Skip to main content
SpringerLink
Log in

Efficient and optimal exponentiation in finite fields

  • Published:
computational complexity Aims and scope Submit manuscript

Abstract

Optimal sequential and parallel algorithms for exponentiation in a finite field containing F q are presented, assuming thatqth powers can be computed for free.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • G. B. Agnew, R. C. Mullin, andS. A. Vanstone, Fast exponentiation inGF(2n). InAdvances in Cryptology—EUROCRYPT'88, ed.C. G. Günther, vol. 330 ofLecture Notes in Computer Science. Springer (Berlin), 1988, 251–255.

    Google Scholar 

  • J. Berstel andS. Brlek, On the length of word chains.Inform. Process. Lett. 26 (1987), 23–28.

    Google Scholar 

  • T. Beth, B. M. Cook, andD. Gollmann, Architectures for exponentiation inGF(2n). InAdvances in Cryptology—CRYPTO'86, ed.A. M. Odlyzko, vol. 263 ofLecture Notes in Computer Science. Springer (Berlin), 1986, 302–310.

    Google Scholar 

  • F. Fich andM. Tompa, The parallel complexity of exponentiating polynomials over finite fields.J. Assoc. Comput. Mach. 35 (1988), 651–667.

    Google Scholar 

  • J. von zur Gathen, Computing powers in parallel.SIAM J. Comput. 16 (1987), 930–945.

    Google Scholar 

  • J. von zur Gathen, Inversion in finite fields using logarithmic depth.J. Symb. Comp. 9 (1990), 175–183.

    Google Scholar 

  • J. von zur Gathen, Processor-efficient exponentiation in finite fields. Inform. Process. Lett., to appear, 1992.

  • J. von zur Gathen andM. Giesbrecht, Constructing normal bases in finite fields.J. Symb. Comp. 10 (1990), 547–570.

    Google Scholar 

  • J. von zur Gathen andG. Seroussi, Boolean circuits versus arithmetic circuits.Inform. and Comput. 91 (1991), 142–154.

    Google Scholar 

  • P. N. Golovanov andV. I. Solodovnikov, Rapid parallel calculation of degrees in a quotient ring of polynomials over a finite field.Mathematical Notes 42 (1987), 987–992.

    Google Scholar 

  • D. E. Knuth,The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Addison-Wesley (Reading MA), 2 edition, 1981.

    Google Scholar 

  • Th. Lengauer and K. Mehlhorn, VLSI complexity, efficient VLSI algorithms and the HILL design system. InAlgorithmics for VLSI, ed.C. Trullemans. Academic Press, 1986, 33–89.

  • G. W. Reitwiesner, Binary arithmetic.Advances in computers, ed. F. L. Alt 1 (1960), 231–308.

    Google Scholar 

  • D. R. Stinson, Some observations on parallel algorithms for fast exponentiation inGF(2n).SIAM J. Comput. 19 (1990), 711–717.

    Google Scholar 

  • C. C. Wang, T. K. Truong, H. M. Shao, L. J. Deutsch, J. K. Omura, andI. S. Reed, VLSI architectures for computing multiplications and inverses inGF(2m).IEEE Trans. Comput. C-34 (1985), 709–717.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Toronto, M55 1A4, Toronto, Ontario, Canada

    Joachim von zur Gathen

Authors
  1. Joachim von zur Gathen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

von zur Gathen, J. Efficient and optimal exponentiation in finite fields. Comput Complexity 1, 360–394 (1991). https://doi.org/10.1007/BF01212964

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01212964

Subject classifications

Search

Navigation