Jonathan A. Poritz

Secure INtrusion-Tolerant Replication on the Internet

This paper describes a Secure INtrusion-Tolerant Replication Architecture (SINTRA) for coordination in asynchronous networks subject to Byzantine faults. SINTRA supplies a number of group communication primitives, such as binary and multi-valued Byzantine agreement, reliable and consistent broadcast, and an atomic broadcast channel. Atomic broadcast immediately provides secure state-machine replication. The protocols are designed for an asynchronous wide-area network, such as the Internet, where messages may be delayed indefinitely, the servers do not have access to a common clock, and up to one third of the servers may fail in potentially malicious ways. Security is achieved through the use of threshold public-key cryptography, in particular through a cryptographic common coin based on the Diffie-Hellman problem that underlies the randomized protocols in SINTRA. The implementation of SINTRA in Java is described and timing measurements are given for a test-bed of servers distributed over three continents. They show that extensive use of public-key cryptography does not impose a large overhead for secure coordination in wide-area networks.

Social Preferences and Price Cap Regulation

This paper analyzes the allocative properties of price cap regulation under very general hypotheses on the nature of societys preferences. We propose a generalized price cap that ensures the convergence to optimal (second best) prices in the long-run equilibrium for virtually any form of the welfare function. Hence, the result of the convergence to Ramsey prices of Laspeyres-type price cap regulation is a particular instance of our more general result. We also provide an explicit and relatively easy to calculate and implement generalized price cap formula for distributionally weighted utilitarian welfare functions, as suggested by Feldstein (1972). Copyright 2002 by Blackwell Publishing Inc.

PARABOLIC VECTOR BUNDLES AND HERMITIAN-YANG-MILLS CONNECTIONS OVER A RIEMANN SURFACE

We study a certain moduli space of irreducible Hermitian-Yang-Mills connections on a unitary vector bundle over a punctured Riemann surface. The connections used have non-trivial holonomy around the punctures lying in fixed conjugacy classes of U (n) and differ from each other by elements of a weighted Sobolev space; these connections give rise to parabolic bundles in the sense of Mehta and Seshadri. We show in fact that the moduli space of stable parabolic bundles can be identified with our moduli space of HYM connections, by proving that every stable bundle admits a unique unitary gauge orbit of Hermitian-Yang-Mills connections.

Who Searches the Searchers? Community Privacy in the Age of Monolithic Search Engines

Privacy has largely been equated with every individuals right to privacy. Accordingly, current efforts to protect privacy on the Internet have sought anonymity by breaking, where possible, links with personally identifiable information (PII)—all uses of aggregated data stripped of PII are considered legitimate. This article argues that we need to use a broader concept, general or group identifying information (GII), because even aggregated data stripped of PII violate privacy at the community level. The search engine companies, or anyone else with access to their log files, can use these data to generate a moment-by-moment view of what is on the collective mind. Such a view can be used in a variety of ways, some with deep economic and even political impact. In order to frame this discussion, it is necessary to examine some of the realities of the search engine-mediated associative interface to the World Wide Web. While this interface has enormous benefits for the networked world, it also fundamentally changes a number of issues underlying various current debates about Internet governance.

Around Polygons in ℝ3 and S3

Abstract: We survey certain moduli spaces in low dimensions and some of the geometric structures that they carry, and then construct identifications among all of these spaces. In particular, we identify the moduli spaces of polygons in ℝ3 and S3, the moduli space of restricted representations of the fundamental group of a punctured 2-sphere, the moduli space of flat connections on a punctured sphere, the moduli space of parabolic bundles on a sphere, the moduli space of weighted points on ℂℙ1 and the symplectic quotient of SO(3) acting diagonally on (S2)n. All of these spaces depend on parameters and some the above identifications require the parameters to be small. One consequence of this work is that these spaces are all biholomorphic with respect to the most natural complex structures they can each be given.

Universal gates in other universes

I describe a new formalization for computation which is similar to traditional circuit models but which depends upon the choice of a family of [semi]groups --- essentially, a choice of the structure group of the universe of the computation. Choosing the symmetric groups results in the reversible version of classical computation; the unitary groups give quantum computation. Other groups can result in models which are stronger or weaker than the traditional models, or are hybrids of classical and quantum computation. One particular example, built out of the semigroup of doubly stochastic matrices, yields classical but probabilistic computation, helping explain why probabilistic computation can be so fast. Another example is a smaller and entirely ℝeal version of the quantum one which uses a (real) rotation matrix in place of the (complex, unitary) Hadamard gate to create algorithms which are exponentially faster than classical ones. I also articulate a conjecture which would help explain the different powers of these different types of computation, and point to many new avenues of investigation permitted by this model.