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Approximate Power Roots in ℤm

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Information Security (ISC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2200))

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Abstract

Some algorithms to search for power residues close to a desired value are reported. They are used in the cryptanalysis of low exponent RSA with partially known clear text.

The work of the second author was partially supported by Ministerio de Ciencia y Tecnología under project TIC 2000-1044.

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References

  1. Batut, C., Belabas, K., Bernardi, D., Cohen, H. and Olivier, M. PARI-GP Number Theory Package. ftp://megrez.math.u-bordeaux.fr/pub/pari/ .

  2. Brickell, E. F. and Odlyzko, M. Cryptanalysis: A survey of recent results. Proc. of the IEEE 76 (1988) 578–593

    Article  Google Scholar 

  3. Cohen, H.: A Course in Computational Algebraic Number Theory, Springer-Verlag, Berlin (1993)

    MATH  Google Scholar 

  4. Coppersmith, D. Small solutions to polynomial equations, and low exponents RSA vulnerabilities. J. Cryptology 10 (1997) 233–260

    Article  MATH  MathSciNet  Google Scholar 

  5. Hastad, J. Solving simultaneous modular equations of low degree. SIAM J. Comp. 17 (1988) 336–341

    Article  MATH  MathSciNet  Google Scholar 

  6. Lenstra, A. K., Lenstra, H. W. and Lovász, L. Factoring polynomials with integer coefficients. Mathematische Annalen, 261 (1982) pp. 513–534

    Article  Google Scholar 

  7. Peralta, R.: A quadratic sieve on the n-dimensional cube. In: Brickell, E. F. (ed.): Advances in Cryptology, CRYPT’92. Lecture Notes in Computer Science, Vol. 740. Springer-Verlag, Berlin Heidelberg New York (1993) 324–332.

    Google Scholar 

  8. Pomerance, C.: The quadratic sieve factoring algorithm. In: Beth, T., Cot, N., and Ingemarsson, I. (eds.): Advances in Cryptology, EUROCRYPT’84. Lecture Notes in Computer Science, Vol. 209. Springer-Verlag, Berlin Heidelberg New York (1985) 169–182.

    Google Scholar 

  9. Niven, I., Zuckerman, H.S. and Montgomery, H.L. An Introduction to the Theory of Numbers, John Wiley & Sons, Inc., New York, (1991)

    Google Scholar 

  10. Rivest, R. L., Shamir, A. and Adleman, L. A method for obtaining digital signatures and public key cryptosystems. Comm. ACM, 21 (1978) 120–126

    Article  MATH  MathSciNet  Google Scholar 

  11. Silverman, R.D.: The multiple polynomial quadratic sieve. Math. Comp. 48 (1987) 329–339

    Article  MATH  MathSciNet  Google Scholar 

  12. Vallée B.: Generation of elements with small modular squares and provably fast integer factoring algorithms. Math. Comp. 56 (1991) 823–849

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. C.S.I.C, Instituto de Física Aplicada, c/Serrano 144, 28006, Madrid, Spain

    Ismael Jiménez Calvo

  2. Dep. de Matemàtica Aplicada IV, Universitat Polit`ecnica de Catalunya, c/Jordi Girona, 1-3, 08034, Barcelona, Spain

    German Sáez Moreno

Authors
  1. Ismael Jiménez Calvo
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  2. German Sáez Moreno
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Editor information

Editors and Affiliations

  1. Department of EECS, University of Wisconsin-Milwaukee, Milwaukee, WI, 53201, USA

    George I. Davida

  2. Techtegrity, LLC, 122 Harrison, Westfield, NJ, 07090, USA

    Yair Frankel

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© 2001 Springer-Verlag Berlin Heidelberg

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Calvo, I.J., Moreno, G.S. (2001). Approximate Power Roots in ℤm . In: Davida, G.I., Frankel, Y. (eds) Information Security. ISC 2001. Lecture Notes in Computer Science, vol 2200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45439-X_21

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  • DOI: https://doi.org/10.1007/3-540-45439-X_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42662-2

  • Online ISBN: 978-3-540-45439-7

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