Limor Lahiani

Secret swarm unit: reactive k-secret sharing

Secret sharing is a basic fundamental cryptographic task. Motivated by the virtual automata abstraction and swarm computing, we investigate an extension of the k-secret sharing scheme, in which the secret components are changed on the fly, independently and without (internal) communication, as a reaction to a global external trigger. The changes are made while maintaining the requirement that k or more secret shares may reveal the secret and no k - 1 or fewer reveal the secret. The application considered is a swarm of mobile processes, each maintaining a share of the secret which may change according to common outside inputs e.g., inputs received by sensors attached to the process. The proposed schemes support addition and removal of processes from the swarm as well as corruption of a small portion of the processes in the swarm.

Self-stabilizing mobile node location management and message routing

We present simple algorithms for achieving self-stabilizing location management and routing in mobile ad-hoc networks. While mobile clients may be susceptible to corruption and stopping failures, mobile networks are often deployed with a reliable GPS oracle, supplying frequent updates of accurate real time and location information to mobile nodes. Information from a GPS oracle provides an external, shared source of consistency for mobile nodes, allowing them to label and timestamp messages, and hence aiding in identification of, and eventual recovery from, corruption and failures. Our algorithms use a GPS oracle. Our algorithms also take advantage of the Virtual Stationary Automata programming abstraction, consisting of mobile clients, virtual timed machines called virtual stationary automata (VSAs), and a local broadcast service connecting VSAs and mobile clients. VSAs are distributed at known locations over the plane, and emulated in a self-stabilizing manner by the mobile nodes in the system. They serve as fault-tolerant building blocks that can interact with mobile clients and each other, and can simplify implementations of services in mobile networks. We implement three self-stabilizing, fault-tolerant services, each built on the prior services: (1) VSA-to-VSA geographic routing, (2) mobile client location management, and (3) mobile client end-to-end routing. We use a greedy version of the classical depth-first search algorithm to route messages between VSAs in different regions. The mobile client location management service is based on home locations: Each client identifier hashes to a set of home locations, regions whose VSAs are periodically updated with the client’s location. VSAs maintain this information and answer queries for client locations. Finally, the VSA-to-VSA routing and location management services are used to implement mobile client end-to-end routing.

Timed virtual stationary automata for mobile networks

We define a programming abstraction for mobile networks called the Timed Virtual Stationary Automata programming layer, consisting of mobile clients, virtual timed I/O automata called virtual stationary automata (VSAs), and a communication service connecting VSAs and client nodes. The VSAs are located at prespecified regions that tile the plane, defining a static virtual infrastructure. We present a self-stabilizing algorithm to emulate a timed VSA using the real mobile nodes that are currently residing in the VSAs region. We also discuss examples of applications whose implementations benefit from the simplicity obtained through use of the VSA abstraction.

Brief announcement: virtual stationary automata for mobile networks

The task of designing algorithms for constantly changing networks is difficult. We focus on mobile ad-hoc networks, where mobile processors attempt to coordinate despite minimal infrastructure support. We develop new techniques to cope with this dynamic, heterogeneous, and chaotic environment. We mask the unpredictable behavior of mobile networks by defining and emulating a virtual infrastructure, consisting of timing-aware and location-aware machines at fixed locations, that mobile nodes can interact with. The static virtual infrastructure allows appplication developers to use simpler algorithms — including many previously developed for fixed networks. Virtual Stationary Automata programming layer. Our programming abstraction consists of a static infrastructure of fixed, timed virtual machines with an explicit notion of real time, called Virtual Stationary Automata (VSAs), distributed at known locations over the plane, and emulated by the real mobile nodes in the system. Each VSA represents a predetermined geographic area and has broadcast capabilities similar to those of the mobile nodes, allowing nearby VSAs and mobile nodes to communicate with one another. This programming layer provides mobile nodes with a virtual infrastructure with which to coordinate their actions. Many practical algorithms depend significantly on timing, and it is reasonable to assume that many mobile nodes have access to reasonably synchronized clocks. In the VSA programming layer, the virtual automata also have access to virtual clocks, guaranteed to not drift too far from real time. Our virtual infrastructure differs in key ways from others that have previously been proposed for mobile ad-hoc networks. The GeoQuorums algorithm [2] was the first to use virtual nodes; the virtual nodes in that work are atomic objects at fixed geographical locations. More general virtual mobile automata were suggested in [1]; our automata are more powerful than those in [1] in that ours include timing capabilities, which are important for many applications. Also, our automata are stationary, and are arranged in a connected pattern that is similar to a traditional wired ne-

Polygonal broadcast, secret maturity, and the firing sensors

Abstract This work considers communication among sensors that are deployed in a geographic region. Each sensor is a computing device with severe resource limitations, low power, slow processing and small memory. The devices are distributed (uniformly) in the geographic region. In this work we present self-stabilizing broadcast, flooding and sense of direction procedures that fit the special characteristics of the system. Imaginary polygon tilings are presented as a general scheme for supporting communication in sensor networks. Broadcasting is a common way of communicating in ad hoc mobile networks such as sensor networks. We present broadcast procedures and show how they are used by a sensor for broadcasting globally and locally, achieving sense of direction and distributing secrets that activate the sensors simultaneously at a particular time without revealing the nature of the upcoming activity.

Secret swarm unit

Secret sharing is a fundamental cryptographic task. Motivated by the virtual automata abstraction and swarm computing, we investigate an extension of the k-secret sharing scheme, in which the secret shares are changed on the fly, independently and without (internal) communication, as a reaction to a global external trigger. The changes are made while maintaining the requirement that k or more secret shares may reconstruct the secret and no k-1 or fewer can do so.The application considered is a swarm of mobile processes, each maintaining a share of the secret which may change according to common outside inputs, e.g., inputs received by sensors attached to the process.The proposed schemes support addition and removal of processes from the swarm, as well as corruption of a small portion of the processes in the swarm.

Brief Announcement: Unique Permutation Hashing

We propose a new open addressing hash function, the unique-permutation hash function , and a performance analysis of its hash computation. A hash function h is simple uniform if items are equally likely to be hashed to any table location (in the first trial). A hash function h is random or strong uniform if the probability of any permutation to be a probe sequence, when using h , is

Brief announcement: polygonal broadcast, secret maturity and the firing sensors

{{1}\over{N!}}

Virtual Stationary Automata for Mobile Networks

, where N is the size of the table. We show that the unique-permutation hash function is strong uniform and therefore has the lowest expected cost; each probe sequence is equally likely to be chosen, when the keys are uniformly chosen. Thus, the unique-permutation hash ensures that each empty table location has the same probability to be assigned with a uniformly chosen key. For constant load factors *** < 1, where *** is the ratio between the number of inserted items and the table size, the expected time for computing the unique-permutation hash function is O (1) and the expected number of table locations that are checked before an empty location is found, during insertion (or search), is also O (1).

Polygonal Broadcast for Sensor Networks

There is a great interest and attention of industry and research communities in the capabilities of small computing devices, called sensors, that use wireless communication among themselves. The applications for such devices in creating a global computing environment may change our view on computers and computing. The new special settings of such systems require careful examination , and rethinking concerning the methodologies and technologies used for coordination. Energy limitation is a concern in sensor networks. One would like to broadcast a message while ensuring that most of the sensors will not have to transmit messages. In a sense, a backbone of the network should be constructed, such that local broadcasts of some radius ¡ of the backbone sensors will ensure global coverage of the geographic region in which the sensors are located. The geographic coverage requirement is a consequence of the possibility for having passive sensors that only receive messages (perhaps in a mode used to harvest more energy) such that other sensors are not aware of their existence. Moreover, the backbone may not be a fixed backbone , but could be an ad-hoc defined backbone for each particular broadcast. The existence of several backbones , spanned by different set of representative sensors, distributes the energy usage in a balanced fashion among the sensors. We present several schemes based on imaginary (or virtual) partition of the plane into (all possible) regular polygons: triangles, squares and hexagons; we call this an imaginary tiling because no permanent tiling or clustering of the sensors is established. Each polygon in the tiling has a representative sensor who is responsible for local-broadcasting the message to all the sensors in its polygon region, the representative can be elected according to different parameters such as, its relative location in the polygon, the maximum available power, the minimum transmitting energy, etc. The polygons representatives form the ad-hoc backbone , they are the only transmitting sensors of a broadcast/flood, while all the others are receiving. The scheme abstracts the specific transmission radius of the devices, by allowing the length of a polygon edge to be a parameter. Our self-stabilizing broadcast schemes are extended to the case in which the sensors are not uniformly distributed. We use polyg-onal flooding in order to cope with empty or hardly populated areas. The polygonal flooding requires (an additional constant factor) more transmissions and storage of arriving messages in the sensors memory. Then we …