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An Extremely Small and Efficient Identification Scheme

  • William D. Banks
  • Daniel Lieman
  • Igor E. Shparlinski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1841)

Abstract

We present a new identification scheme which is based on Legendre symbols modulo a certain hidden prime and which is naturally suited for low power, low memory applications.

Keywords

Prime Number Knapsack Problem Discrete Logarithm Problem Legendre Symbol Integer Factorization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The design and analysis of computer algorithms. Addison-Wesley, Reading (1975)Google Scholar
  2. 2.
    Anshel, M., Goldfeld, D.: Zeta functions, one-way functions, and pseudoran- dom number generators. Duke Math. J. 88, 371–390 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bach, E., Shallit, J.: Algorithmic number theory. MIT Press, Cambridge (1996)zbMATHGoogle Scholar
  4. 4.
    Biham, E., Boneh, D., Reingold, O.: Breaking generalized Diffie-Hellman modulo a composite is not weaker than factoring. Inform. Proc. Letters 70, 83–87 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cohen, H.: A course in Computational Algebraic Number Theory. Springer, Berlin (1997)Google Scholar
  6. 6.
    von zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  7. 7.
    Goldfeld, D., Hoffstein, J.: On the number of Fourier coefficients that determine a modular form. Contemp. Math. 143, 385–393 (1993)MathSciNetGoogle Scholar
  8. 8.
    Hoffstein, J., Lieman, D., Silverman, J.: Polynomial rings and efficient public key authentication. In: Blum, M., Lee, C.H. (eds.) Proc. the Intern. Workshop on Cryptographic Techniques and E-Commerce (CrypTEC 1999). City University of Hong Kong Press (1999) (to appear)Google Scholar
  9. 9.
    McCurley, K.S.: A key distribution system equivalent to factoring. J. Cryptology 1, 95–105 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • William D. Banks
    • 1
  • Daniel Lieman
    • 1
  • Igor E. Shparlinski
    • 2
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Department of ComputingMacquarie UniversitySydneyAustralia

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