Publications of the cosec research group (von zur Gathen, Bonn-Aachen International Center for Information Technology)

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Articles

Joachim von zur Gathen, Daniel Panario & Bruce Richmond (2012). Interval Partitions and Polynomial Factorization. Algorithmica 63, 363-397. Link to electronic version. Local PDF (343KB).

Daniel Loebenberger & Michael Nüsken (2012). Coarse-grained integers. e-print arXiv:1003.2165v2 Link to electronic version. Extended Abstract submitted to ANTS X.

Joachim von zur Gathen, Daniel Panario & Bruce Richmond (2011). Interval Partitions and Polynomial Factorization. To appear in Algorithmica 34pp. Link to electronic version. Published online: 14 June 2011. Local PDF (343KB).

Daniel Loebenberger & Michael Nüsken (2011). Analyzing standards for RSA integers — full version. Submitted to Journal of Cryptology e-print arXiv:1104.4356v2. Local PDF (456KB).

Neyire Deniz Sarier (2011). A new biometric identity based encryption scheme secure against DoS attacks. Security and Communication Networks 4(1), 23-32. Link to electronic version. Local PDF (238KB).

Joachim von zur Gathen (2010). Counting decomposable multivariate polynomials. Applicable Algebra in Engineering, Communication and Computing 22(3), 165-185. Link to electronic version.

Joachim von zur Gathen (2010). Lower bounds for decomposable univariate wild polynomials. To appear in Journal of Symbolic Computation, 34 pages. Local PDF (299KB).

Joachim von zur Gathen (2010). Shift-invariant polynomials and Ritt’s Second Theorem. Contemporary Mathematics 518, 161-184. Local PDF (341KB).

Joachim von zur Gathen, Maurice Mignotte & Igor E. Shparlinski (2010). Approximate polynomial gcd: small degree and small height perturbations. In von zur Gathen et al. (2010c). Link to electronic version. This is a corrected version. Local PDF (216KB).

Joachim von zur Gathen, Maurice Mignotte & Igor E. Shparlinski (2010). Approximate polynomial gcd: small degree and small height perturbations. Journal of Symbolic Computation Link to electronic version.

Daniel Loebenberger & Michael Nüsken (2010). Coarse-grained integers. e-print arXiv:1003.2165v1 Link to electronic version. Local PDF (587KB).

Neyire Deniz Sarier (2010). Improving the Accuracy and Storage Cost in Biometric Remote Authentication Schemes. Journal of Network and Computer Applications 33(3), 268-274. Link to electronic version. Local PDF (284KB).

Joachim von zur Gathen & Igor E. Shparlinski (2009). Subset sum pseudorandom numbers: fast generation and distribution. Journal of Mathematical Cryptology 3(2), 149-163. ISSN (Online) 1862-2984, (Print) 1862-2976. Link to electronic version.

Joachim von zur Gathen, Alfredo Viola & Konstantin Ziegler (2009). Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields. Mathematica Slovaca An Extended Abstract of this paper appeared as von zur Gathen et al. (2010d).

Benjamin Justus & Daniel Loebenberger (2009). Differential Addition in Generalized Edwards Coordinates. ePrint Archive: Report 2009/523 Link to electronic version.

Jean-Luc Beuchat, Nicolas Brisebarre, Jérémie Detrey, Eiji Okamoto, Masaaki Shirase & Tsuyoshi Takagi (2008). Algorithms and arithmetic operators for computing the η_T pairing in characteristic three. IEEE Transactions on ComputersSpecial Section on Special-Purpose Hardware for Cryptography and Cryptanalysis 57(11). Link to electronic version.

Joachim von zur Gathen (2008). Counting decomposable multivariate polynomials. Preprint, 21 pages. Link to electronic version.

Joachim von zur Gathen (2008). Counting decomposable multivariate polynomials. Preprint, 21 pages. Link to electronic version. Abstract in Abstracts of the Ninth International Conference on Finite Fields and their Applications, 21-22. Claude Shannon Institute, Dublin. July, 2009. http://www.shannoninstitute.ie/fq9/AllFq9Abstracts.pdf.

Joachim von zur Gathen (2008). Counting decomposable univariate polynomials. Preprint, 93 pages. Link to electronic version. Extended abstract see von zur Gathen (2009b).

Joachim von zur Gathen (2008). Counting reducible and singular bivariate polynomials. Finite Fields and Their Applications 14(4), 944-978. Link to electronic version. Extended abstract see von zur Gathen (2007b). This online version includes a single-page correction. Local PDF (409KB).

Christoph Puttmann, Jamshid Shokrollahi, Mario Porrmann & Ulrich Rückert (2008). Hardware Accelerators for Elliptic Curve Cryptography. Advances in Radio Science (ARS) (6), 259-264. Link to electronic version.

Joachim von zur Gathen (2007). Counting Reducible and Singular Bivariate Polynomials. Oberwolfach Report 31, 40-41.

Joachim von zur Gathen (2007). Zimmermann Telegram: The Original Draft. Cryptologia 31(1), 2-37. Link to electronic version. Local PDF (2.8MB).

Fabien Laguillaumie & Damien Vergnaud (2007). Multi-Designated Verifiers Signatures: Anonymity without Encryption. Information Processing Letters 102(2-3), 127-132. Link to electronic version. Local PDF (257KB).

Joachim von zur Gathen & Igor E. Shparlinski (2006). GCD of Random Linear Combinations. Algorithmica 46(1), 137-148. ISSN 0178-4617 (Print), 1432-0541 (Online). Link to electronic version. Local PDF (162KB).

Norbert Hungerbühler & Michael Nüsken (2006). Delian metamorphoses. Elemente der Mathematik 1, 1-19. ISSN 0013-6018. Abstract and electronic version.

Preda Mihăilescu (2006). On the class groups of cyclotomic extensions in presence of a solution to Catalan’s equation. Journal of Number Theory 118(1), 123-144.

Joachim von zur Gathen & Michael Nöcker (2005). Polynomial and normal bases for finite fields. Journal of Cryptology 18(4), 337-355. ISSN 0933-2790. Link to electronic version. Local PDF (455KB).

Michael P. Barnett, Joseph F. Capitani, Joachim Von Zur Gathen & Jürgen Gerhard (2004). Symbolic calculation in chemistry: Selected examples. International Journal of Quantum Chemistry 100(2), 80-104. Link to electronic version. See also http://www.mrw.interscience.wiley.com/suppmat/0020-7608/suppmat/100/suppmat_barnett.pdf. Local PDF (475KB).

Joachim von zur Gathen (2004). Friederich Johann Buck: arithmetic puzzles in cryptography. Cryptologia XXVIII(4), 309-324. Link to electronic version. Local PDF (1.5MB).

Joachim von zur Gathen & Jürgen Gerhard (2004). Computing special powers in finite fields. Mathematics of Computation 73(247), 1499-1523. ISSN 0025-5718. Link to electronic version. Article electronically published on September 26, 2003. Local PDF (511KB).

Joachim von zur Gathen, Arnold Knopfmacher, Florian Luca, Lutz G. Lucht & Igor E. Shparlinski (2004). Average order in cyclic groups. Bordeaux Journal of Number Theory 16, 107-123. Local PDF (348KB).

Joachim von zur Gathen & Michael Nöcker (2004). Fast arithmetic with general Gauß periods. Theoretical Computer Science 315, 419-452. Link to electronic version. Local PDF (498KB).

Preda Mihăilescu (2004). Primary units and a proof of Catalan’s conjecture. Journal für die reine und angewandte Mathematik 572, 167-195. Link to electronic version.

Eric Allender, Anna Bernasconi, Carsten Damm, Joachim von zur Gathen, Michael Saks & Igor Shparlinski (2003). Complexity of some arithmetic problems for binary polynomials. computational complexity 12(1/2), 23-47. Link to electronic version. Local PDF (399KB).

Joachim von zur Gathen (2003). Claude Comiers: the first arithmetical cryptography. Cryptologia XXVII(4), 339-349. Link to electronic version. Local PDF (4.9MB).

Joachim von zur Gathen (2003). Irreducible trinomials over finite fields. Mathematics of Computation 72, 1987-2000. Link to electronic version. Local PDF (339KB).

Joachim von zur Gathen, Jaime Gutierrez & Rosario Rubio (2003). Multivariate polynomial decomposition. Applicable Algebra in Engineering, Communication and Computing 14, 11-31. Link to electronic version. Extended abstract see ?. Local PDF (319KB).

Joachim von zur Gathen & Thomas Lücking (2003). Subresultants revisited. Theoretical Computer Science 297, 199-239. Link to electronic version.

Joachim von zur Gathen, Igor Shparlinski & Alistair Sinclair (2003). Finding points on curves over finite fields. SIAM Journal on Computing 32(6), 1436-1448. Link to electronic version. Extended abstract in von zur Gathen & Shparlinski (1995a). Local PDF (363KB).

Preda Mihăilescu (2003). A class number free criterion for Catalan’s conjecture. Journal of Number Theory 99(2), 225-231. ISSN 0022-314X. Link to electronic version.

Joachim von zur Gathen (2002). Review of: Donald E. Knuth, Selected Papers on Analysis of Algorithms. IEEE Annals of the History of Computing 24(2), 98-99.

Joachim von zur Gathen & Jürgen Gerhard (2002). Polynomial factorization over F₂. Mathematics of Computation 71(240), 1677-1698. Link to electronic version. Local PDF (449KB).

Michael Nüsken (2002). Unique Tensor Factorization of Loop-Resistant Algebras over a Field of Finite Characteristic. Journal of Algebra 251(2), 509-528. Abstract and electronic version.

Eric Bach, Joachim von zur Gathen & Hendrik W. Lenstra, Jr. (2001). Factoring Polynomials over Special Finite Fields. Finite Fields and Their Applications 7, 5-28. Link to PDF version. Local PDF (293KB).

Olaf Bonorden, Joachim von zur Gathen, Jürgen Gerhard, Olaf Müller & Michael Nöcker (2001). Factoring a binary polynomial of degree over one million. ACM SIGSAM Bulletin 35(1), 16-18. Link to electronic version. Local PDF (194KB).

Joachim von zur Gathen & Daniel Panario (2001). Factoring Polynomials Over Finite Fields: A Survey. Journal of Symbolic Computation 31(1-2), 3-17. Link to electronic version.

Joachim von zur Gathen & Francesco Pappalardi (2001). Density Estimates Related to Gauß periods. Progress in Computer Science and Applied Logic 20, 33-41. Link to electronic version. Local PDF (243KB).

Jürgen Gerhard (2001). Fast Modular Algorithms for Squarefree Factorization and Hermite Integration. Applicable Algebra in Engineering, Communication and Computing 11(3), 203-226. Author’s homepage.

Shuhong Gao, Joachim von zur Gathen, Daniel Panario & Victor Shoup (2000). Algorithms for Exponentiation in Finite Fields. Journal of Symbolic Computation 29(6), 879-889. Link to electronic version.

Joachim von zur Gathen (2000). Subresultants revisited. Abstract of Invited Talk at East Coast Computer Algebra Day 2000. SIGSAM Bulletin 34(3), 21.

Joachim von zur Gathen & Igor Shparlinski (2000). The CREW PRAM complexity of modular inversion. SIAM Journal on Computing 29(6), 1839-1857. Link to electronic version. Local PDF (306KB).

Sandra Feisel, Joachim von zur Gathen & M. Amin Shokrollahi (1999). Normal bases via general Gauß periods. Mathematics of Computation 68(225), 271-290. Link to electronic version. Local PDF (350KB).

Michael Nüsken (1999). Unique tensor factorization of algebras. Mathematische Annalen 315(3), 341-362. Abstract and electronic version.

Shuhong Gao, Joachim von zur Gathen & Daniel Panario (1998). Gauss periods: orders and cryptographical applications. Mathematics of Computation 67(221), 343-352. Link to electronic version. With microfiche supplement. Local PDF (232KB).

Joachim von zur Gathen (1998). Algebra für Spione, Datenschützer und das Internet: Kryptographie und endliche Körper. Forschungsforum Paderborn 1-98, 8-13. Link to electronic version. Local PDF (428KB).

Joachim von zur Gathen & Silke Hartlieb (1998). Factoring Modular Polynomials. Journal of Symbolic Computation 26(5), 583-606. Link to electronic version. Extended abstract in von zur Gathen & Hartlieb (1996).

Joachim von zur Gathen & Igor Shparlinski (1998). Orders of Gauss Periods in Finite Fields. Applicable Algebra in Engineering, Communication and Computing 9(1), 15-24. Link to electronic version. Extended abstract in von zur Gathen & Shparlinski (1995b). Local PDF (235KB).

Joachim von zur Gathen & Igor E. Shparlinski (1998). Computing components and projections of curves over finite fields. SIAM Journal on Computing 28(3), 822-840. Link to electronic version. Local PDF (360KB).

Joachim von zur Gathen & James R. Roche (1997). Polynomials with two values. Combinatorica 17(3), 345-362. Link to electronic version.

Joachim von zur Gathen, Marek Karpinski & Igor E. Shparlinski (1996). Counting curves and their projections. computational complexity 6, 64-99. Link to electronic version. Extended abstract in von zur Gathen et al. (1993). Local PDF (423KB).

J. von zur Gathen & J. Weiss (1995). Homogeneous Bivariate Decompositions. Journal of Symbolic Computation 19, 409-434. Link to electronic version. Local PDF (381KB).

Mark Giesbrecht (1995). Nearly Optimal Algorithms for Canonical Matrix Forms. SIAM Journal on Computing 24, 948-969.

K. Ma & J. von zur Gathen (1995). The computational complexity of recognizing permutation functions. computational complexity 5(1), 76-97. Link to electronic version.

K. Ma & J. von zur Gathen (1995). Tests for Permutation Functions. Finite Fields and Their Applications 1, 31-56. Link to electronic version.

Joachim von zur Gathen (1992). A polynomial factorization challenge. ACM SIGSAM Bulletin 26, 22-24. Link to electronic version.

Joachim von zur Gathen (1992). Processor-efficient exponentiation in finite fields. Information Processing Letters 41, 81-86. Link to electronic version.

Joachim von zur Gathen & Victor Shoup (1992). Computing Frobenius maps and factoring polynomials. computational complexity 2, 187-224. Link to electronic version.

Joachim von zur Gathen (1991). Efficient and optimal exponentiation in finite fields. computational complexity 1, 360-394. Link to electronic version.

Joachim von zur Gathen (1991). Maximal Bilinear Complexity and Codes. Linear Algebra and its Applications 144, 49-61. Link to electronic version.

Joachim von zur Gathen (1991). Tests for permutation polynomials. SIAM Journal on Computing 20(3), 591-602. Link to electronic version.

Joachim von zur Gathen (1991). Values of polynomials over finite fields. Bulletin of the Australian Mathematical Society 43, 141-146. Link to electronic version.

Joachim von zur Gathen & Gadiel Seroussi (1991). Boolean Circuits versus Arithmetic Circuits. Information and Computation 91, 142-154. Link to electronic version.

Joachim von zur Gathen (1990). Functional Decomposition of Polynomials: the Tame Case. Journal of Symbolic Computation 9, 281-299. Link to electronic version.

Joachim von zur Gathen (1990). Functional Decomposition of Polynomials: the Wild Case. Journal of Symbolic Computation 10, 437-452. Link to electronic version.

Joachim von zur Gathen (1990). Inversion in finite fields using logarithmic depth. Journal of Symbolic Computation 9, 175-183. Link to electronic version.

J. von zur Gathen & M. Giesbrecht (1990). Constructing Normal Bases in Finite Fields. Journal of Symbolic Computation 10, 547-570. ISSN 0747-7171. Link to electronic version.

Keju Ma & Joachim von zur Gathen (1990). Analysis of Euclidean Algorithms for Polynomials over Finite Fields. Journal of Symbolic Computation 9, 429-455. Link to electronic version.

Joachim von zur Gathen (1988). Algebraic complexity theory. Annual Review of Computer Science 3, 317-347. Link to electronic version.

Joachim von zur Gathen (1987). Computing powers in parallel. SIAM Journal on Computing 16, 930-945. Link to electronic version.

Joachim von zur Gathen (1987). Factoring polynomials and primitive elements for special primes. Theoretical Computer Science 52, 77-89. Link to electronic version.

Joachim von zur Gathen (1987). Feasible Arithmetic Computations: Valiant’s Hypothesis. Journal of Symbolic Computation 4, 137-172. Link to electronic version. Local PDF (414KB).

Joachim von zur Gathen (1987). Permanent and determinant. Linear Algebra and its Applications 96, 87-100. Link to electronic version.

Joachim von zur Gathen (1986). Representations and parallel computations for rational functions. SIAM Journal on Computing 15(2), 432-452. Link to electronic version.

Joachim von zur Gathen (1985). Irreducibility of Multivariate Polynomials. Journal of Computer and System Sciences 31(2), 225-264. Link to electronic version.

J. von zur Gathen & E. Kaltofen (1985). Factorization of Multivariate Polynomials Over Finite Fields. Mathematics of Computation 45, 251-261. Link to electronic version.

Joachim von zur Gathen & Erich Kaltofen (1985). Factoring Sparse Multivariate Polynomials. Journal of Computer and System Sciences 31(2), 265-287. Link to electronic version.

Joachim von zur Gathen (1984). Hensel and Newton methods in valuation rings. Mathematics of Computation 42(166), 637-661. Link to electronic version.

Joachim von zur Gathen (1984). Parallel algorithms for algebraic problems. SIAM Journal on Computing 13(4), 802-824.

Joachim von zur Gathen (1983). Computations in rings with valuations. Record of the Third Conference on Foundations of Software Technology and Theoretical Computer Science, Bangalore, ed. Joseph Mathai, 111-128.

Joachim von zur Gathen (1983). Secant spaces to curves. Canadian Journal of Mathematics 35(4), 589-612. Local PDF (354KB).

J. von zur Gathen & V. Strassen (1983). Некоторюе многочленю, имеющие бюсокую сложност вючисления Some polynomials that are hard to compute. (Russian). Kiberneticeskij sbornik, Nov. Ser. 20 59-63. Local PDF (2.1MB).

A. Borodin, J. von zur Gathen & J. E. Hopcroft (1982). Fast parallel matrix and GCD Computations. Information and Control 52, 241-256. Link to electronic version. Local PDF (195KB).

J. von zur Gathen & V. Strassen (1980). Some polynomials that are hard to compute. Theoretical Computer Science 11, 331-335. Link to electronic version. Local PDF (2.0MB).

Joachim von zur Gathen & Malte Sieveking (1978). A bound on solutions of linear integer equalities and inequalities. Proceedings of the American Mathematical Society 72(1), 155-158. Link to electronic version. Local PDF (97KB).

Articles in proceedings

Joachim von zur Gathen (2011). Census of Polynomials. In Fq10 - The Tenth International Conference on Finite Fields and Their Applications, p.8. Local PDF (65KB).

Daniel Loebenberger & Michael Nüsken (2011). Analyzing standards for RSA integers. In Africacrypt 2011, Abderrahmane Nitaj & David Pointcheval, editors, volume 6737 of Lecture Notes in Computer Science, 260-277. Springer. ISBN 978-3-642-21968-9. ISSN 0302-9743. Link to electronic version. Local PDF (242KB).

Laila El Aimani & Yona Raekow (2010). Reselling Digital Content. In FARES 2010, Lisa O’Conner, editor, IEEE Computer Society, 391-396. IEEE Computer Society, 10662 Los Vaqueros Circle Los Alamitos, California 90720-1314. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version. Local PDF (197KB).

Jean-Charles Faugère, Joachim von zur Gathen & Ludovic Perret (2010). Decomposition of Generic Multivariate Polynomials. In Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation ISSAC2010, Munich, Germany, 131-137. Link to electronic version. Local PDF (174KB).

Joachim von zur Gathen (2010). Counting decomposable multivariate polynomials. In Applicable Algebra in Engineering, Communication and Computing, volume 22(3), 165-185. Link to electronic version. Abstract in “Abstracts of the Ninth International Conference on Finite Fields and their Applications”, pages 21-22, Dublin, July 2009, Claude Shannon Institute, http://www.shannoninstitute.ie/fq9/AllFq9Abstracts.pdf. Local PDF (328KB).

Joachim von zur Gathen, Mark Giesbrecht & Konstantin Ziegler (2010). Composition collisions and projective polynomials. Statement of results. In Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation ISSAC2010, Munich, Germany, Stephen Watt, editor, 123-130. ACM Press. Preprint available at http://arxiv.org/abs/1005.1087.

Joachim von zur Gathen, Alfredo Viola & Konstantin Ziegler (2010). Counting Reducible, Powerful, and Relatively Irreducible Multivariate Polynomials over Finite Fields (Extended Abstract). In Proceedings of LATIN 2010, Oaxaca, Mexico, Alejandro López-Ortiz, editor, volume 6034 of Lecture Notes in Computer Science, 243-254. Springer-Verlag, Berlin, Heidelberg. ISBN 978-3-642-12199-9. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version.

Benjamin Justus & Daniel Loebenberger (2010). Differential Addition in Generalized Edwards Coordinates. In Proceedings of the 5th International Workshop on Security, Kobe, Japan, November 2010, Isao Echizen, Noboru Kunihiro & Ryoichi Sasaki, editors, volume 6434 of Lecture Notes in Computer Science, 316-325. Springer-Verlag, Berlin, Heidelberg. ISBN 978-3-642-16824-6. ISSN 0302-9743. Link to electronic version. Local PDF (193KB).

Neyire Deniz Sarier (2010). Generic Constructions of Biometric Identity Based Encryption Systems. In Information Security Theory and Practices. Security and Privacy of Pervasive Systems and Smart Devices, Pierangela Samarati, Michael Tunstall, Joachim Posegga, Konstantinos Markantonakis & Damien Sauveron, editors, volume 6033 of Lecture Notes in Computer Science, 90-105. Springer-Verlag. ISBN 3-642-12367-8. ISSN 0302-9743. Link to electronic version. Best Student Paper Award. Local PDF (280KB).

Neyire Deniz Sarier (2010). Practical multi-factor biometric remote authentication. In Fourth IEEE International Conference on Biometrics: Theory Applications and Systems (BTAS), 1-6. Local PDF (218KB).

Laila El Aimani (2009). Anonymity from Public Key Encryption to Undeniable Signatures. In Africacrypt 2009, B. Preneel, editor, number 5580 in Lecture Notes in Computer Science, 217-234. Springer. ISBN 978-3-642-02383-5. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version.

Laila El Aimani (2009). On Generic Constructions of Designated Confirmer Signatures (The “Encryption of a Signature” Paradigm Revisited). In Progress in Cryptology - INDOCRYPT 2009, Bimal Roy & Nicolas Sendrier, editors, number 5922 in Lecture Notes in Computer Science, To appear. Springer-Verlag, Berlin, Heidelberg. ISBN ?? ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version.

Joachim von zur Gathen (2009). The number of decomposable multivariate polynomials. In Abstracts of the Ninth International Conference on Finite Fields and their Applications, 21-22. Claude Shannon Institute, Dublin. Link to electronic version.

Joachim von zur Gathen (2009). The Number of Decomposable Univariate Polynomials — Extended Abstract. In Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation ISSAC2009, Seoul, Korea, John P. May, editor, 359-366. ISBN 978-1-60558-609-0. Preprint (2008) at http://arxiv.org/abs/0901.0054. Local PDF (226KB).

Daniel Loebenberger (2009). A Simple Derivation for the Frobenius Pseudoprime Test. In WeWORC 2009. Local PDF (107KB).

Daniel Loebenberger & Jens Putzka (2009). Optimization strategies for hardware-based cofactorization. In Selected Areas in Cryptography, M. J. Jacobson, V. Rijmen & R. Safavi-Naini, editors, volume 5867 of Lecture Notes in Computer Science, 170-181. Berlin, Heidelberg. Link to electronic version. Local PDF (238KB).

Daniel Panario (2009). Interval Partitions and Polynomial Factorization (Joint work with Joachim von zur Gathen and Bruce Richmond). In Abstracts of the Ninth International Conference on Finite Fields and their Applications, 45. Claude Shannon Institute, Dublin. Link to electronic version. Final version in Algorithmica 69 (2012), 363-397.

Neyire Deniz Sarier (2009). Biometric Identity Based Signature Revisited. In Public Key Infrastructures, Services and Applications, Fabio Martinelli & Bart Preneel, editors, volume 6391 of Lecture Notes in Computer Science, 271-285. Springer-Verlag. ISBN 978-3-642-16441-5. ISSN 0302-9743. Link to electronic version. Local PDF (272KB).

Neyire Deniz Sarier (2009). A New Approach for Biometric Template Storage and Remote Authentication. In Advances in Biometrics, Massimo Tistarelli & Mark S. Nixon, editors, volume 5558 of Lecture Notes in Computer Science, 909-918. Springer-Verlag. ISBN 978-3-642-01792-6. Link to electronic version.

Neyire Deniz Sarier (2009). A Survey of Distributed Biometric Authentication Systems. In BIOSIG’09, volume 155 of LNI, 43-55. Gesellschaft für Informatik. ISBN 3885792494. Local PDF (180KB).

Florent de Dinechin, Jérémie Detrey & Octavian Creţ (2008). When FPGAs are better at floating-point than microprocessors. In 16th ACM/SIGDA International Symposium on Field-Programmable Gate Arrays (FPGA’08). ACM Press, Monterey, CA, USA. To appear.

Laila El Aimani (2008). Toward a Generic Construction of Universally Convertible Undeniable Signatures from Pairing-Based Signatures. In Progress in Cryptology - INDOCRYPT 2008, Dipanwita Roy Chowdhury, Vincent Rijmen & Abhijit Das, editors, volume 5365 of Lecture Notes in Computer Science, 145-157. Springer-Verlag, Berlin, Heidelberg. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version.

Joachim von zur Gathen (2008). Subset Sum Pseudorandom Generators. In Extended Abstracts of the Second Workshop on Mathematical Cryptology WmC 08, Álvar Ibeas & Jaime Gutiérrez, editors, 20. Link to electronic version.

Joachim von zur Gathen & Igor E. Shparlinski (2008). Approximate polynomial gcd: small degree and small height perturbations. In Proceedings of LATIN 2008, Búzios, Rio de Janeiro, Brazil, Eduardo Sany Laber, Claudson Bornstein, Loana Tito Nogueira & Luerbio Faria, editors, number 4957 in Lecture Notes in Computer Science, 276-283. Springer-Verlag, Berlin, Heidelberg. ISSN 0302-9743. Link to electronic version. Local PDF (179KB).

Christoph Puttmann, Jamshid Shokrollahi & Mario Porrmann (2008). Resource Efficiency of Instruction Set Extensions for Elliptic Curve Cryptography. In Proceedings of the 5th International Conference on Information Technology: New Generations (ITNG ’08), Shahram Latifi, editor, 131-136. IEEE Computer Society Press, Las Vegas, Nevada, USA. Link to electronic version.

Neyire Deniz Sarier (2008). A New Biometric Identity Based Encryption Scheme. In Technical Sessions for 2008 International Symposium on Trusted Computing (TrustCom 2008) in Proceedings of the 9th International Conference for Young Computer Scientists, ICYCS 2008, Zhang Jia Jie, Hunan, China, November 18-21, 2008, Guojun Wang, Jianer Chen, Michael R. Fellows & Huadong Ma, editors, 2061-2066. IEEE Computer Society. ISBN 978-0-7695-3398-8. Link to electronic version. Local PDF (155KB).

Pierre-Louis Cayrel, Ayoub Otmani & Damien Vergnaud (2007). On Kabatianskii-Krouk-Smeets Signatures. In International Workshop on the Arithmetic of Finite Fields, WAIFI 2007, Claude Carlet & Berk Sunar, editors, number 4547 in Lecture Notes in Computer Science, 237-251. Springer-Verlag, Berlin/ Heidelberg. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version. Local PDF (328KB).

Laila El Aimani & Damien Vergnaud (2007). Gradually Convertible Undeniable Signatures (Michels-Petersen-Horster Convertible Undeniable Signatures Revisited). In Applied Cryptography and Network Security, 5th International Conference, ACNS 2007, Jonathan Katz & Moti Yung, editors, number 4521 in Lecture Notes in Computer Science, 478-496. Springer-Verlag, Berlin, Heidelberg. ISBN 978-3-540-72738-5. ISSN 0302-9743 (Print), 1611-3349 (Online). Link to electronic version. Local PDF (353KB).

Joachim von zur Gathen (2007). Counting Reducible and Singular Bivariate Polynomials. In von zur Gathen (2007c), 369-376. Link to electronic version. Final version see von zur Gathen (2008d).

Joachim von zur Gathen (2007). Counting Reducible and Singular Bivariate Polynomials. In Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation ISSAC2007, Waterloo, Ontario, Canada, Christopher W. Brown, editor, 369-376. Link to electronic version. Final version see ?.

Joachim von zur Gathen (2007). Fast arithmetic: tiger in your tank. In Proceedings of Conference on Algorithmic Number Theory, Anne-Maria Ernvall-Hytönen, Matti Jutila, Juhani Karhumäki & Arto Lepistö, editors, 50-63. Turku, Finland.

Joachim von zur Gathen, Amin Shokrollahi & Jamshid Shokrollahi (2007). Efficient Multiplication Using Type 2 Optimal Normal Bases. In International Workshop on the Arithmetic of Finite Fields, WAIFI 2007, Claude Carlet & Berk Sunar, editors, number 4547 in Lecture Notes in Computer Science, 55-68. Springer-Verlag, Berlin/ Heidelberg. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version. Local PDF (254KB).

Joachim von zur Gathen, Amin Shokrollahi & Jamshid Shokrollahi (2007). Efficient Multiplication Using Type 2 Optimal Normal Bases. In WAIFI, Claude Carlet & Berk Sunar, editors, number 4547 in Lecture Notes in Computer Science, 55-68. Springer-Verlag, Berlin/ Heidelberg. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version.

Elisa Gorla, Christoph Puttmann & Jamshid Shokrollahi (2007). Explicit Formulas for Efficient Multiplication in F_3^6m. In Selected Areas in Cryptography, Carlisle Adams, Ali Miri & Michael Wiener, editors, volume 4876 of LNCS, 173-183. Berlin, Heidelberg. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version.

Christoph Puttmann & Jamshid Shokrollahi (2007). MPSoC-coupled Hardware Accelerator for Ellipic Curve Cryptography. In Proceedings of the Western European Workshop on Research in Cryptology (WEWoRC’07), Stefan Lucks, Ahmad reza Sadeghi & Christopher Wolf, editors, 1-10. Bochum. Link to electronic version. Local PDF (209KB).

Jamshid Shokrollahi, Elisa Gorla & Christoph Puttmann (2007). Efficient FPGA-based multipliers for F_3⁹⁷ and F_3^6⋅97. In Field Programmable Logic and Applications, 2007. FPL 2007, Walid Najjar & Koen Bertels, editors, 339-344. Amsterdam, Netherlands. Link to electronic version.

Joachim von zur Gathen (2006). Who was Who in Polynomial Factorization. In Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation ISSAC2006, Genova, Italy, Jean-Guillaume Dumas, editor, 1-2. ACM Press. ISBN 1-59593-276-3. Link to electronic version.

Joachim von zur Gathen & Jamshid Shokrollahi (2006). Fast arithmetic for polynomials over F₂ in hardware. In IEEE Information Theory Workshop (2006), 107-111. IEEE, Punta del Este, Uruguay. Local PDF (152KB).

Joachim von zur Gathen & Jamshid Shokrollahi (2005). Efficient FPGA-based Karatsuba multipliers for polynomials over F₂. In Selected Areas in Cryptography (SAC 2005), Bart Preneel & Stafford Tavares, editors, number 3897 in Lecture Notes in Computer Science, 359-369. Springer-Verlag, Kingston, ON, Canada. ISBN 3-540-33108-5. Link to electronic version. Local PDF (194KB).

Joachim von zur Gathen (2004). Arithmetic Circuits for Discrete Logarithms. In LATIN04, Martin Farach-Colton, editor, number 2976 in Lecture Notes in Computer Science, 557-566. Springer-Verlag, Berlin, Heidelberg. ISBN 978-3-540-21258-4. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version. Local PDF (291KB).

Joachim von zur Gathen & Igor E. Shparlinski (2004). GCD of Random Linear Forms. In Proceedings of 15th International Symposium on Algorithms and Computation ISAAC 2004, Hong Kong, China, volume 3341 of Lecture Notes in Computer Science, 845-846. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-24131-0. ISSN 0302-9743. Link to electronic version.

Joachim von zur Gathen & Igor E. Shparlinski (2004). Polynomial Interpolation from Multiples. In Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, J. Ian Munro, editor, 1125-1130. Link to electronic version. Local PDF (254KB).

Michael Nüsken & Martin Ziegler (2004). Fast Multipoint Evaluation of Bivariate Polynomials. In Algorithms - ESA 2004, Susanne Albers & Tomasz Radzik, editors, number 3221 in Lecture Notes in Computer Science, 544-555. Springer-Verlag, Berlin, Heidelberg. ISBN 978-3-540-23025-0. ISSN 0302-9743 (Print), 1611-3349 (Online). Link to electronic version.

Joachim von zur Gathen (2003). Efficient exponentiation in finite fields. In Tagungsband: Computeralgebra. Universität Kassel 15. - 17. Mai 2003, 8.

C. Grabbe, M. Bednara, J. Shokrollahi, J. Teich & J. von zur Gathen (2003). FPGA Designs of parallel high performance GF(2²³³) Multipliers. In Proc. of the IEEE International Symposium on Circuits and Systems (ISCAS-03), volume II, 268-271. Bangkok, Thailand. Local PDF (244KB).

C. Grabbe, M. Bednara, J. Shokrollahi, J. Teich & J. von zur Gathen (2003). A High Performance VLIW Processor for Finite Field Arithmetic. In Proc. of The 10th Reconfigurable Architectures Workshop (RAW-03). Local PDF (185KB).

M. Bednara, M. Daldrup, J. Shokrollahi, J. Teich & J. von zur Gathen (2002). Reconfigurable Implementation of Elliptic Curve Crypto Algorithms. In Proc. of The 9th Reconfigurable Architectures Workshop (RAW-02), 157-164. Fort Lauderdale FL, USA. Local PDF (193KB).

M. Bednara, M. Daldrup, J. Shokrollahi, J. Teich & J. von zur Gathen (2002). Tradeoff Analysis of FPGA Based Elliptic Curve Cryptography. In Proc. of the IEEE International Symposium on Circuits and Systems (ISCAS-02), volume V, 797-800. Scottsdale, Arizona, U.S.A. Link to PDF version. Local PDF (109KB).

Patrik Ekdahl & Thomas Johansson (2002). A New Version of the Stream Cipher SNOW. In 9th Annual International Workshop, Selected Areas in Cryptography 2002, St. John’s, Newfoundland, Canada, Kaisa Nyberg & Howard Heys, editors, volume 2595 of Lecture Notes in Computer Science, 47-61. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-00622-2. ISSN 0302-9743. Link to electronic version.

Olaf Müller & Michael Nüsken (2002). Never Trust Victor: An Alternative Resettable Zero-Knowledge Proof System. In Progress in Cryptology - INDOCRYPT 2002, Alfred Menezes & Palash Sarkar, editors, number 2551 in Lecture Notes in Computer Science, 79-92. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-00263-4. ISSN 0302-9743. Abstract and electronic version.

Joachim von zur Gathen (2001). Irreducible Trinomials over Finite Fields. In Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation ISSAC2001, London, Canada, Bernard Mourrain, editor, 332-336. ACM Press. Final version in Mathematics of Computation.

Joachim von zur Gathen (2000). Factoring Polynomials Over Finite Fields. In Proceedings of An International Symposium on Applications of Computer Algebra ISACA ’2000, Kolhapur, India, Rajendra Akerkar, editor, 109-114. Allied Publishers Limited.

Joachim von zur Gathen (2000). Gauss periods — old tool, new results. In 5th Pan African Congress of Mathematics, 40. Johannesburg.

Joachim von zur Gathen & Thomas Lücking (2000). Subresultants revisited. In Proceedings of LATIN 2000, Punta del Este, Uruguay, Gastón H. Gonnet, Daniel Panario & Alfredo Viola, editors, number 1776 in Lecture Notes in Computer Science, 318-342. Springer-Verlag. ISSN 0302-9743. Final version in von zur Gathen & Lücking (2003). Local PDF (402KB).

Joachim von zur Gathen & Francesco Pappalardi (2000). Density estimates for Gauß periods. In Proc. Workshop on Cryptography and Computational Number Theory (CCNT’99, Singapore), K.-Y. Lam, I. E. Shparlinski, H. Wang & C. Xing, editors. Birkhäuser Verlag. Final version in Progress in Computer Science and Applied Logic.

Michael Nöcker (2000). Some Remarks on Parallel Exponentiation: Extended Abstract. In Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation ISSAC2000, St. Andrews, Scotland, Carlo Traverso, editor, 250-257.

Gene Cooperman, Sandra Feisel, Joachim von zur Gathen & George Havas (1999). GCD of Many Integers. In COCOON ’99, T. Asano, H. Imai, D. T. Lee, S. Nakano & T. Tokuyama, editors, number 1627 in Lecture Notes in Computer Science, 310-317. Springer-Verlag. ISSN 302-9743 (Print) 1611-3349 (Online). Link to electronic version.

Joachim von zur Gathen (1999). Gauß periods. In Abstracts of the Fifth International Conference on Finite Fields and Applications, 1999, University of Augsburg, 29.

Joachim von zur Gathen & Michael Nöcker (1999). Computing Special Powers in Finite Fields: Extended Abstract. In Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation ISSAC ’99, Vancouver, Canada, Sam Dooley, editor, 83-90. ACM Press. Link to electronic version.

Joachim von zur Gathen & Michael Nöcker (1999). Normal bases, Gauss periods, and fast arithmetic. In Abstracts of the Fifth International Conference on Finite Fields and Applications, University of Augsburg, 70.

Joachim von zur Gathen & Igor Shparlinski (1999). Constructing Elements of Large Order in Finite Fields. In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Marc Fossorier, Hideki Imai, Shu Lin & Alain Poli, editors, number 1719 in Lecture Notes in Computer Science, 404-409. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-66723-7. ISSN 0302-9743. Link to electronic version.

Joachim von zur Gathen & Igor Shparlinski (1998). The CREW PRAM complexity of modular inversion. In Proceedings of LATIN ’98, Campinas, Brazil, C. L. Lucchesi & A. V. Moura, editors, number 1380 in Lecture Notes in Computer Science, 305-315. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-64275-7. ISSN 0302-9743. Link to electronic version. Final version in SIAM Journal on Computing. Local PDF (262KB).

Jürgen Gerhard (1998). High degree solutions of low degree equations. In Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation ISSAC ’98, Rostock, Germany, Oliver Gloor, editor, 284-289. ACM Press. Link to electronic version.

Preda Mihăilescu (1998). Cyclotomy Primality Proving—Recent Developments. In Algorithmic Number Theory, Third International Symposium, ANTS-III, Portland, Oregon, USA, J. P. Buhler, editor, number 1423 in Lecture Notes in Computer Science, 95-110. Springer-Verlag. ISSN 0302-9743. Link to electronic version.

Joachim von zur Gathen & Jürgen Gerhard (1997). Fast Algorithms for Taylor Shifts and Certain Difference Equations. In Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation ISSAC ’97, Maui HI, Wolfgang W. Küchlin, editor, 40-47. ACM Press. Link to electronic version. Local PDF (312KB).

Joachim von zur Gathen & Michael Nöcker (1997). Exponentiation in Finite Fields: Theory and Practice. In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: AAECC-12, Toulouse, France, Teo Mora & Harold Mattson, editors, number 1255 in Lecture Notes in Computer Science, 88-113. Springer-Verlag. ISSN 0302-9743. Link to electronic version. Local PDF (414KB).

Joachim von zur Gathen & Jürgen Gerhard (1996). Arithmetic and Factorization of Polynomials over F₂. In Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation ISSAC ’96, Zürich, Switzerland, Y. N. Lakshman, editor, 1-9. ACM Press. Link to electronic version. Technical report tr-rsfb-96-018, University of Paderborn, Germany, 1996, 43 pages. Final version in Mathematics of Computation. Local PDF (354KB).

Joachim von zur Gathen & Silke Hartlieb (1996). Factoring Modular Polynomials. In Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation ISSAC ’96, Zürich, Switzerland, Lakshman Y. N., editor, 10-17. ACM Press. Link to electronic version. Final version see von zur Gathen & Hartlieb (1998). Local PDF (349KB).

Shuhong Gao, Joachim von zur Gathen & Daniel Panario (1995). Gauss periods and fast exponentiation in finite fields. In Proceedings of LATIN ’95, Valparaíso, Chile, Ricardo Baeza-Yates, Eric Goles & Patricio V. Poblete, editors, number 911 in Lecture Notes in Computer Science, 311-322. Springer-Verlag. ISSN 0302-9743. Link to electronic version. Final versions in Mathematics of Computation and Journal of Symbolic Computation.

Joachim von zur Gathen & Igor E. Shparlinski (1995). Finding points on curves over finite fields. In Proceedings of the 36th Annual IEEE Symposium on Foundations of Computer Science, Milwaukee WI, 284-292. IEEE Computer Society Press. Final version see von zur Gathen et al. (2003c). Local PDF (290KB).

Joachim von zur Gathen & Igor E. Shparlinski (1995). Orders of Gauss Periods in Finite Fields. In Proceedings of 6th International Symposium on Algorithms and Computation ISAAC ’95, Cairns, Australia, J. Staples, P. Eades, N. Katoh & A. Moffat, editors, number 1004 in Lecture Notes in Computer Science, 208-215. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-60573-8. ISSN 0302-9743. Link to electronic version. Final version in von zur Gathen & Shparlinski (1998a).

Shuhong Gao & Joachim von zur Gathen (1994). Berlekamp’s and Niederreiter’s Polynomial Factorization Algorithms. In Finite Fields: Theory, Applications and Algorithms, G. L. Mullen & P. J.-S. Shiue, editors, number 168 in Contemporary Mathematics, 101-115. American Mathematical Society.

Joachim von zur Gathen & Igor E. Shparlinski (1994). Components and projections of curves over finite fields. In Proceedings of 5th International Symposium on Algorithms and Computation ISAAC ’94, Beijing, China, Ding-Zhu Du & Kiang-Sun Zhang, editors, volume 834 of Lecture Notes in Computer Science, 297-305. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-58325-4. ISSN 0302-9743. Link to electronic version. Final version in SIAM Journal on Computing.

K. Ma & J. von zur Gathen (1994). The computational complexity of recognizing permutation functions - Extended Abstract. In Proceedings of the Twenty-sixth Annual ACM Symposium on Theory of Computing, Montréal, Québec, Canada, 392-401. ACM Press, New York, USA. ISBN 0-89791-663-8. Link to electronic version.

Joachim von zur Gathen (1993). Factoring Polynomials Over Finite Fields. In Second International Conference on Finite Fields: Theory, Applications and Algorithms, Las Vegas NV, 115.

Joachim von zur Gathen, Marek Karpinski & Igor E. Shparlinski (1993). Counting curves and their projections. In Proceedings of the Twenty-fifth Annual ACM Symposium on Theory of Computing, San Diego CA, 805-812. ACM Press. Link to electronic version. Final version see von zur Gathen et al. (1996). Local PDF (430KB).

K. Ma & J. von zur Gathen (1993). Counting value sets of functions and testing permutation functions. In Abstracts of Int. Conf. Number Theoretic and Algebraic Methods in Computer Science, Moscow, Russia, 62-65. Final version in computational complexity and Finite Fields and Their Applications. See Ma & von zur Gathen (1995b).

Joachim von zur Gathen & Victor Shoup (1992). Computing Frobenius maps and factoring polynomials. In Proceedings of the Twenty-fourth Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, 97-105. ACM Press. Link to electronic version. Final version in computational complexity, see von zur Gathen & Shoup (1992a).

Joachim von zur Gathen (1991). Efficient exponentiation in finite fields. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, San Juan PR, 384-391. IEEE Computer Society Press, Los Alamitos CA. Final version in computational complexity, see von zur Gathen (1991a).

Joachim von zur Gathen (1990). Polynomials over finite fields with large images. In Proceedings of the 1990 International Symposium on Symbolic and Algebraic Computation ISSAC ’90, Tokyo, Japan, 140-144. ACM Press. Link to electronic version. Final version in Bulletin of the Australian Mathematical Society.

Joachim von zur Gathen (1989). Testing permutation polynomials. In Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, Research Triangle Park NC, 88-92. IEEE Computer Society Press, Los Alamitos CA. Link to electronic version. Final version in SIAM Journal on Computing.

Joachim von zur Gathen, Dexter Kozen & Susan Landau (1987). Functional Decomposition of Polynomials. In Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, Los Angeles CA, 127-131. IEEE Computer Society Press, Washington DC. Link to electronic version. Final version in Journal of Symbolic Computation.

Joachim von zur Gathen (1986). Irreducible Polynomials over Finite Fields. In Proc. 6th Conf. Foundations of Software Technology and Theoretical Computer Science, Delhi, India, number 241 in Lecture Notes in Computer Science, 252-262. Springer-Verlag. ISSN 0302-9743. Link to electronic version.

Joachim von zur Gathen (1986). Parallel Arithmetic computations: a survey. In Proceedings of the 12th International Symposium Mathematical Foundations of Computer Science 1986, Bratislava, Czechosolvakia, Jozef Gruska, Branislav Rovan & Juraj Wiedermann, editors, volume 233 of Lecture Notes in Computer Science, 93-112. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-16783-8. ISSN 0302-9743. Link to electronic version.

Joachim von zur Gathen (1986). Permanent and determinant. In Proceedings of the 27th Annual IEEE Symposium on Foundations of Computer Science, Toronto, Ontario, Canada, 398-401. IEEE Computer Society Press, Washington DC. Final version in Linear Algebra and its Applications.

J. von zur Gathen & G. Seroussi (1986). Boolean Circuits versus Arithmetic Circuits. In Proc. 6th Int. Conf. Computer Science, Santiago, Chile, 171-184. Final version in Information and Computation.

Joachim von zur Gathen (1984). Ecuaciones Lineales sobre Anillos de Valuación. In Proc. 4th Int. Conf. Computer Science Santiago, Chile, 110-120. Local PDF (316KB).

Joachim von zur Gathen (1984). Parallel powering. In Proceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science, Singer Island FL, 31-36. IEEE Computer Society Press. Final version in SIAM Journal on Computing. Local PDF (297KB).

Joachim von zur Gathen (1983). Factoring sparse multivariate polynomials. In Proceedings of the 24th Annual IEEE Symposium on Foundations of Computer Science, Tucson AZ, 172-179. Link to electronic version. Final version see von zur Gathen & Kaltofen (1985b). Local PDF (232KB).

Joachim von zur Gathen (1983). Parallel algorithms for algebraic problems. In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, Boston MA, 17-23. Link to electronic version. Final version in SIAM Journal on Computing.

Joachim von zur Gathen (1983). Representations and parallel Computations for rational Functions. In Proceedings of the 24th Annual IEEE Symposium on Foundations of Computer Science, Tucson AZ, 133-137. IEEE Computer Society Press. Final version in SIAM Journal on Computing. Local PDF (166KB).

J. von zur Gathen & E. Kaltofen (1983). Polynomial-time factorization of multivariate polynomials over finite fields. In Proceedings of the 10th International Colloquium on Automata, Languages and Programming ICALP 1983, Barcelona, Spain, J. Diaz, editor, number 154 in Lecture Notes in Computer Science, 250-263. Springer-Verlag, Berlin. ISBN 3-540-12317-2. Link to electronic version. Final version in Mathematics of Computation.

A. Borodin, J. von zur Gathen & J. E. Hopcroft (1982). Fast parallel matrix and GCD Computations. In Proceedings of the 23rd Annual IEEE Symposium on Foundations of Computer Science, Chicago IL, 65-71. Link to electronic version. Final version see Borodin et al. (1982a).

Articles in collection

Joachim von zur Gathen & Igor E. Shparlinski (2004). Predicting Subset Sum Pseudorandom Generators. In Lecture Notes in Computer Science—Selected Areas in Cryptography: 11th International Workshop, SAC 2004, Waterloo, Canada, August 9-10, 2004, Revised Selected Papers, Helena Handschuh & M. Anwar Hasan, editors, volume 3357, 241-251. Springer-Verlag Heidelberg. ISBN 3-540-24327-5. Link to electronic version. Local PDF (230KB).

Joachim von zur Gathen (2003). Factorization of Polynomials. In Computer Algebra Handbook - Foundations, Applications, Systems, Johannes Grabmeier, Erich Kaltofen & Volker Weispfenning, editors, 24-26. Springer-Verlag, Berlin, Heidelberg, New York. ISBN 3-540-65466-6. Link to the book.

Joachim von zur Gathen (2002). Factorization and Decomposition of Polynomials. In The Concise Handbook of Algebra, Alexander V. Mikhalev & Günter F. Pilz, editors, 159-161. Kluwer Academic Publishers. ISBN 0-7923-7072-4. Link to electronic version. Local PDF (170KB).

Joachim von zur Gathen (2001). Factorization of polynomials. In Encyclopaedia of Mathematics, Supplement III, M. Hazewinkel, editor, 146-147. Kluwer Academic Publishers. ISBN 1-4020-0198-3. Link to the book. Local PDF (207KB).

Joachim von zur Gathen & Igor Shparlinski (2001). Gauß Periods in Finite Fields. In Finite Fields and Applications, Dieter Jungnickel & Harald Niederreiter, editors, 162-177. Springer-Verlag. Link to electronic version. Local PDF (316KB).

Joachim von zur Gathen (2000). Algebra und Algorithmik. In Lexikon der Mathematik, Guido Walz, editor, 43-47. Spektrum Verlag, Heidelberg. ISBN 3-8274-0303-0. Book online (accessible only from uni-paderborn). Local PDF (188KB).

Joachim von zur Gathen (1993). Faktorisieren von Polynomen. In Computeralgebra in Deutschland, 20-22 and 25-26. Fachgruppe Computeralgebra. Local PDF (108KB).

Joachim von zur Gathen (1993). Parallel linear algebra. In Synthesis of parallel algorithms, J. Reif, editor, 573-617. Morgan Kaufmann Publishers.

J. von zur Gathen & M. Sieveking (1976). Weitere zum Erfüllungsproblem polynomial äquivalente kombinatorische Aufgaben. In Komplexität von Entscheidungsproblemen, number 43 in Lecture Notes in Computer Science, 49-71. Springer-Verlag. Link to electronic version. Local PDF (527KB).

Book

Joachim von zur Gathen & Jürgen Gerhard (2003). Modern Computer Algebra. Cambridge University Press, Cambridge, UK, Second edition. ISBN 0-521-82646-2, 800 pages. The book’s homepage. Other available editions: first edition [von zur Gathen & Gerhard (1999)], Chinese edition, Japanese translation.

Jürgen Gerhard (2001). Modular algorithms in symbolic summation and symbolic integration. Number 3218 in Lecture Notes in Computer Science. Springer-Verlag, Berlin, Heidelberg. ISBN 978-3-540-24061-7. Link to electronic version.

Joachim von zur Gathen & Jürgen Gerhard (1999). Modern Computer Algebra. Cambridge University Press, Cambridge, UK, First edition. ISBN 0-521-64176-4. The book’s homepage. Other available editions: Second edition [von zur Gathen & Gerhard (2003)], Chinese edition, Japanese translation.

Technical reports

Carsten Keller (2003). The Java class SecureRandom for generating random prime numbers with cryptoP@d. Technical report, Universität Paderborn, Fak. EIM-M.

Proceedings

Jong Hyuk Park, Hsiao-Hwa Chen, Mohammed Atiquzzaman, Changhoon Lee, Tai hoon Kim & Sang-SooYeo (editors) (2009). Advances in Information Security and Assurance, Third International Conference and Workshops, ISA 2009, Seoul, Korea, number 5576 in Lecture Notes in Computer Science. Springer-Verlag, Berlin, Heidelberg. ISBN 978-3-642-02616-4. ISSN 0302-9743.

Joachim von zur Gathen, José Luis Imaña & Çetin Kaya Koç (editors) (2008). Arithmetic of Finite Fields, volume 5130 of LNCS. Berlin, Heidelberg. ISSN 0302-9743 (Print) 1611-3349 (Online). Link to electronic version.

Phd theses

Jamshid Shokrollahi (2006). Efficient Implementation of Elliptic Curve Cryptography on FPGAs. Ph.D. thesis, Mathematisch-Naturwissenschaftliche Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn. 141 pages.

Michael Nöcker (2001). Data structures for parallel exponentiation in finite fields. Doktorarbeit, Universität Paderborn, Germany. Author’s homepage. Local PDF (3.1MB).

Preda Mihăilescu (1997). Cyclotomy of Rings & Primality Testing. Ph.D. thesis, Swiss Federal Institute of Technology, Zürich, Switzerland. Author’s homepage.

Diploma theses

Kumar Sharad (2012). Certificateless Encryption Scheme Using Biometric Identity. Master’s thesis, Department of Computer Security, b-it, Bonn.

Raoul Blankertz (2011). Decomposition of Polynomials. Diplomarbeit, Universität Bonn, Bonn. Link to electronic version. Local PDF (333KB).

Sanjin Pajo (2005). Secure Distribution of Group Data for the BSCW Collaborative System. Master’s thesis, Rheinische Friedrich-Wilhelms-Universität Bonn.

Kathrin Tofall (2005). Fourier Analysis for Polynomials over Finite Fields. Diplomarbeit, Universität Paderborn. Local PDF (12.5MB).

Carsten Keller (2003). CryptoP@d - a cryptographic toolbox. Diplomarbeit, University of Paderborn.

Olaf Müller (2001). Resettable Zero-Knowledge. Diplomarbeit, Universität Paderborn. Link to electronic version.

Martin Otto (2001). Brauer addition-subtraction chains. Diplomarbeit, University of Paderborn. Link to author’s homepage. Local PDF (2.2MB).

Cristopher Creutzig (2000). Cryptographic Functions and Gröbner Bases. Diplomarbeit, University of Paderborn.

Thomas Lücking (2000). Subresultants. Diplomarbeit, Universität Paderborn. Author’s homepage.

Stefan Wehmeier (1997). Bivariate Polynomials Over Finite Fields. Diplomarbeit, University of Paderborn.

Michael Nöcker (1996). Exponentiation in finite fields: theory and practice. Diplomarbeit, Universität-GH Paderborn. Author’s homepage. Local PDF (1.3MB).

S. Schlink (1996). Normalbasen mit Hilfe von verallgemeinerten Gauß-Perioden. Diplomarbeit, Universität-GH Paderborn, Paderborn.

Miscellaneous

Laila El Aimani (2009). Efficient Confirmer Signatures from the “Signature of a Commitment” Paradigm. Cryptology ePrint Archive, Report 2009/435. Link to electronic version.

Laila El Aimani (2009). On Generic Constructions of Designated Confirmer Signatures (The “Encryption of a Signature” Paradigm Revisited). Cryptology ePrint Archive, Report 2009/403. Link to electronic version.

Laila El Aimani (2009). Toward a Generic Construction of Convertible Undeniable Signatures from Pairing-Based Signatures. Cryptology ePrint Archive, Report 2009/362. Link to electronic version.

Laila El Aimani & Yona Raekow (2009). Exploring Subliminal Channels in Pairing-Based Signatures. WEWoRC 2009.

Michael Nöcker (1999). Normal bases, Gauss periods, and fast arithmetic. Abstract, Fifth International Conference on Finite Fields and Applications, August 2-6, 1999, University of Augsburg.