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On the equivalence of RSA and factoring regarding generic ring algorithms

12th International Conference on the Theory of Application of Cryptology and Information Security

作者： Leander, Gregor Rupp, Andy Ruhr Univ Bochum Horst Gortz Inst IT Secur Univ Str 150 D-4630 Bochum Germany

ISBN: (纸本)9783540494751

To prove or disprove the computational equivalence of solving the RSA problem and factoring integers is a longstanding open problem in cryptography. This paper provides some evidence towards the validity of this equivalence. We show that any efficient generic ring algorithm which solves the (flexible) low-exponent RSA problem can be converted into an efficient factoring algorithm. Thus, the low-exponent RSA problem is intractable w.r.t. generic ring algorithms provided that factoring is hard.

关键词： computational equivalence RSA problem factorization problem generic algorithms

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A generic Approach for Analysis of White-Light Interferometry Data via User-Defined algorithms

A Generic Approach for Analysis of White-Light Interferometr...

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14th International Conference on Computational Science and Its Applications (ICCSA)

作者： Schneider, Max Fey, Dietmar Wenzel, Kay Machleidt, Torsten Univ Erlangen Nurnberg Erlangen Germany Gesell Bild & Signalverarbeitung GBS mbH Ilmenau Germany

ISBN: (纸本)9783319091471;9783319091464

The non-destructive and automatic 3D surface analysis using white-light interferometry has very high demands on the required computing systems. This is due to both, the high volume of data that are collected and the tremendous computational power, required by algorithms which evaluate the data. Furthermore, material characteristics and environmental influences like temperature or ambient light have a not negligible effect on the scan procedure, such that the algorithmic approaches must be adjusted to assess the correct surface profile. Thus, to obtain the desired analysis results and to fulfill the computational requirements, the application developer has to consider the physical characteristics of the white-light interferometry process as well as the attributes of the computational platform used. This paper describes the generic computational module of a new framework for the white-light interferometry surface scanning procedure to address these problems. This framework allows a user-transparent automatic assessment and usage of available computational resources.

关键词： White-light interferometry High-performance computing Function objects GPGPU generic algorithms

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Introspective sorting and selection revisited

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SOFTWARE-PRACTICE & EXPERIENCE 2000年第6期30卷 617-638页

作者： Valois, JD Rensselaer Polytech Inst Dept Comp Sci Troy NY 12180 USA

We describe two improvements to introspective sorting and selection algorithms: a simple rule fine-grained introspection that detects potential worst-case performance after only a small constant number of partitioning steps, and the use of remedial randomization as an intervention strategy in order to reduce the performance penalty for false positives. We present experimental results showing that these techniques provide significant improvements in the running time for worst-case and other troublesome inputs, without sacrificing performance on well-behaved inputs. Copyright (C) 2000 John Wiley & Sons, Ltd.

关键词： Quicksort Find sorting and selection algorithms introspective algorithms hybrid algorithms generic algorithms

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Breaking RSA generically Is Equivalent to Factoring

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第11期62卷 6251-6259页

作者： Aggarwal, Divesh Maurer, Ueli Natl Univ Singapore Dept Comp Sci Ctr Quantum Technol Singapore 117543 Singapore ETH Dept Comp Sci CH-8092 Zurich Switzerland

Let N be a random variable distributed according to some appropriate distribution over the set of products of two primes, such that factoring N is believed to be hard. The RSA assumption states that, given an a chosen uniformly at random from Z(N) and an e is an element of N \ {1} such that gcd(e, phi(N)) = 1, it is computationally hard to find an x is an element of Z(N) such that x(e) - a = 0 (mod N). When complexity-theoretic (relative) lower bounds for certain cryptographic problems in a general model of computation seem to elude discovery, a common practice in cryptography is to give proofs of computational security in meaningful restricted models of computation. An example of such a restricted model that is interesting in cryptography is the generic group model that has been used for proving lower bounds for the discrete logarithm problem and other related problems. A generic model captures that an algorithm does not exploit the bit representation of the elements other than for testing equality. In this paper, we prove that the problem of factoring N can be efficiently reduced to solving the RSA problem on ZN in the generic ring model of computation, where an algorithm can perform ring operations, inverse ring operations, and test equality. This provides evidence toward the soundness of the RSA encryption and digital signature scheme, in particular showing that under the factoring assumption, they are not vulnerable to certain kinds of cryptanalytic attacks.

关键词： generic algorithms reductions factoring RSA

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Secured distributed algorithms without hardness assumptions

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2023年 171卷 130-140页

作者： Barenboim, Leonid Levin, Harel Open Univ Israel Dept Math & Comp Sci POB 808 Raanana Israel Nucl Res Ctr Negev Dept Phys POB 9001 Beer Sheva Israel

We study algorithms in the LOCAL model that produce secured output. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the output of other vertices, with a certain probability. As the extensive research in the distributed algorithms field yielded efficient decentralized algorithms, the discussion about the security of distributed algorithms was somewhat neglected. Nevertheless, many protocols and algorithms were devised in the research area of secure multi-party computation problem. However, the focus in those protocols was to work for every function f at the expense of increasing the round complexity, or the necessity of several computational assumptions. We present a novel approach, which identifies and develops those algorithms that are inherently secure (which means they do not require any further constructions). This approach yields efficient secure algorithms for various labeling and decomposition problems without requiring any hardness assumption, but only a private randomness generator in each vertex.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Distributed algorithms Privacy preserving Graph coloring generic algorithms Multi-party computation

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Small generic hardcore subsets for the discrete logarithm: Short secret DL-keys

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INFORMATION PROCESSING LETTERS 2001年第2期79卷 93-98页

作者： Schnorr, CP Univ Frankfurt Fachbereich Math Informat D-60439 Frankfurt Germany Bell Labs Murray Hill NJ 07974 USA

Let G be a group of prime order q with generator g. We study hardcore subsets H subset of G of the discrete logarithm (DL) log(g) in the model of generic algorithms. In this model we count group operations such as multiplication and division, while computations with non-group data are for free. It is known from Nechaev [Math. Notes 55 (1994) 165] and Shoup [Lecture Notes in Comp. Sci., Vol. 1233, Springer, Berlin, 1997, p. 256] that generic DL-algorithms for the entire group G must perform root 2q generic steps. We show that DL-algorithms for small subsets H subset of G require 1/2m + o(m) generic steps for almost all H of size #H = m with m less than or equal to rootq. Conversely, 1/2m + 1 generic steps are sufficient for all H subset of G of even size m. Our main result justifies to generate secret DL-keys from seeds that are only 1/2 log(2) q bits long. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： computational complexity cryptography discrete logarithm (DL generic algorithms generic complexity hardcore subsets

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Evolution and development of a multicellular organism: Scalability, resilience, and neutral complexification

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ARTIFICIAL LIFE 2006年第3期12卷 381-409页

作者： Federici, Diego Downing, Keith Norwegian Univ Sci & Technol Dept Comp & Informat Sci N-7491 Trondheim Norway

To increase the evolvability of larger search spaces, several indirect encoding strategies have been proposed. Among these, multicellular developmental systems are believed to offer great potential for the evolution of general, scalable, and self-repairing organisms. We reinforce this view, presenting the results achieved by such a model and comparing it against direct encoding. Extra effort has been made to make this comparison both general and meaningful. Embryonal stages, a generic method showing increased evolvability and applicable to any developmental model, are introduced. Development with embryonal stages implements what we refer to as direct neutral complexification: direct genotype complexification by neutral duplication of expressed genes. The results show that, even for high-complexity evolutionary targets, the developmental model proves more scalable. The model also shows emergent self-repair, which is used to produce highly resilient organisms.

关键词： generic algorithms development scalability fault tolerance neutral complexification

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Automatic segmentation of dermoscopy images using self-generating neural networks seeded by genetic algorithm

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PATTERN RECOGNITION 2013年第3期46卷 1012-1019页

作者： Xie, Fengying Bovik, Alan C. Beihang Univ Image Proc Ctr Sch Aeronaut & Astronaut Beijing 100191 Peoples R China Univ Texas Austin Dept Elect & Comp Engn Austin TX 78712 USA

A novel dermoscopy image segmentation algorithm is proposed using a combination of a self-generating neural network (SGNN) and the genetic algorithm (GA). Optimal samples are selected as seeds using GA;taking these seeds as initial neuron trees, a self-generating neural forest (SGNF) is generated by training the rest of the samples using SGNN. Next the number of clusters is determined by optimizing the SD index of cluster validity, and clustering is completed by treating each neuron tree as a cluster. Since SGNN often delivers inconsistent cluster partitions owing to sensitivity relative to the input order of the training samples, GA is combined with SGNN to optimize and stabilize the clustering result. In the post-processing phase, the clusters are merged into lesion and background skin, yielding the segmented dermoscopy image. A series of experiments on the proposed model and the other automatic segmentation methods (including Otsu's thresholding method, k-means, fuzzy c-means (FCM) and statistical region merging (SRM)) reveals that the optimized model delivers better accuracy and segmentation results. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Dermoscopy images Self-generating neural network Image clustering Automatic segmentation generic algorithms

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The role of commutativity in constraint propagation algorithms

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ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS 2000年第6期22卷 1002-1036页

作者： Apt, KR CWI NL-1090 GB Amsterdam Netherlands Univ Amsterdam NL-1012 WX Amsterdam Netherlands

Constraint propagation algorithms form an important part of most of the constraint programming systems. We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In this framework we proceed in two steps. First, we introduce a generic iteration algorithm on partial orderings and prove its correctness in an abstract setting. Then we instantiate this algorithm with specific partial orderings and functions to obtain specific constraint propagation algorithms. In particular, using the notions commutativity and semi-commutativity, we show that the AC-3, PC-2, DAC, and DPC algorithms for achieving (directional) are consistency and (directional) path consistency are instances of a single generic algorithm. The work reported here extends and simplifies that of Apt [1999a].

关键词： constraint propagation generic algorithms commutativity

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The essence of constraint propagation

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THEORETICAL COMPUTER SCIENCE 1999年第1-2期221卷 179-210页

作者： Apt, KR CWI NL-1009 AB Amsterdam Netherlands Univ Amsterdam Dept Math Comp Sci Phys & Astron NL-1012 WX Amsterdam Netherlands

We show that several constraint propagation algorithms (also called (local) consistency, consistency enforcing, Waltz, filtering or narrowing algorithms) are instances of algorithms that deal with chaotic iteration. To this end we propose a simple abstract framework that allows us to classify and compare these algorithms and to establish in a uniform way their basic properties. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： constraint propagation chaotic iteration generic algorithms

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