Publications of Johannes A. Buchmann

Books

Informatik, Festschrift zum 60. Geburtstag von Günter Hotz, Teubner, Stuttgart, Leipzig, 1992, Herausgeber, with H. Ganzinger, W.J. Paul.
Einführung in die Kryptographie, 1.Auflage, Springer-Verlag, 1999, 229p.
Einführung in die Kryptographie, 2., durchges. u. erw. Aufl., Springer-Verlag, 2001, 230 p.
Einführung in die Kryptographie, 3., durchges. u. erw. Aufl., Springer-Verlag, 2004, 266 p.
Introduction to Cryptography, Undergraduate Texts in Mathematics, Springer-Verlag, 2001, 281 p.
Introduction to Cryptography, Undergraduate Texts in Mathematics, Second Edition,  Springer-Verlag, 2004, 335 p.
Introduction to Cryptography, Japanese translation, Springer-Verlag, 2001.
Introducao a Criptografia, Editora Berkeley, 2002, 312 p.
Introduction to Cryptography, translation to Farsi, 2003 .
Introduction to Cryptography, translation to French, to appear.
Introduction to Cryptography, translation to Polish, to appear .
Coding Theory, cryptography and related areas, editor, with T. Hoeholdt, H. Stichtenoth, H. Tapia-Recillas, Springer-Verlag, 1999.
Algorithms for binary quadratic forms, in preparation, accepted by Springer-Verlag.

Papers

Zahlengeometrische Kettenbruchalgorithmen zur Einheitenberechnung, Dissertation, Köln 1982.
A criterion for the equivalence of two ideals, EUROSAM 84, Lecture Notes in Computer Science 174, (1984), 333-340.
A generalization of Voronoi's unit algorithm I, J. Number Theory 20, (1985), 177-191.
A generalization of Voronoi's unit algorithm II, J. Number Theory 20, (1985), 192-209.
Abschätzung der Periodenlänge einer verallgemeinerten Kettenbruchentwicklung, J. Reine Angew. Math. 361, (1985), 27-34.
Computation of independent units in number fields by Dirichlet's method, AAECC-3 1985, Lecture Notes in Computer Science 229, (1986), 302-305, with A. Pethö.
The generalized Voronoi-Algorithm in totally real algebraic number fields, Proceedings EUROCAL 85, Lecture Notes in Computer Science 204, (1986), 479-486.
Generalized continued fractions and number theoretic computations, Mathematisch-Statistische Sektion, Forschungsgesellschaft Joanneum, Bericht Nr. 269, (1986), 1-30.
The computation of the fundamental unit of totally complex quartic orders, Math. Comp. 48, (1987), 39-54.
On principal ideal testing in totally complex quartic fields and the determination of certain cyclotomic constants, Math. Comp. 48, (1987), 55-66, with H.C. Williams.
On the computation of units and class numbers by a generalization of Lagrange's algorithm, J. Number Theory 26, (1987), 8-30.
On the period length of the generalized Lagrange algorithm, J. Number Theory 26, (1987), 31-37.
An algorithm for testing Leopoldt's conjecture, J. Number Theory 27, (1987), 92-105, with J.W. Sands.
On principal ideal testing in algebraic number fields, J. Symbolic Computation, 4, (1987), 11-19, with H.C. Williams.
Zur Komplexität der Berechnung von Einheiten and Klassenzahlen algebraischer Zahlkörper, Habilitationsschrift, Düsseldorf 1987.
A key exchange system based on imaginary quadratic fields, J. Cryptology 1, (1988), 107-118, with H.C. Williams.
On the infrastructure of the principal ideal class of an algebraic number field of unit rank one, Math. Comp. 50, (1988), 569-579, with H.C. Williams.
Computation of independent units in number fields by Dirichlet's method, Math. Comp. 52, (1989), 149-159, with A. Peth[1]ö.
Supplement to computation of independent units in number fields by Dirichlet's method, Math. Comp. 52, (1989), 1-14, with A. Pethö.
Leopoldt's Conjecture in parameterized families, Proc. Am. Math. Soc. 104, (1989), 43-48, with J.W. Sands.
On the computation of totally real quartic fields of small discriminant, Math. Comp. 52, (1989), 161-174, with D. Ford.
Computation of class groups of totally complex quartic fields, Math. Comp. 53, (1989), 387-397, with M. Pohst and J.v.Schmettow.
Computing a lattice basis from a system of generating vectors, Proceedings EUROCAL 87, Springer Lecture Notes in Computer Science 378, (1989), 54-63, with M. Pohst.
On the complexity of computing class groups of algebraic number fields, Proceedings AAECC-6, Springer Lecture Notes in Computer Science 357, (1989), 122-130, with M.     Pohst.
On the computation of unit groups and class groups of totally real quartic fields, Math. Comp. 53, (1989), 387-397, with M. Pohst and J. v. Schmettow.
On the computation of the class number of an algebraic number field, Math. Comp. 53, (1989), 679-688, with H.C. Williams.
On the existence of a short proof for the value of the class number and regulator of a real quadratic field, Proceedings of NATO ASI Number Theory and Applications, Kluwer Academic Publishers 1989, 327-346, with H.C. Williams.
On the complexity and efficiency of a new key exchange system, Proceedings CRYPTO '88, Lecture Notes in Computer Science 434, (1989), 597 - 616, with S. Düllmann and H.C. Williams.
A key exchange system based on real quadratic fields, Proceedings CRYPTO 88, Lecture Notes in Computer Science bf 435, (1989), 335 -343, with H.C. Williams.
Complexity of algorithms in algebraic number theory, Proceedings CNTA 1988, de Gruyter, Berlin 1990, 37-54.
On generalized continued fraction expansions of short period length, Publ. Math. 37, (1990), 109-114.
P-adic computation of real quadratic class numbers, Math. Comp. 54, April 1990, 855 - 868, with J. Sands and H.C. Williams.
A subexponential algorithm for the determination of class groups and regulators of algebraic number fields, Séminaire de Théorie des Nombres, Paris 1988-1989, Birkhäuser      Boston Basel Berlin, 1990, 27-41.
A probabilistic class group and regulator algorithm and its implementation, Proceedings of the Colloquium on Number Theory, Debrecen, 1989, Computational Number Theory, Walter de Gruyter, Berlin 1991, 54-72, with S. Düllmann.
Implementation of a key exchange protocol using real quadratic fields, Proceedings EUROCRYPT 90, Springer Lecture Notes in Computer Science 473, (1991), 8-109,        with H.C. Williams and R. Scheidler.
Some remarks concerning the complexity of computing class groups of quadratic fields, Journal of Complexity 7, (1991), 311-315. with H.C. Williams.
Quadratic fields and cryptography, in Number Theory and Cryptology, Cambridge University Press 1990, 9-26, with H.C. Williams.
On the computation of discrete logarithms in class groups, Proceedings CRYPTO 90, Springer Lecture Notes in Computer Science 537, (1991), 134-139, with S. Düllmann.
Constructing nonresidues in finite fields and the extended Riemann Hypothesis, Proceedings STOC 91, ACM Press 1991, 72-79, with V. Shoup.
Computing the number of points of elliptic curves over finite fields, Proceedings ISSAC 91, ACM Press 1991, 179-182, with V. Müller.
Number theoretic algorithms and cryptology, Proceedings FCT 91, Springer Lecture Notes in Computer Science 529, (1991), 16-21.
Lower bounds for , an elementary approach, Publ. Math. 38, (1991), 145-163. with K. Györy, M. Mignotte, N. Tzanakis.
On short representations of orders and number fields , 1992, with O..v. Sprang.
Distributed class group computation, with S. Düllmann, in Informatik, Festschrift zum 60. Geburtstag von Günter Hotz, Teubner, Stuttgart, Leipzig, 1992.
Tools for proving zero knowledge, Proceedings EUROCRYPT 92, Springer Lecture Notes in Computer Science 658, (1993), 356-365, with I. Biehl, B. Meyer, Christian Thiel, Christoph Thiel.
Enumeration of quartic fields of small discriminant, Math. Comp. 61, (1993), 873-879, with D. Ford and M. Pohst.
A key exchange protocol using real quadratic fields, Journal of Cryptology, 7, (1994), 171-199, with R. Scheidler and H.C. Williams.
An implementation of the general number field sieve, Proceedings CRYPTO 93, Springer Lecture Notes in Computer Science 773, (1994), 159-165, with Jürgen Loho and Jörg Zayer.
Algorithms for quadratic orders, Proceedings of Symposia in Applied Math., 48, (1994), 425-449, with Ingrid Biehl.
Reducing lattice bases by means of approximations, Proceedings of ANTS 94, Springer Lecture Notes in Computer Science 877, (1994), 160-168.
A practical version of the generalized Lagrange algorithm, Exp. Math., 3, (1994), 200-207, with Max Jüntgen and Michael Pohst.
Cryptographic protocols based on the discrete logarithm problem in real quadratic number fields, Proceedings CRYPTO 94, Springer Lecture Notes in Computer Science 839, (1994), 56-60, with I. Biehl and C. Thiel.
Approximating rings of integers in number fields, Séminaire de Théorie des Nombres Bordeaux 6, (1994), 221-260, with H.W. Lenstra Jr.
On unit groups and class groups of quadratic fields of signature (2,1), Math. Comp 62, (1994), 387-390, with M. Pohst and J.v. Schmettow
Algorithms in finite abelian groups, Proceedings of Number Theoretic and Algebraic Methods in Computer Science (NTAMCS) 1993, World Scientific Publisher (1995).
Short representations of quadratic integers, Math. Appl. 325, (1995), 159-185, with Christoph Thiel and Hugh Williams.
Faktorisierung großer Zahlen, Spektrum der Wissenschaften 9, (1996), 80-89.
On smooth ideals in number fields,  J. Number Theory 59, (1996), 82-87, with Christine Hollinger.
Constructing nonresidues in finite fields and the extended Riemann hypothesis, Math. Comp. 65, (1996), 1311-1326, with Victor Shoup.
A one way function based on ideal arithmetic in number fields, Proceedings CRYPTO 97, Springer Lecture Notes in Computer Science 1294, (1997), 385-394, with Sachar Paulus.
On some computational problems in finite abelian groups, Math. Comp. 66, (1997), 1663-1687, with Edlyn Teske and Michael Jacobson.
An analysis of the reduction algorithms for binary quadratic forms, in Voronoi's Impact on Modern Science, Institute of Mathematics Kyiv, 1998, 71-98, with Ingrid Biehl.
Sieving Methods for Class Group Computation, in Algorithmic Algebra and Number Theory , B.H. Matzat, G.-M. Greuel, G.Hiss (eds.), Springer Verlag 1998, 3-10, with M.  Jacobson, S. Neis, P. Theobald, D. Weber.
Zahlentheorie und Kryptographie, Jahrbuch der Akademie der Wissenschaften und Literatur, Mainz, 1998.
La factorisation des grands nombres,  Pour la Science, No. 251, Septembre 1998, 88-96.
On factor refinement in number fields, Math. comp. 68 (1999), 345-350, with F. Eisenbrand.
Discrete Logarithms: Recent Progress, Coding Theory, cryptography and related areas, Springer-Verlag 1999, with D. Weber.
Wie sicher ist die Public-Key-Kryptographie, Tagungsband Systemsicherheit 2000, DuD-Fachbeiträge, 105-116, with M. Maurer.
FlexiPKI - Realisierung einer flexiblen Public-Key-Infrastruktur, Tagungsband Systemsicherheit 2000, DuD-Fachbeiträge, 309-314, with M. Tak and M. Ruppert.
Cryptography based on number fields with large regulator, Journal de Théorie des Nombres Bordeaux 12 (2000), 293-307, with Markus Maurer and Bodo Möller.
Efficient construction of cryptographically strong elliptic curves, INDOCRYPT 2000, LNCS 1977, Springer-Verlag, New York, 191-201, with Harald Baier.
Wie sicher kann Sicherheit sein, in Sicherheitskonzepte für das Internet, G. Müller and Martin Reichenbach, (Hrsg.), Springer-Verlag, 2001, 45-54.
A survey on IQ cryptography, in Public-Key Cryptography and Computational Number Theory, Walter de Gruyter, Berlin - New York, 2001, 1-15, with S. Hamdy.
How secure can security possibly be,  in Safety of Modern Technical Systems, 2001, 587-594, with C. Ludwig.
A signature scheme based on the intractability of computing roots, Design, Codes, and Cryptography 25 (2002), 223-236. with I. Biehl, S. Hamdy, A. Meyer.
An IND-CCA2 Public-Key Cryptosystem with fast decryption, 4th International Conference on Information Security and Cryptology ICIS'01, LNCS 2288, 2002, 51-71, with K. Sakurai and T. Takagi
Aus- und Weiterbildung in IT-Sicherheit,  in IT-Sicherheit im verteilten Chaos, Tagungsband 8. Deutscher IT-Sicherheitskongress des BSI 2003, SecuMedia Verlag, 2003, 179-190, with C. Busch and H. Baier.
Number field cryptography, in High Primes and Misdemeanors: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, vol. 41 of Fields Institute Communications, 2004, 111-121, with T. Takagi, U. Vollmer.
Computing the structure of a finite abelian group, to appear in Math. Comp., with A. Schmidt.
Post quantum signatures, e-print archive., with C. Coronado, M. Döring, D. Engelbert, C. Ludwig, R. Overbeck, A. Schmidt, U. Vollmer, R. Weinmann.
Practical lattice basis sampling reduction, Proceedings ANTS VII, LNCS 4076, 2006, 222-237, with C. Ludwig.
An Evaluated Certification Services System for the German National Root CA -- Legally binding and trustworthy Transactions in E-Business and E-Government, in Proceedings of "The 2005 International Conference on e-Business, Enterprise Information Systems, e-Government, and Outsourcing (EEE'05)", 103-108, with A. Wiesmaier, M. Lippert, E. Karatsiolis, G. Raptis
The Workshop -- Implementing Well Structured Enterprise Applications, in Proceedings of "The 2005 International Conference on Software Engineering Research and Practice (SERP'05)", 947-953, with A. Wiesmaier, E. Karatsiolis, M. Lippert
Outflanking and securely using the PIN/TAN-System in Proceedings of "The 2005 International Conference on Security and Management (SAM'05)", with A. Wiesmaier, M. Fischer, M. Lippert.
Directory Based Registration in Public-Key Infrastructures,  in Proceedings of the 4th International Workshop for Applied PKI, IWAP 2005, 17-32, with M. Lippert, E. Karatsiolis, A. Wiesmaier.
Formal Proof for the Functional Correctness of RSA-PSS, submitted,  with C. Lindenberg and K. Wirt.
Block ciphers sensitive to Gröbner Basis Attacks, in Proceedings of CTRSA 2006, Springer LNCS, 313-331, with A. Pychkine and R. Weinmann.
A zero-dimensional Gröbner basis for AES–128,  in Proceedings of FSE 2006, with A. Pychkine and R. Weinmann.
Intrinsically Legal-For-Trade Objects by Digital Signatures,  Lecture Notes in Informatics 2006, 218-221, with A. Wiesmaier, U. Rauchschwalbe, C. Ludwig, B. Henhapl, M. Ruppert.
Perspectives for cryptographic long-term security, Communications of the ACM, 49, 2006, 50-56, with A. May, U. Vollmer.
CMSS -- An Improved Merkle Signature Scheme, with Luis Carlos Coronado Garcia and Erik Dahmen and Martin Doering and Elena Klintsevich,, Cryptology ePrint Archive: Report 2006/320, in Proceedings of Indocrypt 2006.

Lecture Notes

Introduction to theoretical crytography, Vorlesungsskipt 1991 with I. Biehl.
Algorithms for factoring integers, lecture notes, 1992, with V. Müller.
Primality testing, lecture notes, 1992, with V. Müller.
Einführung in die Computeralgebra, Vorlesung, 1992, with V. Müller.
Informatik I, Darmstadt, 1999.
Informatik II, Saarbrücken, 1993, with V. Müller.

PKI, Darmstadt 2005.