Reverse Edge Cut-Set Bounds for Secure Network Coding

We consider the problem of secure communication over a network in the presence of wiretappers. We give a new cut-set bound on secrecy capacity which takes into account the contribution of both forward and backward edges crossing the cut, and the connectivity between their endpoints in the rest of the network. We show the bound is tight on a class of networks, which demonstrates that it is not possible to find a tighter bound by considering only cut-set edges and their connectivity

Secure Network Function Computation for Linear Functions -- Part I: Source Security

In this paper, we put forward secure network function computation over a directed acyclic network. In such a network, a sink node is required to compute with zero error a target function of which the inputs are generated as source messages at multiple source nodes, while a wiretapper, who can access any one but not more than one wiretap set in a given collection of wiretap sets, is not allowed to obtain any information about a security function of the source messages. The secure computing capacity for the above model is defined as the maximum average number of times that the target function can be securely computed with zero error at the sink node with the given collection of wiretap sets and security function for one use of the network. The characterization of this capacity is in general overwhelmingly difficult. In the current paper, we consider securely computing linear functions with a wiretapper who can eavesdrop any subset of edges up to a certain size r, referred to as the security level, with the security function being the identity function. We first prove an upper bound on the secure computing capacity, which is applicable to arbitrary network topologies and arbitrary security levels. When the security level r is equal to 0, our upper bound reduces to the computing capacity without security consideration. We discover the surprising fact that for some models, there is no penalty on the secure computing capacity compared with the computing capacity without security consideration. We further obtain an equivalent expression of the upper bound by using a graph-theoretic approach, and accordingly we develop an efficient approach for computing this bound. Furthermore, we present a construction of linear function-computing secure network codes and obtain a lower bound on the secure computing capacity

Byzantine Modification Detection in Multicast Networks With Random Network Coding

An information-theoretic approach for detecting Byzantine or adversarial modifications in networks employing random linear network coding is described. Each exogenous source packet is augmented with a flexible number of hash symbols that are obtained as a polynomial function of the data symbols. This approach depends only on the adversary not knowing the random coding coefficients of all other packets received by the sink nodes when designing its adversarial packets. We show how the detection probability varies with the overhead (ratio of hash to data symbols), coding field size, and the amount of information unknown to the adversary about the random code

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

The Security of Practical Quantum Key Distribution

Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on the eavesdropper's power. The first two sections provide a concise up-to-date review of QKD, biased toward the practical side. The rest of the paper presents the essential theoretical tools that have been developed to assess the security of the main experimental platforms (discrete variables, continuous variables and distributed-phase-reference protocols).Comment: Identical to the published version, up to cosmetic editorial change

Capacities of erasure networks

textWe have investigated, in various multiple senses, the “capacity” of several models of erasure networks. The defining characteristic of a memoryless erasure network is that each channel between any two nodes is an independent erasure channel. The models that we explore differ in the absence or presence of interference at either the transmitters, the receivers, or both; and in the availability of feedback at the transmitters. The crux of this work involves the investigation and analysis of several different performance measures for these networks: traditional information capacity (including multicast capacity and feeback capacity), secrecy capacity, and transport capacity.Electrical and Computer Engineerin