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93
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 149 (21 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 96 (9 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
A generic library of floatingpoint numbers and its application to exact computing
 In 14th International Conference on Theorem Proving in Higher Order Logics
, 2001
"... Abstract. In this paper we present a general library to reason about floatingpoint numbers within the Coq system. Most of the results of the library are proved for an arbitrary floatingpoint format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i. ..."
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Cited by 53 (6 self)
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Abstract. In this paper we present a general library to reason about floatingpoint numbers within the Coq system. Most of the results of the library are proved for an arbitrary floatingpoint format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors. 1
Mining Your Ps and Qs: Detection of Widespread Weak Keys in Network Devices
"... RSA and DSA can fail catastrophically when used with malfunctioning random number generators, but the extent to which these problems arise in practice has never been comprehensively studied at Internet scale. We perform the largest ever network survey of TLS and SSH servers and present evidence that ..."
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Cited by 52 (9 self)
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RSA and DSA can fail catastrophically when used with malfunctioning random number generators, but the extent to which these problems arise in practice has never been comprehensively studied at Internet scale. We perform the largest ever network survey of TLS and SSH servers and present evidence that vulnerable keys are surprisingly widespread. We find that 0.75 % of TLS certificates share keys due to insufficient entropy during key generation, and we suspect that another 1.70 % come from the same faulty implementations and may be susceptible to compromise. Even more alarmingly, we are able to obtain RSA private keys for 0.50 % of TLS hosts and 0.03 % of SSH hosts, because their public keys shared nontrivial common factors due to entropy problems, and DSA private keys for 1.03 % of SSH hosts, because of insufficient signature randomness. We cluster and investigate the vulnerable hosts, finding that the vast majority appear to be headless or embedded devices. In experiments with three software components commonly used by these devices, we are able to reproduce the vulnerabilities and identify specific software behaviors that induce them, including a boottime entropy hole in the Linux random number generator. Finally, we suggest defenses and draw lessons for developers, users, and the security community. 1
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 35 (9 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.
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 30 (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...
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 30 (9 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.
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 28 (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 28 (15 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
Pseudonymizing Unix Log Files
, 2002
"... Unix systems in many cases record personal data in log files. We present tools that help in practice to retrofit privacy protection into existing Unix audit systems. Our tools are based on an approach to pseudonymizing Unix log files while balancing user requirements for anonymity and the service pr ..."
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Cited by 27 (3 self)
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Unix systems in many cases record personal data in log files. We present tools that help in practice to retrofit privacy protection into existing Unix audit systems. Our tools are based on an approach to pseudonymizing Unix log files while balancing user requirements for anonymity and the service provider's requirements for accountability. By pseudonymizing identifying data in log files the association between the data and the real persons is hidden. Only upon good cause shown, such as a proceeding attack scenario, the identifying data behind the pseudonyms can be revealed. We develop a trust model as well as an architecture that integrates seamlessly with existing Unix systems. Finally, we provide performance measurements demonstrating that the tools are sufficiently fast for use at large sites.