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65
Computing Persistent Homology
 Discrete Comput. Geom
"... 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 enabl ..."
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Cited by 101 (20 self)
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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 nonfields. Instead, we give an algorithm for computing individual persistent homology groups over an arbitrary PIDs in any dimension.
An algorithm for solving the discrete log problem on hyperelliptic curves
, 2000
"... Abstract. We present an indexcalculus 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 de ..."
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Cited by 78 (6 self)
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Abstract. We present an indexcalculus 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
FOXBOX: A System for Manipulating Symbolic Objects in Black Box Representation
, 1998
"... 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 variabl ..."
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Cited by 29 (12 self)
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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...
System Design Methodologies for a Wireless Security Processing Platform
, 2002
"... 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 pr ..."
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Cited by 28 (8 self)
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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.
Automated Recovery in a Secure Bootstrap Process
, 1998
"... 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 arch ..."
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Cited by 26 (10 self)
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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 networkaccessible repository.
Guaranteed proofs using interval arithmetic
 Proceedings of the 17th Symposium on Computer Arithmetic, Cape Cod
, 2005
"... This paper presents a set of tools for mechanical reasoning of numerical bounds using interval arithmetic. The tools implement two techniques for reducing decorrelation: interval splitting and Taylor’s series expansions. Although the tools are designed for the proof assistant system PVS, expertise o ..."
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Cited by 22 (11 self)
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This paper presents a set of tools for mechanical reasoning of numerical bounds using interval arithmetic. The tools implement two techniques for reducing decorrelation: interval splitting and Taylor’s series expansions. Although the tools are designed for the proof assistant system PVS, expertise on PVS is not required. The ultimate goal of the tools is to provide guaranteed proofs of numerical properties with a minimal humantheorem prover interaction. 1
An adaptable and extensible geometry kernel
 In Proc. Workshop on Algorithm Engineering
, 2001
"... ii ..."
Optimizing the use of high performance software libraries
 In Languages and Compilers for Parallel Computing
, 2000
"... 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 compil ..."
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Cited by 22 (7 self)
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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 domainspecific 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
LiDIA  A library for computational number theory
 SFB 124C1, Fachbereich Informatik, Universitt des Saarlandes
, 1995
"... 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 ..."
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Cited by 22 (2 self)
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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
Computing machineefficient polynomial approximations
 TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2006
"... 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 ..."
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Cited by 20 (6 self)
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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 floatingpoint 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 degreei 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.