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AG Codes and Kryptographie Bildinformationen anzeigen

AG Codes and Kryptographie

Prof. Dr. Johannes Blömer

Prof. Dr. Johannes Blömer

PACE - Paderborn Center for Advanced Studies

Vorstand - Professor

Institut für Industriemathematik

Vorstand - Professor

Codes und Kryptographie

Leiter - Professor

Digitale Zukunft

Mitglied - Professor

+49 5251 60-6651
+49 5251 60-6618

Do, 11:00-12:00

Fürstenallee 11
33102 Paderborn

Universität Paderborn

Vizepräsident - Professor - Vizepräsident für Forschung und wissenschaftlichen Nachwuchs

+49 5251 60-6651


Liste im Research Information System öffnen


Dynamic Searchable Encryption with Access Control

J. Blömer, N. Löken, in: 12th International Symposium on Foundations and Practice of Security, FPS 2019, Springer, 2019

We present a searchable encryption scheme for dynamic document collections in a multi-user scenario. Our scheme features fine-grained access control to search results, as well as access control to operations such as adding documents to the document collection, or changing individual documents. The scheme features verifiability of search results. Our scheme also satisfies the forward privacy notion crucial for the security of dynamic searchable encryption schemes.

How well do SEM algorithms imitate EM algorithms? A non-asymptotic analysis for mixture models

J. Blömer, S. Brauer, K. Bujna, D. Kuntze, Advances in Data Analysis and Classification (2019)

Personal Cross-Platform Reputation

J. Blömer, N. Löken, in: Security and Trust Management, STM 2019, 2019

We propose a novel personal reputation system for cross-platform reputation. We observe that, in certain usage scenarios, e.g. crowd work, the rater anonymity property typically imposed on reputation systems is not necessary. Instead, we propose a relaxed notion of rater anonymity that is more applicable in the crowd work scenario. This allows us to construct a secure personal reputation system from simple cryptographic primitives.

Updatable Anonymous Credentials and Applications to Incentive Systems

J. Blömer, J. Bobolz, D.P. Diemert, F. Eidens, in: Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security - CCS '19, 2019

In this paper, we introduce updatable anonymous credential systems (UACS) and use them to construct a new privacy-preserving incentive system. In a UACS, a user holding a credential certifying some attributes can interact with the corresponding issuer to update his attributes. During this, the issuer knows which update function is run, but does not learn the user's previous attributes. Hence the update process preserves anonymity of the user. One example for a class of update functions are additive updates of integer attributes, where the issuer increments an unknown integer attribute value v by some known value k. This kind of update is motivated by an application of UACS to incentive systems. Users in an incentive system can anonymously accumulate points, e.g. in a shop at checkout, and spend them later, e.g. for a discount.


Cloud Architectures for Searchable Encryption

J. Blömer, N. Löken, in: Proceedings of the 13th International Conference on Availability, Reliability and Security, ARES 2018, ACM, 2018, pp. 25:1--25:10

Coresets for Fuzzy K-Means with Applications

J. Blömer, S. Brauer, K. Bujna, in: 29th International Symposium on Algorithms and Computation (ISAAC 2018), Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2018, pp. 46:1--46:12

Delegatable Attribute-based Anonymous Credentials from Dynamically Malleable Signatures

J. Blömer, J. Bobolz, in: ACNS 2018 Applied Cryptography & Network security, 2018

In this paper, we introduce the notion of delegatable attribute-based anonymous credentials (DAAC). Such systems offer fine-grained anonymous access control and they give the credential holder the ability to issue more restricted credentials to other users. In our model, credentials are parameterized with attributes that (1) express what the credential holder himself has been certified and (2) define which attributes he may issue to others. Furthermore, we present a practical construction of DAAC. For this construction, we deviate from the usual approach of embedding a certificate chain in the credential. Instead, we introduce a novel approach for which we identify a new primitive we call dynamically malleable signatures (DMS) as the main ingredient. This primitive may be of independent interest. We also give a first instantiation of DMS with efficient protocols.

Enhanced Security of Attribute-Based Signatures

J. Blömer, F. Eidens, J. Juhnke, in: The International Conference on Cryptology And Network Security (CANS), Springer, 2018, pp. 235-255

Fully-Featured Anonymous Credentials with Reputation System

K. Bemmann, J. Blömer, J. Bobolz, H. Bröcher, D.P. Diemert, F. Eidens, L. Eilers, J.F. Haltermann, J. Juhnke, B. Otour, L.A. Porzenheim, S. Pukrop, E. Schilling, M. Schlichtig, M. Stienemeier, in: Proceedings of the 13th International Conference on Availability, Reliability and Security - ARES '18, ACM, 2018

We present CLARC (Cryptographic Library for Anonymous Reputation and Credentials), an anonymous credentials system (ACS) combined with an anonymous reputation system. Using CLARC, users can receive attribute-based credentials from issuers. They can efficiently prove that their credentials satisfy complex (access) policies in a privacy-preserving way. This implements anonymous access control with complex policies. Furthermore, CLARC is the first ACS that is combined with an anonymous reputation system where users can anonymously rate services. A user who gets access to a service via a credential, also anonymously receives a review token to rate the service. If a user creates more than a single rating, this can be detected by anyone, preventing users from spamming ratings to sway public opinion. To evaluate feasibility of our construction, we present an open-source prototype implementation.

Practical, Anonymous, and Publicly Linkable Universally-Composable Reputation Systems

J. Blömer, F. Eidens, J. Juhnke, in: Topics in Cryptology - {CT-RSA} 2018 - The Cryptographers' Track at the {RSA} Conference 2018, Proceedings, Springer International Publishing, 2018, pp. 470-490

Provably Anonymous Communication Based on Trusted Execution Environments

J. Blömer, J. Bobolz, C. Scheideler, A. Setzer, 2018

In this paper, we investigate the use of trusted execution environments (TEEs, such as Intel's SGX) for an anonymous communication infrastructure over untrusted networks. For this, we present the general idea of exploiting trusted execution environments for the purpose of anonymous communication, including a continuous-time security framework that models strong anonymity guarantees in the presence of an adversary that observes all network traffic and can adaptively corrupt a constant fraction of participating nodes. In our framework, a participating node can generate a number of unlinkable pseudonyms. Messages are sent from and to pseudonyms, allowing both senders and receivers of messages to remain anonymous. We introduce a concrete construction, which shows viability of our TEE-based approach to anonymous communication. The construction draws from techniques from cryptography and overlay networks. Our techniques are very general and can be used as a basis for future constructions with similar goals.

    Voronoi Cells of Lattices with Respect to Arbitrary Norms

    J. Blömer, K. Kohn, SIAM Journal on Applied Algebra and Geometry. (2018), 2(2), pp. 314-338


    Attribute-Based Encryption as a Service for Access Control in Large-Scale Organizations

    J. Blömer, P. Günther, V. Krummel, N. Löken, in: Foundations and Practice of Security, Springer International Publishing, 2017, pp. 3-17

    Subtleties in Security Definitions for Predicate Encryption with Public Index

    J. Blömer, G. Liske, in: Proceedings of the International Conference of Mathematical Aspects of Computer and Information Sciences (MACIS), Springer International Publishing, 2017, pp. 438-453


    A Theoretical Analysis of the Fuzzy K-Means Problem

    J. Blömer, S. Brauer, K. Bujna, in: 2016 IEEE 16th International Conference on Data Mining (ICDM), IEEE, 2016, pp. 805-810

    One of the most popular fuzzy clustering techniques is the fuzzy K-means algorithm (also known as fuzzy-c-means or FCM algorithm). In contrast to the K-means and K-median problem, the underlying fuzzy K-means problem has not been studied from a theoretical point of view. In particular, there are no algorithms with approximation guarantees similar to the famous K-means++ algorithm known for the fuzzy K-means problem. This work initiates the study of the fuzzy K-means problem from an algorithmic and complexity theoretic perspective. We show that optimal solutions for the fuzzy K-means problem cannot, in general, be expressed by radicals over the input points. Surprisingly, this already holds for simple inputs in one-dimensional space. Hence, one cannot expect to compute optimal solutions exactly. We give the first (1+eps)-approximation algorithms for the fuzzy K-means problem. First, we present a deterministic approximation algorithm whose runtime is polynomial in N and linear in the dimension D of the input set, given that K is constant, i.e. a polynomial time approximation scheme (PTAS) for fixed K. We achieve this result by showing that for each soft clustering there exists a hard clustering with similar properties. Second, by using techniques known from coreset constructions for the K-means problem, we develop a deterministic approximation algorithm that runs in time almost linear in N but exponential in the dimension D. We complement these results with a randomized algorithm which imposes some natural restrictions on the sought solution and whose runtime is comparable to some of the most efficient approximation algorithms for K-means, i.e. linear in the number of points and the dimension, but exponential in the number of clusters.

      Adaptive Seeding for Gaussian Mixture Models

      J. Blömer, K. Bujna, in: Advances in Knowledge Discovery and Data Mining, Springer International Publishing, 2016, pp. 296-308

      Construction of Fully CCA-Secure Predicate Encryptions from Pair Encoding Schemes

      J. Blömer, G. Liske, in: Proceedings of the CT-RSA 2016, 2016, pp. 431-447

      This paper presents a new framework for constructing fully CCA-secure predicate encryption schemes from pair encoding schemes. Our construction is the first in the context of predicate encryption which uses the technique of well-formedness proofs known from public key encryption. The resulting constructions are simpler and more efficient compared to the schemes achieved using known generic transformations from CPA-secure to CCA-secure schemes. The reduction costs of our framework are comparable to the reduction costs of the underlying CPA-secure framework. We achieve this last result by applying the dual system encryption methodology in a novel way.

        Effizienz und Sicherheit paarungsbasierter Kryptographie

        J. Blömer, P. Günther, Tagungsband des 26. Fraunhofer SIT Smartcard-Workshops, 2016

        Singular Curve Point Decompression Attack

        J. Blömer, P. Günther, in: 2015 Workshop on Fault Diagnosis and Tolerance in Cryptography (FDTC), IEEE, 2016

        Theoretical Analysis of the k-Means Algorithm – A Survey

        J. Blömer, C. Lammersen, M. Schmidt, C. Sohler, in: Algorithm Engineering, Springer International Publishing, 2016, pp. 81-116


        Anonymous and Publicly Linkable Reputation Systems

        J. Blömer, J. Juhnke, C. Kolb, in: Proceedings of the 18th International Conference on Financial Cryptography and Data Security (FC), 2015, pp. 478--488

        Reputation systems are used to compute and publish reputation scores for services or products. We consider reputation systems where users are allowed to rate products that they purchased previously. To obtain trustworthy reputations, they are allowed to rate these products only once. As long as users rate products once, they stay anonymous. Everybody is able to detect users deviating from the rate-products-only-once policy and the anonymity of such dishonest users can be revoked by a system manager. In this paper we present formal models for such reputation systems and their security. Based on group signatures presented by Boneh, Boyen, and Shacham we design an efficient reputation system that meets all our requirements.

        Short Group Signatures with Distributed Traceability

        J. Blömer, J. Juhnke, N. Löken, in: Proceedings of the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS), 2015, pp. 166-180

        Group signatures, introduced by Chaum and van Heyst [15], are an important primitive in cryptography. In group signature schemes every group member can anonymously sign messages on behalf of the group. In case of disputes a dedicated opening manager is able to trace signatures - he can extract the identity of the producer of a given signature. A formal model for static group signatures schemes and their security is defined by Bellare, Micciancio, and Warinschi [4], the case of dynamic groups is considered by Bellare, Shi, and Zhang [5]. Both models define group signature schemes with a single opening manager. The main difference between these models is that the number of group members in static schemes is fixed, while in dynamic schemes group members can join the group over time.

          Voronoi Cells of Lattices with Respect to Arbitrary Norms

          J. Blömer, K. Kohn, Universität Paderborn, 2015

          Motivated by the deterministic single exponential time algorithm of Micciancio and Voulgaris for solving the shortest and closest vector problem for the Euclidean norm, we study the geometry and complexity of Voronoi cells of lattices with respect to arbitrary norms.On the positive side, we show that for strictly convex and smooth norms the geometry of Voronoi cells of lattices in any dimension is similar to the Euclidean case, i.e., the Voronoi cells are defined by the so-called Voronoi-relevant vectors and the facets of a Voronoi cell are in one-to-one correspondence with these vectors. On the negative side, we show that combinatorially Voronoi cells for arbitrary strictly convex and smooth norms are much more complicated than in the Euclidean case.In particular, we construct a family of three-dimensional lattices whose number of Voronoi-relevant vectors with respect to the l_3-norm is unbounded.Since the algorithm of Micciancio and Voulgaris and its run time analysis crucially dependonthefactthatfortheEuclidean normthenumber of Voronoi-relevant vectors is single exponential in the lattice dimension, this indicates that the techniques of Micciancio and Voulgaris cannot be extended to achieve deterministic single exponential time algorithms for lattice problems with respect to arbitrary l_p-norms.


          A Practical Second-Order Fault Attack against a Real-World Pairing Implementation

          J. Blömer, R. Gomes da Silva, P. Günther, J. Krämer, J. Seifert, in: Proceedings of Fault Tolerance and Diagnosis in Cryptography(FDTC), 2014, pp. 123--136

          Several fault attacks against pairing-based cryptography have been described theoretically in recent years. Interestingly, none of these have been practically evaluated. We accomplished this task and prove that fault attacks against pairing-based cryptography are indeed possible and are even practical — thus posing a serious threat. Moreover, we successfully conducted a second-order fault attack against an open source implementation of the eta pairing on an AVR XMEGA A1. We injected the first fault into the computation of the Miller Algorithm and applied the second fault to skip the final exponentiation completely. We introduce a low-cost setup that allowed us to generate multiple independent faults in one computation. The setup implements these faults by clock glitches which induce instruction skips. With this setup we conducted the first practical fault attack against a complete pairing computation.

            A Theoretical and Experimental Comparison of the EM and SEM Algorithm

            J. Blömer, K. Bujna, D. Kuntze, in: 2014 22nd International Conference on Pattern Recognition, IEEE, 2014

            Analysis of Agglomerative Clustering

            M.R. Ackermann, J. Blömer, D. Kuntze, C. Sohler, Algorithmica (2014), 69

            Constructing CCA-secure predicate encapsulation schemes from CPA-secure schemes and universal one-way hash functions

            J. Blömer, G. Liske, 2014

            We present a new transformation of chosen-plaintext secure predicate encryption schemes with public index into chosen-ciphertext secure schemes. Our construction requires only a universal one-way hash function and is selectively secure in the standard model. The transformation is not generic but can be applied to various existing schemes constructed from bilinear groups. Using common structural properties of these schemes we provide an efficient and simple transformation without overhead in form of one-time signatures or message authentication codes as required in the known generic transformations.

            Tampering attacks in pairing-based cryptography

            J. Blömer, P. Günther, G. Liske, in: Proceedings of Fault Tolerance and Diagnosis in Cryptography(FDTC), 2014, pp. 1--7

            In the last decade pairings have become an important, and often indispensable, ingredient in the construction of identity-based and attribute-based cryptosystems, as well as group signatures and credential systems. Consequently, the applicability of timing, power, or fault attacks to implementations of pairings is an important research topic. We will review some of the known results in this area.


              Direct Chosen-Ciphertext Secure Attribute-Based Key Encapsulations without Random Oracles

              J. Blömer, G. Liske, 2013

              We present a new technique to realize attribute-based encryption (ABE) schemes secure in the standard model against chosen-ciphertext attacks (CCA-secure). Our approach is to extend certain concrete chosen-plaintext secure (CPA-secure) ABE schemes to achieve more efficient constructions than the known generic constructions of CCA-secure ABE schemes. We restrict ourselves to the construction of attribute-based key encapsulation mechanisms (KEMs) and present two concrete CCA-secure schemes: a key-policy attribute-based KEM that is based on Goyal's key-policy ABE and a ciphertext-policy attribute-based KEM that is based on Waters' ciphertext-policy ABE. To achieve our goals, we use an appropriate hash function and need to extend the public parameters and the ciphertexts of the underlying CPA-secure encryption schemes only by a single group element. Moreover, we use the same hardness assumptions as the underlying CPA-secure encryption schemes.

              Improved Side Channel Attacks on Pairing Based Cryptography

              J. Blömer, P. Günther, G. Liske, in: Constructive Side-Channel Analysis and Secure Design, Springer Berlin Heidelberg, 2013, pp. 154-168

              Securing Critical Unattended Systems with Identity Based Cryptography - A Case Study

              J. Blömer, P. Günther, V. Krummel, in: Proceedings of the 5th International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS), 2013, pp. 98-105

              Unattended systems are key ingredients of various critical infrastruc-tures like networks of self service terminals or automated teller machines.For cost and efficiency reasons they should mostly run autonomously.Unattended systems are attractive and lucrative targets for various kindsof attacks, including attacks on the integrity of their components and thecommunication between components. In this paper, we propose a gen-eral cryptographic framework to protect unattended systems. We alsodemonstrate that instantiating the framework with techniques from iden-tity based cryptography is particularly well-suited to efficiently secureunattended systems.


                Turing und Kryptografie

                J. Blömer, Informatik-Spektrum (2012), 35(4)

                Ich beschreibe die deutsche Enigma-Verschlüsselungsmaschine und skizziere, wie sie von den Codebrechern von Bletchely Park um Alan Turing gebrochen wurde. Besonderes Augenmerk lege ich auf die Beiträge Alan Turings und die Bedeutung seiner Leistung für die Entwicklung moderner Kryptografie.


                  Hardness and Non-Approximability of Bregman Clustering Problems.

                  M.R. Ackermann, J. Blömer, C. Scholz, 2011

                  How to Share a Secret

                  J. Blömer, in: Algorithms Unplugged, Springer Berlin Heidelberg, 2011, pp. 159-168

                  Solving the Closest Vector Problem with respect to Lp Norms

                  J. Blömer, S. Naewe, in: arXiv:1104.3720, 2011

                  In this paper, we present a deterministic algorithm for the closest vector problem for all l_p-norms, 1 < p < \infty, and all polyhedral norms, especially for the l_1-norm and the l_{\infty}-norm. We achieve our results by introducing a new lattice problem, the lattice membership problem. We describe a deterministic algorithm for the lattice membership problem, which is a generalization of Lenstra's algorithm for integer programming. We also describe a polynomial time reduction from the closest vector problem to the lattice membership problem. This approach leads to a deterministic algorithm that solves the closest vector problem for all l_p-norms, 1 < p < \infty, in time p log_2 (r)^{O (1)} n^{(5/2+o(1))n} and for all polyhedral norms in time (s log_2 (r))^{O (1)} n^{(2+o(1))n}, where s is the number of constraints defining the polytope and r is an upper bound on the coefficients used to describe the convex body.


                    Bregman Clustering for Separable Instances

                    M.R. Ackermann, J. Blömer, in: SWAT 2010, Springer Berlin Heidelberg, 2010, pp. 212-223

                    Clustering for Metric and Nonmetric Distance Measures

                    M.R. Ackermann, J. Blömer, C. Sohler, ACM Trans. Algorithms (2010)(4), pp. 59:1--59:26

                    Engineering self-coordinating software intensive systems

                    W. Schäfer, A. Trächtler, M. Birattari, J. Blömer, M. Dorigo, G. Engels, R. O'Grady, M. Platzner, F. Rammig, W. Reif, in: Proceedings of the FSE/SDP workshop on Future of software engineering research - FoSER '10, ACM Press, 2010

                    On the initialization of dynamic models for speech features

                    A. Krueger, V. Leutnant, R. Haeb-Umbach, M. Ackermann, J. Blömer, Proc. of ITG Fachtagung Sprachkommunikation. ITG, Bochum, Germany (2010)


                    Coresets and Approximate Clustering for Bregman Divergences

                    M.R. Ackermann, J. Blömer, in: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2009, pp. 1088-1097

                    Sampling methods for shortest vectors, closest vectors and successive minima

                    J. Blömer, S. Naewe, Theoretical Computer Science (2009)(18), pp. 1648 - 1665


                    A Probabilistic Zero-Test for Expressions Involving Roots of Rational Numbers

                    J. Blömer, in: Algorithms — ESA’ 98, Springer Berlin Heidelberg, 2007, pp. 151-162

                    Analysis of Countermeasures Against Access Driven Cache Attacks on AES

                    J. Blömer, V. Krummel, in: Selected Areas in Cryptography, Springer Berlin Heidelberg, 2007, pp. 96-109

                    Key Revocation with Interval Cover Families

                    J. Blömer, A. May, in: Selected Areas in Cryptography, Springer Berlin Heidelberg, 2007, pp. 325-341

                    Low Secret Exponent RSA Revisited

                    J. Blömer, A. May, in: Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2007, pp. 4-19


                    Fault Based Collision Attacks on AES

                    J. Blömer, V. Krummel, in: Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2006, pp. 106-120

                    Randomness and Secrecy - A Brief Introduction

                    J. Blömer, Journal of Universal Computer Science (J.UCS) (2006)(6), pp. 654--671

                    We give a brief introduction to probabilistic encryptions. This serves as an example how randomness plays a pivotal role in cryptographic systems that satisfy advanced security concepts.

                      Sign Change Fault Attacks on Elliptic Curve Cryptosystems

                      J. Blömer, M. Otto, J. Seifert, in: Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2006, pp. 36-52

                      Wagner’s Attack on a Secure CRT-RSA Algorithm Reconsidered

                      J. Blömer, M. Otto, in: Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2006, pp. 13-23


                      A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers

                      J. Blömer, A. May, in: EUROCRYPT 2005, Springer Berlin Heidelberg, 2005, pp. 251-267


                      A Generalized Wiener Attack on RSA

                      J. Blömer, A. May, in: Public Key Cryptography – PKC 2004, Springer Berlin Heidelberg, 2004, pp. 1-13

                      A new CRT-RSA algorithm secure against bellcore attacks

                      J. Blömer, M. Otto, J. Seifert, in: Proceedings of the 10th ACM conference on Computer and communication security - CCS '03, ACM Press, 2004

                      Provably Secure Masking of AES

                      J. Blömer, J. Guajardo, V. Krummel, in: Selected Areas in Cryptography, Springer Berlin Heidelberg, 2004, pp. 69-83


                      Fault Based Cryptanalysis of the Advanced Encryption Standard (AES)

                      J. Blömer, J. Seifert, in: Financial Cryptography, Springer Berlin Heidelberg, 2003, pp. 162-181

                      New Partial Key Exposure Attacks on RSA

                      J. Blömer, A. May, in: Advances in Cryptology - CRYPTO 2003, Springer Berlin Heidelberg, 2003, pp. 27-43


                      Priority encoding transmission

                      A. Albanese, J. Blömer, J. Edmonds, M. Luby, M. Sudan, in: Proceedings 35th Annual Symposium on Foundations of Computer Science, IEEE Comput. Soc. Press, 2002

                      Priority encoding transmission

                      A. Albanese, J. Blömer, J. Edmonds, M. Luby, M. Sudan, IEEE Transactions on Information Theory (2002), 42(6), pp. 1737-1744


                      Closest Vectors, Successive Minima, and Dual HKZ-Bases of Lattices

                      J. Blömer, in: Automata, Languages and Programming, Springer Berlin Heidelberg, 2000, pp. 248-259


                      On the complexity of computing short linearly independent vectors and short bases in a lattice

                      J. Blömer, J. Seifert, in: Proceedings of the thirty-first annual ACM symposium on Theory of computing - STOC '99, ACM Press, 1999


                      A lower bound for a class of graph based loss resilient codes

                      J. Blömer, B. Trachsler, Technical report/Departement of Computer Science, ETH Zürich (1998)


                      Denesting by bounded degree radicals

                      J. Blömer, in: Algorithms — ESA '97, Springer Berlin Heidelberg, 1997, pp. 53-63

                      The rank of sparse random matrices over finite fields

                      J. Blömer, R. Karp, E. Welzl, Random Structures \& Algorithms (1997)(4), pp. 407-419


                      An XOR-based erasure-resilient coding scheme

                      J. Blömer, M. Kalfane, R. Karp, M. Karpinski, M. Luby, D. Zuckerman, 1995

                      Approximate matching of polygonal shapes

                      H. Alt, B. Behrends, J. Blömer, Annals of Mathematics and Artificial Intelligence (1995), 13(3)

                      For two given simple polygonsP, Q, the problem is to determine a rigid motionI ofQ giving the best possible match betweenP andQ, i.e. minimizing the Hausdorff distance betweenP andI(Q). Faster algorithms as the one for the general problem are obtained for special cases, namely thatI is restricted to translations or even to translations only in one specified direction. It turns out that determining pseudo-optimal solutions, i.e. ones that differ from the optimum by just a constant factor, can be done much more efficiently than determining optimal solutions. In the most general case, the algorithm for the pseudo-optimal solution is based on the surprising fact that for the optimal possible match betweenP and an imageI(Q) ofQ, the distance between the centroids of the edges of the convex hulls ofP andI(Q) is a constant multiple of the Hausdorff distance betweenP andI(Q). It is also shown that the Hausdorff distance between two polygons can be determined in timeO(n logn), wheren is the total number of vertices.


                        How to denest Ramanujan's nested radicals

                        J. Blömer, in: Proceedings., 33rd Annual Symposium on Foundations of Computer Science, IEEE, 1992

                        Resemblance and symmetries of geometric patterns

                        H. Alt, J. Blömer, in: Data structures and efficient algorithms, Springer Berlin Heidelberg, 1992, pp. 1-24

                        Simplifying Expressions Involving Radicals

                        J. Blömer, PhD thesis, Freie Universität Berlin, Fachbereich Mathematik und Informatik, 1992


                        Approximate matching of polygonal shapes (extended abstract)

                        H. Alt, B. Behrends, J. Blömer, in: Proceedings of the seventh annual symposium on Computational geometry - SCG '91, ACM Press, 1991

                        Computing sums of radicals in polynomial time

                        J. Blömer, in: Proceedings 32nd Annual Symposium of Foundations of Computer Science, IEEE Comput. Soc. Press, 1991


                        Approximation of convex polygons

                        H. Alt, J. Blömer, H. Wagener, in: Automata, Languages and Programming, Springer-Verlag, 1990, pp. 703-716

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