Skip to main content
SpringerLink
Log in

Approximate Power Roots in ℤm

  • Conference paper
  • First Online:
Information Security (ISC 2001)

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

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. German Sáez Moreno
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42662-2

  • Online ISBN: 978-3-540-45439-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation