Random Oracles in a Quantum World

The interest in post-quantum cryptography - classical systems that remain secure in the presence of a quantum adversary - has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove security in the quantum-accessible random oracle model where the adversary can query the random oracle with quantum states. We begin by separating the classical and quantum-accessible random oracle models by presenting a scheme that is secure when the adversary is given classical access to the random oracle, but is insecure when the adversary can make quantum oracle queries. We then set out to develop generic conditions under which a classical random oracle proof implies security in the quantum-accessible random oracle model. We introduce the concept of a history-free reduction which is a category of classical random oracle reductions that basically determine oracle answers independently of the history of previous queries, and we prove that such reductions imply security in the quantum model. We then show that certain post-quantum proposals, including ones based on lattices, can be proven secure using history-free reductions and are therefore post-quantum secure. We conclude with a rich set of open problems in this area.Comment: 38 pages, v2: many substantial changes and extensions, merged with a related paper by Boneh and Zhandr

Evolutionary L∞ identification and model reduction for robust control

An evolutionary approach for modern robust control oriented system identification and model reduction in the frequency domain is proposed. The technique provides both an optimized nominal model and a 'worst-case' additive or multiplicative uncertainty bounding function which is compatible with robust control design methodologies. In addition, the evolutionary approach is applicable to both continuous- and discrete-time systems without the need for linear parametrization or a confined problem domain for deterministic convex optimization. The proposed method is validated against a laboratory multiple-input multiple-output (MIMO) test rig and benchmark problems, which show a higher fitting accuracy and provides a tighter L�¢���� error bound than existing methods in the literature do

Extra argumentality - affectees, landmarks, and voice

This article investigates sentences with additional core arguments of a special type in three languages, viz. German, English, and Mandarin. These additional arguments, called extra arguments in the article, form a crosslinguistically homogeneous class by virtue of their structural and semantic similarities, with so-called "raised possessors" forming just a sub-group among them. Structurally, extra arguments may not be the most deeply embedded arguments in a sentence. Semantically, their referents are felt to stand in a specific relation to the referent of the/a more deeply embedded argument. There are two major thematic relations that are instantiated by extra arguments, viz. affectees and landmarks. These thematic role notions are justified in the context of and partly in contrast to, Dowty's (1991) proto-role approach. An affectee combines proto-agent with proto-patient properties in eventualities that are construed as involving causation. A landmark is a ground with respect to some spatial configuration denoted by the predication at hand, but a figure at the highest level of gestalt partitioning that is relevant in a clause. Thereby, both affectees and landmarks are inherently hybrid categories. The account of extra argumentality is couched in a neo-Davidsonian event semantics in the spirit of Kratzer (1996, 2003), and voice heads are assumed to introduce affectee arguments and landmark arguments right above VP

Dynamic importance sampling for uniformly recurrent markov chains

Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested by a large deviation lower bound analysis. Recent work, however, has suggested that such schemes do not work well in many situations. In this paper we consider dynamic importance sampling in the setting of uniformly recurrent Markov chains. By ``dynamic'' we mean that in the course of a single simulation, the change of measure can depend on the outcome of the simulation up till that time. Based on a control-theoretic approach to large deviations, the existence of asymptotically optimal dynamic schemes is demonstrated in great generality. The implementation of the dynamic schemes is carried out with the help of a limiting Bellman equation. Numerical examples are presented to contrast the dynamic and standard schemes.Comment: Published at http://dx.doi.org/10.1214/105051604000001016 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sum-of-Squares approach to feedback control of laminar wake flows

A novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of long-time averages of flow quantities is presented. It applies to reduced-order finite-dimensional models of fluid flows, expressed as a set of first-order nonlinear ordinary differential equations with the right-hand side being a polynomial function in the state variables and in the controls. The key idea, first discussed in Chernyshenko et al. 2014, Philos. T. Roy. Soc. 372(2020), is that the difficulties of treating and optimising long-time averages of a cost are relaxed by using the upper/lower bounds of such averages as the objective function. In this setting, control design reduces to finding a feedback controller that optimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controller itself and a tunable polynomial function. A numerically tractable approach to the solution of such optimisation problems, based on Sum-of-Squares techniques and semidefinite programming, is proposed. To showcase the methodology, the mitigation of the fluctuation kinetic energy in the unsteady wake behind a circular cylinder in the laminar regime at Re=100, via controlled angular motions of the surface, is numerically investigated. A compact reduced-order model that resolves the long-term behaviour of the fluid flow and the effects of actuation, is derived using Proper Orthogonal Decomposition and Galerkin projection. In a full-information setting, feedback controllers are then designed to reduce the long-time average of the kinetic energy associated with the limit cycle. These controllers are then implemented in direct numerical simulations of the actuated flow. Control performance, energy efficiency, and physical control mechanisms identified are analysed. Key elements, implications and future work are discussed