Uncovering Algebraic Structures in the MPC Landscape

A fundamental problem in the theory of secure multi-party computation (MPC) is to characterize functions with more than 2 parties which admit MPC protocols with information-theoretic security against passive corruption. This question has seen little progress since the work of Chor and Ishai (1996), which demonstrated difficulties in resolving it. In this work, we make significant progress towards resolving this question in the important case of aggregating functionalities, in which m parties P1, . . . , Pm hold inputs x1, . . . , xm and an aggregating party P0 must learn f(x1,...,xm). We uncover a rich class of algebraic structures that are closely related to secure computability, namely, “Commuting Permutations Systems” (CPS) and its variants. We present an extensive set of results relating these algebraic structures among themselves and to MPC, including new protocols, impossibility results and separations. Our results include a necessary algebraic condition and slightly stronger sufficient algebraic condition for a function to admit information-theoretically secure MPC protocols. We also introduce and study new models of minimally interactive MPC (called UNIMPC and UNIMPC*), which not only help in understanding our positive and negative results better, but also open up new avenues for studying the cryptographic complexity landscape of multi-party functionalities. Our positive results include novel protocols in these models, which may be of independent practical interest. Finally, we extend our results to a definition that requires UC security as well as semi-honest security (which we term strong security). In this model we are able to carry out the characterization of all computable functions, except for a gap in the case of aggregating functionalities

Hierarchical Clustering in Λ{\Lambda}CDM Cosmologies via Persistence Energy

In this research, we investigate the structural evolution of the cosmic web, employing advanced methodologies from Topological Data Analysis. Our approach involves leveraging LITE, an innovative method from recent literature that embeds persistence diagrams into elements of vector spaces. Utilizing this methodology, we analyze three quintessential cosmic structures: clusters, filaments, and voids. A central discovery is the correlation between \textit{Persistence Energy} and redshift values, linking persistent homology with cosmic evolution and providing insights into the dynamics of cosmic structures.Comment: 12 pages, 9 figures, minor change

Template-based hardware-software codesign for high-performance embedded numerical accelerators

Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 129-132).Sophisticated algorithms for control, state estimation and equalization have tremendous potential to improve performance and create new capabilities in embedded and mobile systems. Traditional implementation approaches are not well suited for porting these algorithmic solutions into practical implementations within embedded system constraints. Most of the technical challenges arise from design approach that manipulates only one level in the design stack, thus being forced to conform to constraints imposed by other levels without question. In tightly constrained environments, like embedded and mobile systems, such approaches have a hard time efficiently delivering and delivering efficiency. In this work we offer a solution that cuts through all the design stack layers. We build flexible structures at the hardware, software and algorithm level, and approach the solution through design space exploration. To do this efficiently we use a template-based hardware-software development flow. The main incentive for template use is, as in software development, to relax the generality vs. efficiency/performance type tradeoffs that appear in solutions striving to achieve run-time flexibility. As a form of static polymorphism, templates typically incur very little performance overhead once the design is instantiated, thus offering the possibility to defer many design decisions until later stages when more is known about the overall system design. However, simply including templates into design flow is not sufficient to result in benefits greater than some level of code reuse. In our work we propose using templates as flexible interfaces between various levels in the design stack. As such, template parameters become the common language that designers at different levels of design hierarchy can use to succinctly express their assumptions and ideas. Thus, it is of great benefit if template parameters map directly and intuitively into models at every level. To showcase the approach we implement a numerical accelerator for embedded Model Predictive Control (MPC) algorithm. While most of this work and design flow are quite general, their full power is realized in search for good solutions to a specific problem. This is best understood in direct comparison with recent works on embedded and high-speed MPC implementations. The controllers we generate outperform published works by a handsome margin in both speed and power consumption, while taking very little time to generate.by Ranko Radovin Sredojević.Ph.D

Applications of Genetic Algorithms to a Variety of Problems in Physics and Astronomy

Genetic algorithms are search techniques that borrow ideas from the biological process of evolution. By means of natural selection, genetic algorithms can be employed as robust numerical optimizers on problems that would normally be extremely problematic due to ill-behaved search spaces. The genetic algorithm has an advantage in that it is a global optimization strategy, as opposed to more conventional methods, which will often terminate at local maxima. The success and resourcefulness of genetic algorithms as problem-solving strategies are quickly gaining recognition among researchers of diverse areas of study. In this thesis I elaborate on applications of a genetic algorithm to several problems in physics and astronomy. First, the concepts behind functional optimization are discussed, as well as several computational strategies for locating optima. The basic ideas behind genetic algorithms and their operations are then outlined, as well as advantages and disadvantages of the genetic algorithm over the previously discussed optimization techniques. Then the results of several applications of a genetic algorithm are discussed. The majority are relatively simple problems (involving the fitting of only one or two parameters) that nicely illustrate the genetic algorithm’s approach to optimization of “fitness,” and its ability to reproduce familiar results. The last two problems discussed are non-trivial and demonstrate the genetic algorithm’s robustness. The first of these was the calculation of the mass of the radio source Sagittarius A*, believed to be a supermassive black hole at the center of the Milky Way, which required that the genetic algorithm find several orbital elements associated with an orbiting star. The results obtained with the genetic algorithm were in good agreement with those obtained by Genzel et al [19]. Then discussed was the problem of parametrization of thermonuclear reaction rates. This problem is especially interesting because attempts at fitting several rates prior to the implementation of the genetic algorithm proved to be unsuccessful. Some of the rates varied with temperature over many orders of magnitude, and required the genetic algorithm to find as many as twenty-eight parameters. A relatively good fit was obtained for all of the rates. In the applications of genetic algorithms discussed in this thesis, it has been found that they can outperform conventional optimization strategies for difficult, multidimensional problems, and can perform at least as well as conventional methods when applied to more trivial problems

Raziel: Private and Verifiable Smart Contracts on Blockchains

Raziel combines secure multi-party computation and proof-carrying code to provide privacy, correctness and verifiability guarantees for smart contracts on blockchains. Effectively solving DAO and Gyges attacks, this paper describes an implementation and presents examples to demonstrate its practical viability (e.g., private and verifiable crowdfundings and investment funds). Additionally, we show how to use Zero-Knowledge Proofs of Proofs (i.e., Proof-Carrying Code certificates) to prove the validity of smart contracts to third parties before their execution without revealing anything else. Finally, we show how miners could get rewarded for generating pre-processing data for secure multi-party computation.Comment: Support: cothority/ByzCoin/OmniLedge

On Fully Secure MPC with Solitary Output

We study the possibility of achieving full security, with guaranteed output delivery, for secure multiparty computation of functionalities where only one party receives output, to which we refer as solitary functionalities. In the standard setting where all parties receive an output, full security typically requires an honest majority; otherwise even just achieving fairness is impossible. However, for solitary functionalities, fairness is clearly not an issue. This raises the following question: Is full security with no honest majority possible for all solitary functionalities? We give a negative answer to this question, by showing the existence of solitary functionalities that cannot be computed with full security. While such a result cannot be proved using fairness based arguments, our proof builds on the classical proof technique of Cleve (STOC 1986) for ruling out fair coin-tossing and extends it in a nontrivial way. On the positive side, we show that full security against any number of malicious parties is achievable for many natural and useful solitary functionalities, including ones for which the multi-output version cannot be realized with full security

Can Alice and Bob Guarantee Output to Carol?

In the setting of solitary output computations, only a single designated party learns the output of some function applied to the private inputs of all participating parties with the guarantee that nothing beyond the output is revealed. The setting of solitary output functionalities is a special case of secure multiparty computation, which allows a set of mutually distrusting parties to compute some function of their private inputs. The computation should guarantee some security properties, such as correctness, privacy, fairness, and output delivery. Full security captures all these properties together. Solitary output computation is a common setting that has become increasingly important, as it is relevant to many real-world scenarios, such as federated learning and set disjointness. In the set-disjointness problem, a set of parties with private datasets wish to convey to another party whether they have a common input. In this work, we investigate the limits of achieving set-disjointness which already has numerous applications and whose feasibility (under non-trivial conditions) was left open in the work of Halevi et al. (TCC 2019). Towards resolving this, we completely characterize the set of Boolean functions that can be computed in the three-party setting in the face of a malicious adversary that corrupts up to two of the parties. As a corollary, we characterize the family of set-disjointness functions that can be computed in this setting, providing somewhat surprising results regarding this family and resolving the open question posed by Halevi et al

Cosmic Microwave Background (CMB) distortions: a new window into the physics of inflation

The Cosmic Microwave Background (CMB) spectrum in the frequency domain is extremely close to a perfect black-body. However, we know there must be tiny distortions of the CMB spectrum which are within the sensitivity of proposed satellite missions, such as PRISM and PIXIE. These spectral distortions provide a potential powerful source of information about the origin of the primordial density perturbations in the early Universe, i.e. the inflationary paradigm. In order to achieve a more solid comprehension, we will first introduce our theoretical framework, based on the Cosmological Standard Model, and the Theory of cosmological perturbations, which represents the traditional approach in Cosmology. In particular we will see how primordial density perturbations, of order 10-5, around a background solution produced the seeds for the Universe we see today. Thereafter, we will consider various aspects related to CMB spectral distortions: what they consist in, their main properties and why they are so important. Recent works proved that a cross correlation between the so-called µ-type (i.e. chemical potential type) distortions and the CMB temperature anisotropy ΔT/T could constraint the level of primordial non-Gaussianity (NG) via the parameter fNLloc at very small scales so far unexplored, lesser than about a Mpc, and potentially with a precision much higher than the present constraints from CMB anisotropies. The most up-to-date and guaranteed constraints on primordial NG come from Planck data and give fNLloc = 2.5 ± 5.7; however, authors of a recent paper (Pajer & Zaldarriaga, 2012) claimed that a cosmic variance limited experiment could in principle reach Δ fNLloc ~ O(10-3), which is the typical level predicted by the standard single-field models of slow-roll inflation. That is a quite bold claim and in this work we will focus on a computation at second-order in the cosmological perturbations to quantify some non-primordial signals that can act as a source of contamination to the measurement of the level of primordial non-Gaussianity. One could be lead to think that a calculation of such kind should in principle follow the same derivation as the bispectrum formula TTT, but this idea, although legitimate, is actually incorrect. In fact, we will see that asserting this second-order contamination is an highly non trivial task and we will discover a few crucial subtleties hidden in the calculation which must be treated very carefully. The procedure we will follow is surely going to shine a light on the very brief and incomplete derivations and implied assumptions in the research literature. In addition to it, we will develop an analytical formula, initially not intended, which provides the basis for a full numerical calculation once plugged into the Second Order Non Gaussianity (SONG) code. The main goals of this Thesis are therefore to present some remarkable results on recent developments in Cosmology, becoming aware of what we know, and, where possible, to take a step toward what we do not know, clarifying some aspects about CMB spectral distortions that have not been yet explored

Gravitational Wave Decay: Implications for cosmological scalar-tensor theories

The recent discovery that gravitational waves and light travel with the same speed, with an error below $10^{-15}$, has greatly constrained the parameter space of infrared modifications of gravity. In this thesis we study the phenomenology of gravitational-wave propagation in modifications of gravity relevant for dark energy with an additional scalar degree of freedom. Of particular interest are Horndeski and Beyond Horndeski models surviving after the event GW170817. Here the dark energy field is responsible for the spontaneous breaking of Lorentz invariance on cosmological scales. This implies that gravitons $gamma$ can experience new dispersion phenomena and in particular they can decay into dark energy fluctuations $pi$. First, we study the perturbative decay channels $gamma ightarrow pipi$ and $gamma ightarrowgammapi$ in Beyond Horndeski models. The first process is found to be large and thus incompatible with recent gravitational-wave observations. This provides a very stringent constraint for the particular coefficient $m{4}{2}$ of the Effective Field Theory of Dark Energy or, in the covariant language, on quartic Beyond Horndeski operators. We then study how the same coupling affects at loop level the propagation of gravitons. It is found that the new contribution modifies the dispersion relation in a way that is incompatible with current observations, giving bounds of the same magnitude as the decay. Next, we improve our analysis of the decay by taking into account the large occupation number of gravitons and dark energy fluctuations in realistic situations. When the operators $m_3^3$ (cubic Horndeski) and $m{4}{2}$ are present, we show that the gravitational wave acts as a classical background for $pi$ and affects its dynamics, with $pi$ growing exponentially. In the regime of small gravitational-wave amplitude, we compute analytically the produced $pi$ and the change in the gravitational wave. For the operator $m_3^3$, $pi$ self-interactions are of the same order as the resonance and affect the growth in a way that cannot be described analytically. For the operator $m{4}{2}$, in some regimes self-interactions remain under control and our analysis improves the bounds from the perturbative decay, ruling out quartic Beyond Horndeski operators from having any relevance for cosmological applications. Finally, we show that in the regime of large amplitude for the gravitational wave $pi$ becomes unstable. If $m_3^3$ takes values relevant for cosmological applications, we conclude that dark energy fluctuations feature ghost and gradient instabilities in presence of gravitational waves of typical binary systems. Taking into account the populations of binary systems, we find that the instability is triggered in the whole Universe. The fate of the instability and the subsequent time-evolution of the system depends on the UV completion, so that the theory may end up in a state very different from the original one. In conclusion, the only dark-energy theories with sizeable cosmological effects that avoid these problems are $k$-essence models, with a possible conformal coupling with matter