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Journal of Cryptology

, Volume 3, Issue 3, pp 149–155 | Cite as

On the Chor—Rivest knapsack cryptosystem

  • H. W. LenstraJr.
Article

Abstract

Among all public-key cryptosystems that depend on the knapsack problem, the system proposed by Chor and Rivest (IEEE Trans. Inform. Theory34 (1988), 901–909) is one of the few that have not been broken. The main difficulty in implementing their system is the computation of discrete logarithms in large finite fields. In this note we describe the “powerline system,” which is a modification of the Chor-Rivest system that does not have this shortcoming. The powerline system, which is not a knapsack system, is at least as secure as the original Chor-Rivest system.

Key words

Public-key cryptosystem Finite field 

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References

  1. [1]
    E. F. Brickell, A. M. Odlyzko, Cryptanalysis: a survey of recent results, Proc. IEEE 76 (1988), 578–593.Google Scholar
  2. [2]
    B.-Z. Chor, Two Issues in Public Key Cryptography, RSA Bit Security and a New Knapsack Type System, MIT Press, Cambridge, Mass., 1986.Google Scholar
  3. [3]
    B. Chor, R. L. Rivest, A knapsack-type public key cryptosystem based on arithmetic in finite fields, IEEE Trans. Inform. Theory 34 (1988), 901–909.Google Scholar
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    A.K. Lenstra, Factorization of polynomials, in: H. W. Lenstra, Jr., and R. Tijdeman (eds), Computational Methods in Number Theory, pp. 169–198, Mathematical Centre Tracts 154/155, Mathematisch Centrum, Amsterdam, 1982.Google Scholar

Copyright information

© International Association for Cryptologic Research 1991

Authors and Affiliations

  • H. W. LenstraJr.
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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