We introduce a new notion of multiverse threshold signatures (MTS). In an MTS scheme, multiple universes – each defined by a set of (possibly overlapping) signers, their weights, and a specific security threshold – can co-exist. A universe can be (adaptively) created via a non-interactive asynchronous setup. Crucially, each party in the multiverse holds constant-sized keys and releases compact signatures with size and computation time both independent of the number of universes. Given sufficient partial signatures over a message from the members of a specific universe, an aggregator can produce a short aggregate signature relative to that universe.We construct an MTS scheme building on BLS signatures. Our scheme is practical, and can be used to reduce bandwidth complexity and computational costs in decentralized oracle networks. As an example data point, consider a multiverse containing 2000 nodes and 100 universes (parameters inspired by Chainlink’s use in the wild), each of which contains arbitrarily large subsets of nodes and arbitrary thresholds. Each node computes and outputs 1 group element as its partial signature; the aggregator performs under 0.7 seconds of work for each aggregate signature, and the final signature of size 192 bytes takes 6.4 ms (or 198K EVM gas units) to verify. For this setting, prior approaches, when used to construct MTS, yield schemes that have one of the following drawbacks: (i) partial signatures that are 48× larger, (ii) have aggregation times 311× worse, or (iii) have signature size 39× and verification gas costs 3.38× larger. We also provide an open-source implementation and a detailed evaluation.

Timed-release encryption can encrypt a message to a future time such that it can only be decrypted after that time. Potential applications include sealed bid auctions, scheduled confidential transactions, and digital time capsules. To enable such applications as decentralized smart contracts, we explore how to use timed-release encryption on blockchains.

An important problem for secure communication is that of achieving jam resistance, without any prior shared secret between the sender and receiver, and without limits on the assumed computational power of the attacker. To date, only one system has been proposed for this, the BBC system, which is based on coding theory using codes derived from arbitrary hash functions. It is unfortunate that only one, narrow solution has been found for this important problem. We now propose a new algorithm for this problem: the HBT algorithm. It is very different from BBC, using codes based on monotone Boolean functions (MBF), rather than hash functions. It is also more general. We show that despite being very different from BBC, the latter can be viewed as a special case of it. In fact, a theorem proves that all such codes are special cases of this new system. We give empirical results suggesting that this new approach is useful, and describe directions for future research.

A new method is given for speeding up learning in a deep neural network with many hidden layers, by partially partitioning the network rather than fully interconnecting the layers. Empirical results are shown both for learning a simple Boolean function on a standard back-prop network, and for learning two different, complex, real-world vision tasks on a more sophisticated convolutional network. In all cases, the performance of the proposed system was better than traditional systems. The partially-partitioned network outperformed both the fully-partitioned and fully-unpartitioned networks.

We present algorithms that permit increased efficiency in the calculation of conservation functions for cellular automata, and report results obtained from implementations of these algorithms to report conservation laws for 1-D cellular automata of higher order than any previously known. We introduce the notion of trivial and core conservation functions to distinguish truly new conservation functions from simple extensions of lower-order ones. We give new theorems related to these concepts, and show our use of them to derive more efficient algorithms for finding conservation functions. We then present the complete list of conservation functions up to order 16 for the 256 elementary 1-D binary cellular automata. These include CAs that were not previously known to have nontrivial conservation functions.

Visualization can be an effective means for analyzing security data and teaching students different concepts about various security algorithms. At the Air Force Academy, interactive visualizations are used to teach ciphers to students in a cryptography course. In the course of preparing student visualizations about the RC4 cipher characteristics, an anomaly was discovered in the basic encryption algorithm. This paper describes the anomaly and the process of how it was discovered through visualization.

We present two new types of neural networks (both of which can be trained with ordinary error backpropagation) and we present a new algorithm for learning a probability density function (pdf) from example vectors. It is normally difficult to invert a neural network, but for the new bijective neural network, it is efficient to find an input producing any desired output, and such an input is guaranteed to exist and to be unique. Furthermore, it can be used as one component in building a pdf neural network, which is a neural network with a nonnegative output, and for which it is guaranteed that the integral of the output is exactly 1.0 (as in a pdf function). Both of these can be used for supervised learning using standard error backpropagation. Finally, the new pdf learning algorithm is capable of using those networks to learn a pdf given i.i.d. samples drawn from that pdf, and to then generate new vectors from the learned pdf. This, in turn, allows inversion of a function with non-unique inverses, where each inverse is generated with just a single evaluation of the network.

Slow learning of neural-network function approximators can frequently be attributed to interference, which occurs when learning in one area of the input space causes unlearning in another area. To mitigate the effect of unlearning, this paper develops an algorithm that adjusts the weights of an arbitrary, nonlinearly parameterized network such that the potential for future interference during learning is reduced. This is accomplished by the reduction of a biobjective cost function that combines the approximation error and a term that measures interference. An analysis of the algorithm's convergence properties shows that learning with this algorithm reduces future unlearning. The algorithm can be used either during online learning or can be used to condition a network to have immunity from interference during a future learning stage. A simple example demonstrates how interference manifests itself in a network and how less interference can lead to more efficient learning. Simulations demonstrate how this new learning algorithm speeds up the training in various situations due to the extra cost function term.

We investigate new approaches to dynamic-programming-based optimal control of continuous time-and-space systems. We use neural networks to approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation which is a first-order, nonlinear, partial differential equation. We derive the gradient descent rule for integrating this equation inside the domain, given the conditions on the boundary. We apply this approach to the "car-on-the-hill" which is a 2D highly nonlinear control problem. We discuss the results obtained and point out a low quality of approximation of the value function and of the derived control. We attribute this bad approximation to the fact that the HJB equation has many generalized solutions other than the value function, and our gradient descent method converges to one among these functions, thus possibly failing to find the correct value function. We illustrate this limitation on a simple 1D control problem.

Interference in neural networks occurs when learning in one area of the input space causes unlearning in another area. Networks that are less susceptible to interference are referred to as spatially local networks. To obtain a better understanding of these properties, a theoretical framework, consisting of a measure of interference and a measure of network localization, is developed. These measures incorporate not only the network weights and architecture but also the learning algorithm. Using this framework to analyze sigmoidal, multilayer perceptron (MLP) networks that employ the backpropagation learning algorithm on the quadratic cost function, we address a familiar misconception that single-hidden-layer sigmoidal networks are inherently nonlocal by demonstrating that given a sufficiently large number of adjustable weights, single-hidden-layer sigmoidal MLP's exist that are arbitrarily local and retain the ability to approximate any continuous function on a compact domain.