Publikationen

2013

Das folgende pdf-File ist eine erweiterte und polierte Fassung der Arbeit
Factoring Integers by CVP Algorithms
erschienen in Number Theory and Cryptography, Eds. M. Fischlin und S. Katzenbeisser, Springer LNCS 8260, pp. 73--93, 2013
Claus Peter Schnorr
Universität Frankfurt
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2012

Solving Subset Sum Problems of Density close to 1 by "randomized" BKZ-reduction.
IACR Cryptology ePrint Archive 2012: 620 (2012)
Claus Peter Schnorr und Taras Shevchenko
Universität Frankfurt
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2011

Accelerated and Improved Slide- and LLL-Reduction
Erschienen unter TR11-050 bei ECCC (Electronic Colloquium on Computational Complexity).
Claus Peter Schnorr
Universität Frankfurt
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2010

Average Time Fast SVP and CVP Algorithms for Low Density Lattices and the Factorization of Integers
Technical Report.
Claus Peter Schnorr
Universität Frankfurt
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Average Time Fast SVP and CVP Algorithms for Low Density Lattices and the Factorization of Integers
Lecture at the conference: Numbers, Sequences, Lattices: Dynamical Analysis of Algorithms. Caen, 3-4 June 2010.
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2008

Identification and signatures based on NP--hard problems of indefinite quadratic forms.

R.J.Hartung and Claus-Peter Schnorr,
J. Math. Crypt. 1 (2007), 1-15
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2007

    • A Cryptanalysis of the Double-Round Quadratic Cryptosystem.
      A. Scemama
      10th International Conference on Information Security and Cryptology (ICISC'07), Seoul, 29-30 Novembre 2007.
      Lecture Notes in Computer Science, LNCS 4817, 2007.
      Download the paper:


    • Public Key Identification Based on the Equivalence of Quadratic Forms.
      R.J.Hartung, C.P.Schnorr
      Mathematical Foundations of Computer Science 2007 (MFCS 2007), Cesky Krumlov, Czech Republic, August 26-31, 2007
      LNCS, Springer 2007.
      Download corrected version:

      Link to original paper (on SpringerLink)

    • Progress on LLL and Lattice Reduction.
      C.P.Schnorr
      LLL+25, Caen, France, June 29 -- July 1, 2007
      published by Springer, 2010, Eds. P. Nguyen and B. Vallee: The LLL Algorithm
      Download the paper:

      Lecture slides:

2006

    • Blockwise Lattice Basis Reduction Revisited
      C.P.Schnorr
      Codes and Lattices in Cryptography, TU Darmstadt, 25--27. Sept. 2006.
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    • Fast LLL-Type Lattice Reduction
      C.P.Schnorr
      Information and Computation, Elsevier, 204, pp. 1-25, 2006.
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    • Enhancing the security of perfect blind DL-signatures.
      C.P.Schnorr
      Information Sciences, Elsevier, 176, pp. 1305-1320. 2006.
      Download the paper:

2004

    • Primale/duale Segment-Reduktion von Gitterbasen
      Henrik Koy
      Download the slides:

2003.

2001.

  • New Practical Algorithms For The Approximate Shortest Lattice Vector
    C.P.Schnorr
    Manuscript
    Download the paper:

  • Security of Blind Discrete Log Signatures Against Interactive Attacks
    C.P.Schnorr
    Proceedings of ICICS 2001
    Lecture Notes in Computer Science Vol.2229, Springer-Verlag, pp.1-13, 2001.
    Copyright: © IACR
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  • Universally Composable Commitments
    R.Canetti, M.Fischlin
    Advances in Cryptology - Crypto 2001
    Lecture Notes in Computer Science, Vol.2139, pp.19-40, Springer-Verlag, 2001.
    Copyright: © IACR
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  • Security Of DL-Encryption and Signatures Against Generic Attacks - A Survey
    C.P.Schnorr
    Public-Key Cryptography and Computational Number Theory Conference, Warsaw, September, 2000.
    Proceedings published 2001 by Walter De Gruyter (eds: K.Alster, H.C.Williams and J.Urbanowicz).
    Download the paper:


  • Identification Protocols Secure Against Reset Attacks
    M.Bellare, M.Fischlin, S.Goldwasser, S.Micali
    Advances in Cryptology - Eurocrypt 2001
    Lecture Notes in Computer Science, Vol.2045, pp.495-511, Springer-Verlag, 2001.
    Copyright: © IACR
  • A Cost-Effective Pay-Per-Multiplication Comparison Method for Millionaires
    M.Fischlin
    RSA Security 2001 Cryptographer's Track
    Lecture Notes in Computer Science, Vol.2020, pp.457-471, Springer-Verlag, 2001.
    Copyright: © Springer-Verlag
    Read the abstract or download the paper:


  • Segment LLL-Reduction of Lattice Bases
    H.Koy, C.P.Schnorr
    Cryptography and Lattices Conference (CalC) 2001
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  • Segment LLL-Reduction with Floating Point Orthogonalization
    H.Koy, C.P.Schnorr
    Cryptography and Lattices Conference (CalC) 2001
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  • Small Generic Hardcore Subsets for the Discrete Logarithm: Short Secret DL-Keys
    C.P.Schnorr
    Information Processing Letter 79 (2001), pp. 93-98.
    Download the paper:


2000.

1999.

  • Tensor-Based Trapdoors for CVP and Their Application to Public Key Cryptography
    R.Fischlin, J.-P. Seifert
    7th IMA International Conference "Cryptography and Coding" '99
    Lecture Notes in Computer Science, Vol.1746, Springer-Verlag, pp.244-257, 1999.
    Copyright: © Springer-Verlag 1999.
    Read the abstract or download the paper:


  • Extending Wiener's Attack in the Presence of Many Decrypting Exponents
    N.Howgrave-Graham, J.-P. Seifert
    Secure Networking - CQRE [Secure] '99
    Lecture Notes in Computer Science, Vol.1740, Springer-Verlag, pp.153-166, 1999.
    Copyright: © Springer-Verlag 1999.

  • The Complexity of the Extended GCD Problem
    George Havas, Jean-Pierre Seifert
    24th International Symposium, MFCS'99
    Lecture Notes in Computer Science, Vol.1672, Springer-Verlag, pp.103-113, 1999.
    Copyright: © Springer-Verlag 1999.

  • Security Of Discrete Log Cryptosystems in the Random Oracle + Generic Model
    C.P.Schnorr, M.Jakobsson
    The Mathematics of Public-Key Cryptography, The Fields Institute, Toronto (Canada).
    Download the paper:


  • Security Of Almost All Discrete Log Bits
    C.P.Schnorr
    ECCC-Report TR98-033
    Download the .dvi version.

  • Pseudorandom Function Tribe Ensembles Based on One-Way Permutations: Improvements and Applications
    M.Fischlin
    A preliminary version appeared in
    Advances in Cryptology - Eurocrypt '99
    Lecture Notes in Computer Science, Vol.1592, Springer-Verlag, pp.429-444, 1999.
    Copyright: © IACR
    Read the abstract or download the .ps (US letter), .dvi, or gnuzipped .ps.gz (US letter) version.

  • On the Complexity of Computing Short Linearly Independent Vectors and Short Bases in a Lattice
    J.Blömer, J.-P. Seifert
    31st Annual ACM Symposium on Theory of Computing (STOC) '99.

  • Bipoles
    M.Sieveking
    Preprint.
    Download the .dvi or the gnuzipped .ps.gz version.

1998.

  • Almost Optimal (on the average) Combinatorial Algorithms for Boolean Matrix Product Witnesses, Computing the Diameter
    C.P.Schnorr, C.R.Subramanian
    Random '98
    Lecture Notes in Computer Science, Vol.1588, Springer-Verlag, 1998.

  • Hardness of Approximating Shortest Integer Relations among Rational Numbers
    C.Rössner, J.-P. Seifert
    Theoretical Computer Science 209(1-2) (1998) 287-297.

  • Cryptographic Limitations on Parallelizing Membership and Equivalence Queries with Applications to Random Self-Reductions
    M.Fischlin
    9th International Conference on Algorithmic Learning Theory - ALT'98
    Lecture Notes in Artificial Intelligence/Computer Science, Vol.1501, Springer-Verlag, pp.72-84, 1998
    Copyright: © Springer-Verlag
    Read the abstract.

  • The Black-Box Model for Cryptographic Primitives
    C.P.Schnorr, S.Vaudenay
    Journal of Cryptology, Vol.11, pp. 125-140, 1998.
    Available from Springer Link.

  • On the Security of Server Aided RSA Protocols
    J.Merkle, R.Werchner
    Workshop on Public Key Cryptography PKC, 1998.

1997.

  • Lower Bounds for the Signature Size of Incremental Schemes
    M.Fischlin
    IEEE Symposium on Foundations of Computer Science (FOCS) 1997.
    Read the abstract or download the paper:


  • Factoring via Strong Lattice Reduction Algorithm
    H.Ritter, C.Rössner
    Technical Report, Universität Frankfurt am Main, Mai 1997.
    Download the .ps or gnuzipped .ps.gz version.

  • Diophantine Approximation of a Plane
    C.Rössner, C.P.Schnorr
    Technical Report, Universität Frankfurt am Main, Mai 1997.
    Download the .ps or gnuzipped .ps.gz version.

  • Stronger Security Proofs for RSA and Rabin Bits
    R.Fischlin, C.P.Schnorr
    Advances in Cryptology - Eurocrypt '97
    Lecture Notes in Computer Science, Vol.1233, Springer-Verlag, pp.267-279, 1997.
    Journal version published in 2000.

  • Incremental Cryptography and Memory Checkers
    M.Fischlin
    Advances in Cryptology - Eurocrypt '97
    Lecture Notes in Computer Science, Vol.1233, Springer-Verlag, pp.393-408, 1997.
    Read the abstract or download the .ps or gnuzipped .ps.gz version.

  • Practical Memory Checkers for Stacks, Queues and Deques
    M.Fischlin
    Information Security and Privacy - ACISP '97
    Lecture Notes in Computer Science, Vol.1270, Springer-Verlag, pp.114-125, 1997.
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1996.

  • The Generalized Gauss Algorithm
    M.Kaib, C.P.Schnorr
    Journal of Algorithms, Vol.21(3), pp.565-578, 1996.
    Download the .ps, .dvi, or gnuzipped .ps.gz version.

  • Security of 2 t-Root Indentification and Signatures
    C.P.Schnorr
    Advances in Cryptology - Crypto '96
    Lecture Notes in Computer Science, Vol.1109, Springer Verlag, pp.143-156,1996.Download the .ps, Download correction "Factoring N via proper 2 t-Roots of 1 mod N" presented at Eurocrypt '97 rump session:


  • Breaking Knapsack Cryptosystems by Max-Norm Enumeration
    H.Ritter
    1st International Conference of the Theory and Appications of Cryptology - Pragocrypt '96, pp. 480-492,1996.
    Download the paper:


  • Approximating Good Simultaneous Diophantine Approximations is almost NP-hard
    C.Rössner, J.-P.Seifert
    21st International Symposium on Mathematical Foundations of Computer Science (MFCS'96)
    Lecture Notes in Computer Science, Vol.???, Springer-Verlag, pp. , 1996.
    Download the .ps or gnuzipped .ps.gz version.

  • The Complexity of Approximate Optima for Greatest Common Divisor Computations
    C.Rössner, J.-P.Seifert
    Proceedings of the 2nd International Algorithmic Number Theory Symposium, ANTS-II, 1996.
    Download the .ps or gnuzipped .ps.gz version.

  • An Optimal, Stable Continued Fraction Algorithm for Arbitrary Dimension
    C.Rössner, C.P.Schnorr
    5th IPCO Conference on Integer Programming and Combinatorial Optimization.Springer LNCS 1084,
    31 - 43, 1996.
    Download the .ps or gnuzipped .ps.gz version.

  • On the Hardness of Approximating Shortest Integer Relations among Rational Numbers
    C.Rössner, J.-P.Seifert
    Computing: The Australasian Theory Symposium (CATS) '96.
    Download the .ps or gnuzipped .ps.gz version.

1995.

  • Computation of Highly Regular Nearby Points
    C.Rössner, C.P.Schnorr
    3rd Israel Symposium on the Theory of Computing and Systems, 1995.
    Download the .ps or gnuzipped .ps.gz version.

  • Attacking the Chor-Rivest Cryptosystem by Improved Lattice Reduction
    C.P.Schnorr, H.H.Hörner
    Advances in Cryptology - Eurocrypt '95
    Lecture Notes in Computer Science, Vol. 921, Springer Verlag, pp.1-12,1995.
    Read the abstract or download the paper:


1994.

  • Further Attacks on the Birational Permutation Signature Schemes.
    T.Theobald
    Advances in Cryptology - Crypto '94
    Lecture Notes in Computer Science, Vol.839, Springer Verlag, pp. 136-147, 1994.
    Download the paper:


  • Block Reduction for Arbitrary Norms
    M.Kaib, H.Ritter
    Technical Report, Universität Frankfurt am Main, 1994.
    Download the .ps or gnuzipped .ps.gz version.

  • A Stable Integer Relation Algorithm
    C.Rössner, C.P.Schnorr
    Technical Report 94-016, ICSI, Berkeley, CA, 1994.
    Download the .ps or gnuzipped .ps.gz version.

  • Parallel FFT-Hashing
    C.P.Schnorr, S.Vaudenay
    Fast Software Encryption - Cambridge Security Workshop
    Lecture Notes in Computer Science, Vol. 809, Springer Verlag, pp.149-156,1994.
    Download the .ps, .dvi, or gnuzipped .ps.gz version.

  • Black Box Cryptanalysis of Hash Networks based on Multipermutations
    C.P.Schnorr, S.Vaudenay
    Advances in Cryptology - Eurocrypt '94
    Lecture Notes in Computer Science, Vol.950, Springer Verlag,1995.
    Available from S.Vaudenay's Publications.

  • Block Reduced Lattice Bases and Successive Minima
    C.P.Schnorr
    Combinatorics, Probability and Computing 3, pp.507-533, 1994.
    Download the paper:


  • A Fast Variant of the Gaussian Reduction Algorithm
    M.Kaib
    International Symposium on Algorithmic Number Theory, 1994.
    Download the .ps, .dvi, or gnuzipped .ps.gz version.

  • Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems
    C.P.Schnorr, M.Euchner
    Mathematical Programming, Vol.66, pp.181-191,1994.
    Download the .ps, .dvi, or gnuzipped .ps.gz version.

1993.

  • Factoring Integers and Computing Discrete Logorithms via Diophantine Approximation
    C.P.Schnorr
    Advances in Computational Complexity
    AMS DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol.13, pp.171-182, 1993.
    Download the paper:


  • Local Randomness in Polynomial Random Number and Random Function Generators
    H.Niederreiter, C.P.Schnorr
    SIAM Jounral on Computing, Vol.22(4), pp.684-694, 1993
    Download the .ps, .dvi, or gnuzipped .ps.gz version.

1992.

  • Local Randomness in Candidate One-Way Functions
    H.Niederreiter, C.P.Schnorr
    Advances in Cryptology - Eurocrypt '92
    Lecture Notes in Computer Science, Vol.658, Springer Verlag,1993.
    Journal version published in 1993.

  • Improved Low-Density Subset Sum Algorithms
    M.J.Coster, A.Joux, B.A.LaMacchia, A.M.Odlyzko, C.P.Schnorr, J.Stern
    Computational Complexity 2, 1992.
    Download the paper:


  • The Multiplicative Complexity of Quadratic Boolean Forms
    R. Mirwald, C.P.Schnorr
    TCS, Vol.102(2), pp.307-328, 1992.

1991.

  • Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems
    C.P.Schnorr, M.Euchner
    Fundamentals of Computation Theory - FCT '91
    Lecture Notes in Computer Science, Vol.591, Springer Verlag, pp.68-85,1991.
    Journal version published in 1994.

  • Factoring Integers and Computing Discrete Logorithms via Diophantine Approximation
    C.P.Schnorr
    Advances in Cryptology - Eurocrypt '91
    Lecture Notes in Computer Science, Vol.547, Springer Verlag, pp.171-181,1991.
    Journal version published in 1993.

  • Efficient Signature Generation by Smart Cards
    C.P.Schnorr
    Journal of Cryptology, Vol.4, pp.161-174, 1991.
    Download the .ps, .dvi, or gnuzipped .ps.gz version.

  • Efficient, Perfect Random Number Generators
    S.Micali, C.P.Schnorr
    Journal of Cryptology, Vol.3, pp.157-172, 1991.

1990.

  • Krokin-Zolotarev Bases and Successive Minimal of a Lattice and its Reciprocal Lattice
    JC.Lagarias, W.H.Lenstra, C.P.Schnorr
    Combinatorica, Vol. 10, pp.333-348, 1990.

  • Fast Signature Generation with a Fiat Shamir-Like Scheme
    H.Ong, C.P.Schnorr
    Advances in Cryptology - Eurocrypt '90
    Lecture Notes in Computer Science, Vol.473, Springer Verlag, pp.432-440,1991.
    Download the .ps, .dvi, or gnuzipped .ps.gz version.

1989.

  • Efficient Identification and Signatures for Smart Cards
    C.P.Schnorr
    Advances in Cryptology - Crypto '89
    Lecture Notes in Computer Science, Vol.435, Springer Verlag, pp.235-251,1990.
    Journal version published in 1991.

  • Polynomial Time algorithms for Finding Integer Relations among real Numbers
    J. Håstad, B.Just, J.C.Lagarias, C.P.Schnorr
    SIAM Journal on Computing, Vol.18(5), pp.859-881, 1989.


1988.

  • RSA and Rabin Function: Certain Parts are as Hard as the Whole
    W.Alexi, B.Chor, O.Goldreich, C.P.Schnorr
    SIAM Journal on Computing, Vol.17, pp.194-209, 1988.pdf


  • A more Efficient Algorithm for Lattice Basis Reduction
    C.P.Schnorr
    Journal of Algorithms, Vol. 9, pp.47-62, 1988, Download the pdf


1987.

  • Approximating Integer Lattices by Lattices with Cyclic Factor Group
    A.Paz, C.P.Schnorr
    14.th International Colloquium on Automata, Languages and Programming - ICALP '87
    Lecture Notes in Computer Science, Vol.267, Springer Verlag, pp.386-393,1987.

  • A Hierarchy of Polynomial Time Lattice Basis Reduction
    C.P.Schnorr
    Theoretical Computer Science, Vol.53, pp.201-224, 1987.

  • Solution of x²+ky²= m (mod n) with Application to Digital Signatures
    J.Pollard, C.P.Schnorr
    IEEE Transaction on Information Theory, Vol 22, pp.702-709, 1987.

  • An O(n³ log n) Deterministic and an O(n³) Las Vegas Isomorphism Test for Trivalent Graphs
    Z.Galil, C.Hoffmann, E.Luks, C.P.Schnorr, A.Weber
    Journal of the ACM, Vol.34(3), pp.513-531, 1987.

  • The Multiplicative Complexity of Quadratic Boolean Forms
    R. Mirwald, C.P.Schnorr
    Proceedings Foundation on Computer Science - FOCS '87, pp.141-150, 1987.
    Journal version published in 1992.

1986 or earlier.

  • An Optimal Sorting Algorithm for Mesh Connected Computers
    C.P.Schnorr, A.Shamir
    Proceedings of Symposium om Theoretical Computer Science - STOC '86, pp.255-263, 1986.

  • Zufälligkeit und Wahrscheinlichkeit
    C.P.Schnorr
    Springer LNM 218 (1971).
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