Arithmetic complexity via effective names for random sequences

We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably, Schnorr, and Kurtz random sets, weakly 1-generics and their complementary classes, we find that there exist characterizations of the third and fourth levels of the arithmetic hierarchy purely in terms of these notions. More generally, there exists an equivalence between arithmetic complexity and existence of numberings for classes of left-r.e. sets with shift-persistent elements. While some classes (such as Martin-L\"{o}f randoms and Kurtz non-randoms) have left-r.e. numberings, there is no canonical, or acceptable, left-r.e. numbering for any class of left-r.e. randoms. Finally, we note some fundamental differences between left-r.e. numberings for sets and reals

Small generic hardcore subsets for the discrete logarithm: short secret DL-Keys

Abstract Let G be a group of prime order q with generator g. We study hardcore subsets H ⊂ G of the discrete logarithm (DL) log g in the model of generic algorithms. In this model we count group operations such as multiplication and division, while computations with non-group data are for free. It is known from Nechaev [Math. Notes 55 (1994

A Machine-Checked Formalization of the Generic Model and the Random Oracle Model

Most approaches to the formal analyses of cryptographic protocols make the perfect cryptography assumption, i.e. the hypothese that there is no way to obtain knowledge about the plaintext pertaining to a ciphertext without knowing the key. Ideally, one would prefer to rely on a weaker hypothesis on the computational cost of gaining information about the plaintext pertaining to a ciphertext without knowing the key. Such a view is permitted by the Generic Model and the Random Oracle Model which provide non-standard computational models in which one may reason about the computational cost of breaking a cryptographic scheme. Using the proof assistant Coq, we provide a machine-checked account of the Generic Model and the Random Oracle Mode

Keep Me In, Coach: The Short- and Long-Term Effects of Targeted Academic Coaching

To boost college graduation rates, policymakers often advocate for academic supports such as coaching or mentoring. Proactive and intensive coaching interventions are effective, but are costly and difficult to scale. We evaluate a relatively lower-cost group coaching program targeted at first-year college students placed on academic probation. Participants attend a workshop where coaches aim to normalize failure and improve self-confidence. Coaches also facilitate a process whereby participants reflect on their academic difficulties, devise solutions to address their challenges, and create an action plan. Participants then hold a one-time follow-up meeting with their coach or visit a campus resource. Using a difference-in-discontinuity design, we show that the program raises students’ first-year GPA by 14.6 percent of a standard deviation, and decreases the probability of first-year dropout by 8.5 percentage points. Effects are concentrated among lower-income students who also experience a significant increase in the probability of graduating. Finally, using administrative data, we provide the first evidence that coaching/mentoring may have substantial long-run effects, as we document significant gains in lower-income students’ earnings seven to nine years following entry to the university. Our findings indicate that targeted, group coaching can be an effective way to improve marginal students’ academic and early career outcomes

Sustainable Energy Storage

This Final Design Review document covers the work we, students at California Polytechnic State University – San Luis Obispo, have performed in collaboration with Mr. Harish Bhutani and Dr. Mohammad Noori. The project’s intent is to create an energy storage system for off-grid and developing region applications using alternative technologies to lithium-ion battery storage. We plan to manufacture and assemble a scale model of the energy storage system to prove effectiveness and practicality. This system will store enough energy to power basic appliances and essential devices for a house or community. The chosen design direction will be a flywheel, as it is very energy dense and is less complex than other options. The following will outline the entire design process, including the ideas we created, the design challenges, and the testing of our physical build. To meet climate change goals set around the globe, our world needs to head towards a more sustainable future, and the energy sector is no exception. This project aims to help with the research and design of this new field and present a final product that will have a meaningful impact on our world

Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search

By applying Grover's quantum search algorithm to the lattice algorithms of Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and Stehl\'{e}, we obtain improved asymptotic quantum results for solving the shortest vector problem. With quantum computers we can provably find a shortest vector in time $2^{1.799n + o(n)}$, improving upon the classical time complexity of $2^{2.465n + o(n)}$ of Pujol and Stehl\'{e} and the $2^{2n + o(n)}$ of Micciancio and Voulgaris, while heuristically we expect to find a shortest vector in time $2^{0.312n + o(n)}$, improving upon the classical time complexity of $2^{0.384n + o(n)}$ of Wang et al. These quantum complexities will be an important guide for the selection of parameters for post-quantum cryptosystems based on the hardness of the shortest vector problem.Comment: 19 page