Knapsack Encryption

  • Manfred R. Schroeder
Part of the Springer Series in Information Sciences book series (SSINF, volume 7)


As a diversion we return in this chapter to another (once) promising public-key encryption scheme using a trap-door function: Knapsack encryption. It, too, is based on residue arithmetic, but uses multiplication rather than exponentiation, making it easier to instrument and theoretically more transparent.


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  1. 14.1
    1 N. J. A. Sloane: “Error-Correcting Codes and Cryptography,” in The Mathematical Gardener, ed. by D. Klarner (Prindle Weber Schmidt, Boston 1981) pp. 347–382. Republished in Cryptologia 6, 128–153, 258–278 (1982)Google Scholar
  2. 14.2
    R. C. Merkle, M. E. Hellman: Hiding information and signatures in trapdoor knapsacks. IEEE Trans. IT-24, 525–530 (1978)Google Scholar
  3. 14.
    A. Shamir: “A Polyominal Time Algorithm for Breaking Merkle-Hellman Cryptosystems,” Internal Report Applied Mathematics, The Weizmann Institute, Rehovot, IsraelGoogle Scholar
  4. 14.4
    Y. Desmedt, J. Vandewalle, R. Govaerts: “Critical Analysis of the Security of Knapsack Public Key Algorithms,” in Proceedings of the IEEE International Symposium on Information Theory ( IEEE, New York 1982 ) pp. 115–116Google Scholar
  5. 14.
    J. C. Lagarias (personal communication)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Manfred R. Schroeder
    • 1
    • 2
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenFed. Rep. of Germany
  2. 2.Acoustics Speech and Mechanics ResearchBell LaboratoriesMurray HillUSA

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