Abstract
Among all public-key cryptosystems that depend on the knapsack problem, the system proposed by Chor and Rivest (IEEE Trans. Inform. Theory 34 (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.
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E. F. Brickell, A. M. Odlyzko, Cryptanalysis: a survey of recent results, Proc. IEEE 76 (1988), 578–593.
B.-Z. Chor, Two Issues in Public Key Cryptography, RSA Bit Security and a New Knapsack Type System, MIT Press, Cambridge, Mass., 1986.
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.
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.
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The author was supported by NSF under Grant Nos. DMS 87-06176 and DMS 90-02939, and by NSA/MSP under Grant No. MDA90-H-4043.
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Lenstra, H.W. On the Chor—Rivest knapsack cryptosystem. J. Cryptology 3, 149–155 (1991). https://doi.org/10.1007/BF00196908
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DOI: https://doi.org/10.1007/BF00196908