic unit devices, each unit device separately substantially controlled by a respective user, and each unit device securing plural substantially different symmetric cryptographic keys;
• a substantially distinct common key, for each distinct pair of node device and unit device, stored in the respective node device and stored in the respective unit device, and the common key for that respective pair of node and unit substantially available to that respective node and that respective unit exclusively;
• and
• the node devices configured to cooperate in cryptographic transformation of information received by a first one of the node devices from plural unit devices and the resulting information, after cooperating transformation including by substantially all the other nodes, communicated to plural unit devices,
• where the cryptographic apparatus is configured for digitally mixing at least a batch of items of information to substantially thwart traffic analysis of communication between the unit devices, and further comprises:
• one of the nodes, the entry node, first in at least a fixed cascade ordering of the nodes, including communication means to receive from plural unit devices at least parts of a batch comprising plural items of information;
• a different one of the nodes from the first node, the exit node, the last node in the at least fixed cascade ordering, including communication means to provide to respective plural unit devices at least respective parts of a batch comprising plural items of information;
• intermediate communication means at least connecting the nodes, pairwise, in the at least fixed ordering, forming a pairwise communication cascade from the entry node to the exit node;
• each node including means to transform each item of information in an input batch, the input batch received over a respective communication means, into an item of information in an output batch, the output batch sent over the corresponding communication means to the next node in the at least fixed ordering and by the exit node to, at least in parts, at least some of the unit devices;
• the transformation means of a node for its respective input batch including means to change the order of the items of information in the input batch into a substantially unpredictable, at least without secret key information available to the node, order in its respective output batch;
• and
• the transformation means of a node for its respective input batch including means to make the correspondence between the information item in the input batch, when they correspond to the information item in its respective output batch, substantially unrecognizable, at least without secret key information available to the node.