We show that the persistent homology of a filtered d- dimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analysis establishes the existence of a simple description of persistent homology groups over arbitrary fields. It also enables us to derive a natural algorithm for computing persistent homology of spaces in arbitrary dimension over any field. This results generalizes and extends the previously known algorithm that was restricted to subcomplexes of S and Z2 coefficients. Finally, our study implies the lack of a simple classification over non-fields. Instead, we give an algorithm for computing individual persistent homology groups over an arbitrary PIDs in any dimension.

Abstract. We present an index-calculus algorithm for the computation of discrete logarithms in the Jacobian of hyperelliptic curves defined over finite fields. The complexity predicts that it is faster than the Rho method for genus greater than 4. To demonstrate the efficiency of our approach, we describe our breaking of a cryptosystem based on a curve of genus 6 recently proposed by Koblitz. 1

The FOXBOX system puts in practice the black box representation of symbolic objects and provides algorithms for performing the symbolic calculus with such representations. Black box objects are stored as functions. For instance: a black box polynomial is a procedure that takes values for the variables as input and evaluates the polynomial at that given point. FOXBOX can compute the greatest common divisor and factorize polynomials in black box representation, producing as output new black boxes. It also can compute the standard sparse distributed representation of a black box polynomial, for example, one which was computed for an irreducible factor. We establish that the black box representation of objects can push the size of symbolic expressions far beyond what standard data structures could handle before. Furthermore, FOXBOX demonstrates the generic program design methodology. The FOXBOX system is written in C++. C++ template arguments provide for abstract domain types. Currently, F...

Integrity is rarely a valid presupposition in many systems architectures, yet it is necessary to make any security guarantees. To address this problem, we have designed a secure bootstrap process, AEGIS, which presumes a minimal amount of integrity, and which we have prototyped on the Intel x86 architecture. The basic principle is sequencing the bootstrap process as a chain of progressively higher levels of abstraction, and requiring each layer to check a digital signature of the next layer before control is passed to it. A major design decision is the consequence of a failed integrity check. A simplistic strategy is to simply halt the bootstrap process. However, as we show in this paper, the AEGIS bootstrap process can be augmented with automated recovery procedures which preserve the security properties of AEGIS under the additional assumption of the availability of a trusted repository. We describe two means by which such a repository can be implemented, and focus our attention on a network-accessible repository.

Security protocols are critical to enabling the growth of a wide range of wireless data services and applications. However, they impose a high computational burden that is mismatched with the modest processing capabilities and battery resources available on wireless clients. Bridging the security processing gap, while retaining sufficient programmability in order to support a wide range of current and future security protocol standards, requires the use of novel system architectures and design methodologies.

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Abstract. This paper describes how the use of software libraries, which is prevalent in high performance computing, can benefit from compiler optimizations in much the same way that conventional computer languages do. We explain how the compilation of these informal languages differs from the compilation of more conventional computer languages. In particular, such compilation requires precise pointer analysis, requires domain-specific information about the library’s semantics, and requires a configurable compilation scheme. Finally, we show that the combination of dataflow analysis and pattern matching form a powerful tool for performing configurable optimizations. 1

this paper we describe LiDIA, a new library for computational number theory. Why do we work on a new library for computational number theory when such powerful tools as Pari [1], Kant

Polynomial approximations are almost always used when implementing functions on a computing system. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet, the polynomial approximations that are actually implemented do have coefficients that are represented with a finite—and sometimes small—number of bits. This is due to the finiteness of the floating-point representations (for software implementations), and to the need to have small, hence fast and/or inexpensive, multipliers (for hardware implementations). We then have to consider polynomial approximations for which the degree-i coefficient has at most mi fractional bits; in other words, it is a rational number with denominator 2mi. We provide a general and efficient method for finding the best polynomial approximation under this constraint. Moreover, our method also applies if some other constraints (such as requiring some coefficients to be equal to some predefined constants or minimizing relative error instead of absolute error) are required.

Scientific programs rely heavily on software libraries. This paper describes the limitations of this reliance and shows how it degrades software quality. We offer a solution that uses a compiler to automatically optimize library implementations and the application programs that use them. Using examples and experiments with the PLAPACK parallel linear algebra library and the MPI message passing interface, we present our solution, which includes a simple declarative annotation language that describes certain aspects of a library's implementation. We also show how our approach can yield simpler scientific programs that are easier to understand, modify and maintain.