Constructing Pseudo-Random Permutations with a Prescribed Structure

We show how to construct pseudo-random permutations that satisfy a certain cycle restriction, for example that the permutation be cyclic (consisting of one cycle containing all the elements) or an involution (a self-inverse permutation) with no fixed points. The construction can be based on any (unrestricted) pseudo-random permutation. The resulting permutations are defined succinctly and their evaluation at a given point is efficient. Furthermore, they enjoy a fast forward property, i.e. it is possible to iterate them at a very small cost. Received 10 August 2000 and revised 30 September 2000 Online publication 9 April 2001     

Low frequency scattering by a resistive plate

For a plane wave incident on a resistive plate, the first two terms in the low frequency expansion of the far field are determined. Since the magnetic dipole is not excited if the resistivity is nonzero, the leading term is simply the electric dipole contribution, and is identical to that for a perfectly conducting plate. The resistivity appears explicitly in the next term which can be expressed in terms of potentials. Some implications of the results are discussed, and the method is illustrated in the case of a circular disk.     

Completeness in Two-Party Secure Computation: A Computational View

A Secure Function Evaluation (SFE) of a two-variable function f(·,·) is a protocol that allows two parties with inputs x and y to evaluate f(x,y) in a manner where neither party learns "more than is necessary". A rich body of work deals with the study of completeness for secure two-party computation. A function f is complete for SFE if a protocol for securely evaluating f allows the secure evaluation of all (efficiently computable) functions. The questions investigated are which functions are complete for SFE, which functions have SFE protocols unconditionally and whether there are functions that are neither complete nor have efficient SFE protocols. The previous study of these questions was mainly conducted from an information theoretic point of view and provided strong answers in the form of combinatorial properties. However, we show that there are major differences between the information theoretic and computational settings. In particular, we show functions that are considered as having SFE unconditionally by the combinatorial criteria but are actually complete in the computational setting. We initiate the fully computational study of these fundamental questions. Somewhat surprisingly, we manage to provide an almost full characterization of the complete functions in this model as well. More precisely, we present a computational criterion (called computational row non-transitivity) for a function f to be complete for the asymmetric case. Furthermore, we show a matching criterion called computational row transitivity for f to have a simple SFE (based on no additional assumptions). This criterion is close to the negation of the computational row non-transitivity and thus we essentially characterize all "nice" functions as either complete or having SFE unconditionally.     

Efficient handoff rerouting algorithms: a competitive on-line algorithmic approach

This paper considers the design of handoff rerouting algorithms for reducing the overall session cost in personal communication systems (PCS). Most modern communication systems that are used as an infrastructure for PCS networks are based on connection-based technologies. In these systems, the session cost is composed of two components. The setup cost represents the cost associated with the handoff operations, and the hold cost determines the expense related to the use of network resources held by the connection. This work introduces for the first time, rerouting algorithms for general graphs which are cost effective in terms of their worst-case analysis. The algorithms are analyzed using a competitive analysis approach, and it is proved that the competitive ratio of the proposed algorithms is a small constant of which the precise value depends on the ratio between the setup costs and the hold costs of the links. We also prove a lower bound of 2 on the competitive ratio of any online algorithm, which means that the proposed algorithms are close in terms of worst case behavior to the best possible rerouting algorithm. In addition, experimental results also show that the proposed algorithms indeed balance between the session setup cost and the hold cost, yielding overall lower cost when compared to other algorithms described in the literature.     

Orientation development in thermotropic liquid crystal polymers

Thermotropic liquid crystal polymers are a new class of polymeric materials that consist of rigid backbone molecules and thus, even in the quiescent condition, take extended chain conformation to form optically anisotropic melts. A systematic investigation was carried out on how this type of material responds to two basic flow fields: shear and elongation. Rheological properties of the polymer in these flow fields have also been measured. It was found that a high level of molecular orientation was readily obtained by elongational flow but not with shear flow. Specifically, extraordinarily high orientation was obtained when the melt was subjected to small elongational strains, whiel shear strain or shear rate had little effect. A possible mechanism to explain these behaviors is illustrated based on the existing observations or theories of rodlike molecules. This finding was used to interpret the orientation distribution in the extruded and injection-molded articles.     

Cell Identification Codes for Tracking Mobile Users

The minimization of the wireless cost of tracking mobile users is a crucial issue in wireless networks. Some of the previous strategies addressing this issue leave an open gap, by requiring the use of information that is not generally available to the user (for example, the distance traveled by the user). For this reason, both the implementation of some of these strategies and the performance comparison to existing strategies is not clear. In this work we propose to close this gap by the use of Cell Identification Codes (CIC) for tracking mobile users. Each cell periodically broadcasts a short message which identifies the cell and its orientation relatively to other cells in the network. This information is used by the users to efficiently update their location. We propose several cell identification encoding schemes, which are used to implement different tracking strategies, and analyze the amount of information required by each tracking strategy. One of our major results is that there is no need to transmit a code which is unique for each cell. For example, a 3 bits CIC is sufficient to implement a distance-based tracking strategy in a two-dimensional system. In addition, we propose a combination of timer and movement tracking strategy, based on either a one-bit or a two-bit CIC, depending on system topology and user mobility. An important property of our framework is that the overall performance cost, and hence its comparison to existing methods, is evaluated for each tracking strategy. The CIC-based strategies are shown to outperform the geographic-based method currently used in existing networks, and the timer-based method, over a wide range of parameters. Moreover, this superiority increases as the number of users per cell increases.     

Deductive verification of alternating systems

Alternating systems are models of computer programs whose behavior is governed by the actions of multiple agents with, potentially, different goals. Examples include control systems, resource schedulers, security protocols, auctions and election mechanisms. Proving properties about such systems has emerged as an important new area of study in formal verification, with the development of logical frameworks such as the alternating temporal logic ATL*. Techniques for model checking ATL* over finite-state systems have been well studied, but many important systems are infinite-state and thus their verification requires, either explicitly or implicitly, some form of deductive reasoning. This paper presents a theoretical framework for the analysis of alternating infinite-state systems. It describes models of computation, of various degrees of generality, and alternating-time logics such as ATL* and its variations. It then develops a proof system that allows to prove arbitrary ATL* properties over these infinite-state models. The proof system is shown to be complete relative to validities in the weakest possible assertion language. The paper then derives auxiliary proof rules and verification diagrams techniques and applies them to security protocols, deriving a new formal proof of fairness of a multi-party contract signing protocol where the model of the protocol and of the properties contains both game-theoretic and infinite-state (parameterized) aspects.     

A quantum mechanical model of consciousness and the emergence of ‘I’

There have been suggestions that the unity of consciousness may be related to the kind of holism depicted only in quantum physics. This argument will be clarified and strengthened. It requires the brain to contain a quantum system with the right properties — a Bose-Einstein condensate. It probably does contain one such system, as both theory and experiment have indicated. In fact, we cannot pay full attention to a quantum whole and its parts simultaneously, though we may oscillate between the two. In a quantum theory of consciousness, emergent meanings arise as an inevitable consequence of Heisenberg's Uncertainty Principle.