Complexity of Multi-Value Byzantine Agreement

In this paper, we consider the problem of maximizing the throughput of Byzantine agreement, given that the sum capacity of all links in between nodes in the system is finite. We have proposed a highly efficient Byzantine agreement algorithm on values of length l>1 bits. This algorithm uses error detecting network codes to ensure that fault-free nodes will never disagree, and routing scheme that is adaptive to the result of error detection. Our algorithm has a bit complexity of n(n-1)l/(n-t), which leads to a linear cost (O(n)) per bit agreed upon, and overcomes the quadratic lower bound (Omega(n^2)) in the literature. Such linear per bit complexity has only been achieved in the literature by allowing a positive probability of error. Our algorithm achieves the linear per bit complexity while guaranteeing agreement is achieved correctly even in the worst case. We also conjecture that our algorithm can be used to achieve agreement throughput arbitrarily close to the agreement capacity of a network, when the sum capacity is given

Ethernet - a survey on its fields of application

During the last decades, Ethernet progressively became the most widely used local area networking (LAN) technology. Apart from LAN installations, Ethernet became also attractive for many other fields of application, ranging from industry to avionics, telecommunication, and multimedia. The expanded application of this technology is mainly due to its significant assets like reduced cost, backward-compatibility, flexibility, and expandability. However, this new trend raises some problems concerning the services of the protocol and the requirements for each application. Therefore, specific adaptations prove essential to integrate this communication technology in each field of application. Our primary objective is to show how Ethernet has been enhanced to comply with the specific requirements of several application fields, particularly in transport, embedded and multimedia contexts. The paper first describes the common Ethernet LAN technology and highlights its main features. It reviews the most important specific Ethernet versions with respect to each application field’s requirements. Finally, we compare these different fields of application and we particularly focus on the fundamental concepts and the quality of service capabilities of each proposal

Resilient Network Coding in the Presence of Byzantine Adversaries

Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces distributed polynomial-time rate-optimal network codes that work in the presence of Byzantine nodes. We present algorithms that target adversaries with different attacking capabilities. When the adversary can eavesdrop on all links and jam zO links, our first algorithm achieves a rate of C - 2zO, where C is the network capacity. In contrast, when the adversary has limited eavesdropping capabilities, we provide algorithms that achieve the higher rate of C - zO. Our algorithms attain the optimal rate given the strength of the adversary. They are information-theoretically secure. They operate in a distributed manner, assume no knowledge of the topology, and can be designed and implemented in polynomial time. Furthermore, only the source and destination need to be modified; nonmalicious nodes inside the network are oblivious to the presence of adversaries and implement a classical distributed network code. Finally, our algorithms work over wired and wireless networks