35,146 research outputs found
How to Securely Compute the Modulo-Two Sum of Binary Sources
In secure multiparty computation, mutually distrusting users in a network
want to collaborate to compute functions of data which is distributed among the
users. The users should not learn any additional information about the data of
others than what they may infer from their own data and the functions they are
computing. Previous works have mostly considered the worst case context (i.e.,
without assuming any distribution for the data); Lee and Abbe (2014) is a
notable exception. Here, we study the average case (i.e., we work with a
distribution on the data) where correctness and privacy is only desired
asymptotically.
For concreteness and simplicity, we consider a secure version of the function
computation problem of K\"orner and Marton (1979) where two users observe a
doubly symmetric binary source with parameter p and the third user wants to
compute the XOR. We show that the amount of communication and randomness
resources required depends on the level of correctness desired. When zero-error
and perfect privacy are required, the results of Data et al. (2014) show that
it can be achieved if and only if a total rate of 1 bit is communicated between
every pair of users and private randomness at the rate of 1 is used up. In
contrast, we show here that, if we only want the probability of error to vanish
asymptotically in block length, it can be achieved by a lower rate (binary
entropy of p) for all the links and for private randomness; this also
guarantees perfect privacy. We also show that no smaller rates are possible
even if privacy is only required asymptotically.Comment: 6 pages, 1 figure, extended version of submission to IEEE Information
Theory Workshop, 201
Signal propagation and noisy circuits
The information carried by a signal decays when the signal is corrupted by random noise. This occurs when a message is transmitted over a noisy channel, as well as when a noisy component performs computation. We first study this signal decay in the context of communication and obtain a tight bound on the rate at which information decreases as a signal crosses a noisy channel. We then use this information theoretic result to obtain depth lower bounds in the noisy circuit model of computation defined by von Neumann. In this model, each component fails (produces 1 instead of 0 or vice-versa) independently with a fixed probability, and yet the output of the circuit is required to be correct with high probability. Von Neumann showed how to construct circuits in this model that reliably compute a function and are no more than a constant factor deeper than noiseless circuits for the function. We provide a lower bound on the multiplicative increase in circuit depth necessary for reliable computation, and an upper bound on the maximum level of noise at which reliable computation is possible
Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation
Sensor networks potentially feature large numbers of nodes that can sense
their environment over time, communicate with each other over a wireless
network, and process information. They differ from data networks in that the
network as a whole may be designed for a specific application. We study the
theoretical foundations of such large scale sensor networks, addressing four
fundamental issues- connectivity, capacity, clocks and function computation.
To begin with, a sensor network must be connected so that information can
indeed be exchanged between nodes. The connectivity graph of an ad-hoc network
is modeled as a random graph and the critical range for asymptotic connectivity
is determined, as well as the critical number of neighbors that a node needs to
connect to. Next, given connectivity, we address the issue of how much data can
be transported over the sensor network. We present fundamental bounds on
capacity under several models, as well as architectural implications for how
wireless communication should be organized.
Temporal information is important both for the applications of sensor
networks as well as their operation.We present fundamental bounds on the
synchronizability of clocks in networks, and also present and analyze
algorithms for clock synchronization. Finally we turn to the issue of gathering
relevant information, that sensor networks are designed to do. One needs to
study optimal strategies for in-network aggregation of data, in order to
reliably compute a composite function of sensor measurements, as well as the
complexity of doing so. We address the issue of how such computation can be
performed efficiently in a sensor network and the algorithms for doing so, for
some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE
Neural computation of arithmetic functions
A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n -bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions
Programmable neural logic
Circuits of threshold elements (Boolean input, Boolean output neurons) have been shown to be surprisingly powerful. Useful functions such as XOR, ADD and MULTIPLY can be implemented by such circuits more efficiently than by traditional AND/OR circuits. In view of that, we have designed and built a programmable threshold element. The weights are stored on polysilicon floating gates, providing long-term retention without refresh. The weight value is increased using tunneling and decreased via hot electron injection. A weight is stored on a single transistor allowing the development of dense arrays of threshold elements. A 16-input programmable neuron was fabricated in the standard 2 μm double-poly, analog process available from MOSIS.
We also designed and fabricated the multiple threshold element introduced in [5]. It presents the advantage of reducing the area of the layout from O(n^2) to O(n); (n being the number of variables) for a broad class of Boolean functions, in particular symmetric Boolean functions such as PARITY.
A long term goal of this research is to incorporate programmable single/multiple threshold elements, as building blocks in field programmable gate arrays
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