Patents Pending | Earth Computing Inc. | Paul Borrill
Mathematical Foundation
Groupoid semantics for timeless networks
and secure classical key distribution
David Reutter
Department of Computer Science, University of Oxford
[email protected]
Jamie Vicary
Department of Computer Science, University of Oxford
[email protected]
Abstract—We provide a mathematical foundation for timeless
networks, a new paradigm for distributed communication which
has recently been proposed. Our approach is based on groubits,
generalizations of classical bits arising from groupoids with spe-
cial properties. Our techniques give a clean mathematical model
for timeless networks, and allow the description and verification
of a number of interesting protocols, including message routing
without timeouts, and information theoretically–secure classical
key distribution, under minimal security assumptions. We also
build classical-physics implementations of a number of quantum
protocols on networks of groubits, including dense coding and
teleportation.
I. INTRODUCTION
A. Overview
In this paper we study the foundations of timeless networks,
a new paradigm for distributed communication presented re-
cently by Borrill [1] and currently under commercial devel-
opment by Earth Computing1. We study a mathematically-
The read operation destroys a groubit and creates a conven-
tional bit, while the write operation destroys a conventional
bit and creates a new groubit. Pairs of groubits can also be
connected by a link, enabling the Tick operation, where A and
B label the two connected nodes, and ⊕ is addition modulo 2:
• Tick((AL,AI
),(BL,BI
) =((AL,AI
⊕BL
),(BL,BI
⊕AL
))
Intuitively, for each node in the pair, we flip the internal bit
just when the other node has logical bit equal to 1. Nodes can
belong to multiple links, in general forming a graph topology.
B. Assumptions
We make some assumptions about these groubit operations.
• Atomicity. The operations Init, Swap, Read, Write and
Tick are implemented atomically.
• Security. A user can never discover any information about
the state of a node, except via Read.
We emphasize that claims we make about the functionality
arxiv.org/abs/1707.00966