Slider-Crank Demonstration MQP

The slider-crank mechanism is a particular four-bar linkage configuration that exhibits both linear and rotational motion simultaneously. The position, velocity, acceleration and shaking forces generated by a slider-crank mechanism during operation can be determined analytically. The following report details the successful design, fabrication and testing of a pneumatically powered slider-crank mechanism for the purpose of classroom demonstration and experimentation. Transducers mounted to the mechanism record kinematic and dynamic force data during operation, which can then be compared to analytical values. The mechanism is capable of operating in balanced and unbalanced configurations so that the magnitude of shaking forces can be compared

zkQMC: Zero-Knowledge Proofs For (Some) Probabilistic Computations Using Quasi-Randomness

We initiate research into efficiently embedding probabilistic computations in probabilistic proofs by introducing techniques for capturing Monte Carlo methods and Las Vegas algorithms in zero knowledge and exploring several potential applications of these techniques. We design and demonstrate a technique for proving the integrity of certain randomized computations, such as uncertainty quantification methods, in non-interactive zero knowledge (NIZK) by replacing conventional randomness with low-discrepancy sequences. This technique, known as the Quasi-Monte Carlo (QMC) method, functions as a form of weak algorithmic derandomization to efficiently produce adversarial-resistant worst-case uncertainty bounds for the results of Monte Carlo simulations. The adversarial resistance provided by this approach allows the integrity of results to be verifiable both in interactive and non-interactive zero knowledge without the need for additional statistical or cryptographic assumptions. To test these techniques, we design a custom domain specific language and implement an associated compiler toolchain that builds zkSNARK gadgets for expressing QMC methods. We demonstrate the power of this technique by using this framework to benchmark zkSNARKs for various examples in statistics and physics. Using $N$ samples, our framework produces zkSNARKs for numerical integration problems of dimension $d$ with $O\left(\frac{(\log N)^d}{N}\right)$ worst-case error bounds. Additionally, we prove a new result using discrepancy theory to efficiently and soundly estimate the output of computations with uncertain data with an $O\left(d\frac{\log N}{\sqrt[d]{N}}\right)$ worst-case error bound. Finally, we show how this work can be applied more generally to allow zero-knowledge proofs to capture a subset of decision problems in $\mathsf{BPP}$, $\mathsf{RP}$, and $\mathsf{ZPP}$

Less is more: refinement proofs for probabilistic proofs

There has been intense interest over the last decade in implementations of _probabilistic proofs_ (IPs, SNARKs, PCPs, and so on): protocols in which an untrusted party proves to a verifier that a given computation was executed properly, possibly in zero knowledge. Nevertheless, implementations still do not scale beyond small computations. A central source of overhead is the _front-end_: translating from the abstract computation to a set of equivalent arithmetic constraints. This paper introduces a general-purpose framework, called Distiller, in which a user translates to constraints not the original computation but an abstracted _specification_ of it. Distiller is the first in this area to perform such transformations in a way that is provably safe. Furthermore, by taking the idea of encode a check in the constraints to its literal logical extreme, Distiller exposes many new opportunities for constraint reduction, resulting in cost reductions for benchmark computations of 1.3–50$\times$, and in some cases, better asymptotics

Zombie: Middleboxes that Don’t Snoop

Zero-knowledge middleboxes (ZKMBs) are a recent paradigm in which clients get privacy while middleboxes enforce policy: clients prove in zero knowledge that the plaintext underlying their encrypted traffic complies with network policies, such as DNS filtering. However, prior work had impractically poor performance and was limited in functionality. This work presents Zombie, the first system built using the ZKMB paradigm. Zombie introduces techniques that push ZKMBs to the verge of practicality: preprocessing (to move the bulk of proof generation to idle times between requests), asynchrony (to remove proving and verifying costs from the critical path), and batching (to amortize some of the verification work). Zombie’s choices, together with these techniques, provide a factor of 3.5$\times$ speedup in total computation done by client and middlebox, lowering the critical path overhead for a DNS filtering application to less than 300ms (on commodity hardware) or (in the asynchronous configuration) to 0. As an additional contribution that is likely of independent interest, Zombie introduces a portfolio of techniques to efficiently encode regular expressions in probabilistic (and zero knowledge) proofs; these techniques offer significant asymptotic and constant factor improvements in performance over a standard baseline. Zombie builds on this portfolio to support policies based on regular expressions, such as data loss prevention

A Step Forward in Kinesthetic Activities for Teaching Kinematics in Introductory Physics

We present a set of kinesthetic activities that utilize a local positioning system to teach kinematics in the physics classroom or laboratory. The activities build on previously reported activities in scope and complexity, incorporating two-dimensional motion and the simultaneous motions of multiple bodies. In these activities, students act out motions illustrated in graphs of kinematic quantities while holding a local positioning system device that tracks their position. Students are able to watch the data as they are graphed in real-time. These activities provide a kinesthetic experience of kinematics by allowing students to analyze their own movement rather than just the movement of specialized laboratory equipment