Self-Healing Computation

In the problem of reliable multiparty computation (RC), there are $n$ parties, each with an individual input, and the parties want to jointly compute a function $f$ over $n$ inputs. The problem is complicated by the fact that an omniscient adversary controls a hidden fraction of the parties. We describe a self-healing algorithm for this problem. In particular, for a fixed function $f$, with $n$ parties and $m$ gates, we describe how to perform RC repeatedly as the inputs to $f$ change. Our algorithm maintains the following properties, even when an adversary controls up to $t \leq (\frac{1}{4} - \epsilon) n$ parties, for any constant $\epsilon >0$. First, our algorithm performs each reliable computation with the following amortized resource costs: $O(m + n \log n)$ messages, $O(m + n \log n)$ computational operations, and $O(\ell)$ latency, where $\ell$ is the depth of the circuit that computes $f$. Second, the expected total number of corruptions is $O(t (\log^{*} m)^2)$, after which the adversarially controlled parties are effectively quarantined so that they cause no more corruptions.Comment: 17 pages and 1 figure. It is submitted to SSS'1

An efficient self-healing key distribution scheme

Self-healing key distribution schemes enable a group user to recover session keys from two broadcast messages he received before and after those sessions, even if the broadcast messages for the middle sessions are lost due to network failure. These schemes are quite suitable in supporting secure communication over unreliable networks such as sensor networks and ad hoc networks. An efficient self-healing key distribution scheme is proposed in this paper. The scheme bases on the concept of access polynomial and self-healing key distribution model constructed by Hong et al. The new scheme reduces communication and computation overheads greatly yet still keeps the constant storageoverhead

Emergent velocity agreement in robot networks

In this paper we propose and prove correct a new self-stabilizing velocity agreement (flocking) algorithm for oblivious and asynchronous robot networks. Our algorithm allows a flock of uniform robots to follow a flock head emergent during the computation whatever its direction in plane. Robots are asynchronous, oblivious and do not share a common coordinate system. Our solution includes three modules architectured as follows: creation of a common coordinate system that also allows the emergence of a flock-head, setting up the flock pattern and moving the flock. The novelty of our approach steams in identifying the necessary conditions on the flock pattern placement and the velocity of the flock-head (rotation, translation or speed) that allow the flock to both follow the exact same head and to preserve the flock pattern. Additionally, our system is self-healing and self-stabilizing. In the event of the head leave (the leading robot disappears or is damaged and cannot be recognized by the other robots) the flock agrees on another head and follows the trajectory of the new head. Also, robots are oblivious (they do not recall the result of their previous computations) and we make no assumption on their initial position. The step complexity of our solution is O(n)

Efficient Utility-Driven Self-Healing Employing Adaptation Rules for Large Dynamic Architectures

Self-adaptation can be realized in various ways. Rule-based approaches prescribe the adaptation to be executed if the system or environment satisfy certain conditions and result in scalable solutions, however, with often only satisfying adaptation decisions. In contrast, utility-driven approaches determine optimal adaptation decisions by using an often costly optimization step, which typically does not scale well for larger problems. We propose a rule-based and utility-driven approach that achieves the beneficial properties of each of these directions such that the adaptation decisions are optimal while the computation remains scalable since an expensive optimization step can be avoided. The approach can be used for the architecture-based self-healing of large software systems. We define the utility for large dynamic architectures of such systems based on patterns capturing issues the self-healing must address and we use patternbased adaptation rules to resolve the issues. Defining the utility as well as the adaptation rules pattern-based allows us to compute the impact of each rule application on the overall utility and to realize an incremental and efficient utility-driven self-healing. We demonstrate the efficiency and optimality of our scheme in comparative experiments with a static rule-based scheme as a baseline and a utility-driven approach using a constraint solver

Self-Healing Tile Sets

Biology provides the synthetic chemist with a tantalizing and frustrating challenge: to create complex objects, defined from the molecular scale up to meters, that construct themselves from elementary components, and perhaps even reproduce themselves. This is the challenge of bottom-up fabrication. The most compelling answer to this challenge was formulated in the early 1980s by Ned Seeman, who realized that the information carried by DNA strands provides a means to program molecular self-assembly, with potential applications including DNA scaffolds for crystallography [19] or for molecular electronic circuits [15]. This insight opened the doors to engineering with the rich set of phenomena available in nucleic acid chemistry [20]

Memcomputing: a computing paradigm to store and process information on the same physical platform

In present day technology, storing and processing of information occur on physically distinct regions of space. Not only does this result in space limitations; it also translates into unwanted delays in retrieving and processing of relevant information. There is, however, a class of two-terminal passive circuit elements with memory, memristive, memcapacitive and meminductive systems -- collectively called memelements -- that perform both information processing and storing of the initial, intermediate and final computational data on the same physical platform. Importantly, the states of these memelements adjust to input signals and provide analog capabilities unavailable in standard circuit elements, resulting in adaptive circuitry, and providing analog massively-parallel computation. All these features are tantalizingly similar to those encountered in the biological realm, thus offering new opportunities for biologically-inspired computation. Of particular importance is the fact that these memelements emerge naturally in nanoscale systems, and are therefore a consequence and a natural by-product of the continued miniaturization of electronic devices. We will discuss the various possibilities offered by memcomputing, discuss the criteria that need to be satisfied to realize this paradigm, and provide an example showing the solution of the shortest-path problem and demonstrate the healing property of the solution path.Comment: The first part of this paper has been published in Nature Physics 9, 200-202 (2013). The second part has been expanded and is now included in arXiv:1304.167

Generalized Self-Healing Key Distribution using Vector Space Access Structure

Abstract. We propose and analyze a generalized self-healing key distribution using vector space access structure in order to reach more flexible performance of the scheme. Our self-healing technique enables better performance gain over previous approaches in terms of storage, communication and computation complexity. We provide rigorous treatment of security of our scheme in an appropriate security framework and show it is computationally secure and achieves forward and backward secrecy