A New Trapdoor Knapsack Public Key Cryptosystem

  • R. M. F. Goodman
  • A. J. McAuley
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 209)


This paper presents a new trapdoor-knapsack public-key-cryptosystem. The encryption equation is based on the general modular knapsack equation, but unlike the Merkle-Hellman scheme the knapsack components do not have to have a superincreasing structure. The trapdoor is based on transformations between the modular and radix form of the knapsack components, via the Chinese Remainder Theorem. The resulting cryptosystem has high density and has a typical message block size of 2000 bits and a public key of 14K bits. The security is based on factoring a number composed of 256 bit prime factors. The major advantage of the scheme when compared with the RSA scheme is one of speed. Typically, knapsack schemes such as the one proposed here are capable of throughput speeds which are orders of magnitude faster than the RSA scheme.


cryptography ciphers codes knapsack problem public key 


  1. 1.
    W. Diffie and M. Hellman, “New directions in cryptography”, IEEE Trans. on Information Theory, IT-22, pp 644–654, Nov. 1976.CrossRefMathSciNetGoogle Scholar
  2. 2.
    R. Rivest, A. Shamir, and L. Adelman, “On digital signatures and public key cryptosystems”, Comm. of the ACM, Vol. 21, No. 2, pp. 120–126, Feb 1978.zbMATHCrossRefGoogle Scholar
  3. 3.
    R.C. Merkle and M.E. Hellman, “Hiding information and signatures in trapdoor knapsacks”, IEEE Trans. on Information Theory, IT-24, pp 525–530, Sept. 1978.CrossRefGoogle Scholar
  4. 4.
    Y. Desmet, J. Vandewalle, and R. Govaerts, “A critical analysis of the security of knapsack public key cryptosystems”, IEEE Symp. on Information Theory, Les Arcs, France, June 1982.Google Scholar
  5. 5.
    E.F. Brickell, “Solving low density knapsacks”, Sandia National Laboratories, Albuquerque, New Mexico, USA, 13p, 1983.Google Scholar
  6. 6.
    J.C. Lagarias, and A.M. Odlyzko, “Solving low-density subset sum problems”, Bell Laboratories, Murray Hill, New Jersey, USA, 38p, 1983.Google Scholar
  7. 7.
    D.E. Knuth, The Art of Computer Programming, Vol. 1., “Fundamental Algorithms”, Addison-Wesley, 1968.Google Scholar
  8. 8.
    S.C. Lu, and L.N. Lee, “A simple and effective public key cryptosystem”, Comsat Tech. Rev., Vol. 9., pp15–24, Spring 1979.Google Scholar
  9. 9.
    J.M. Goethals, and C. Couvreur, “A cryptanalytic attack on the Lu-Lee public key cryptosystem, Phillips J. Res., Vol. 35, pp. 301–306, 1980.zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • R. M. F. Goodman
    • 1
  • A. J. McAuley
    • 1
  1. 1.Department of Electronic EngineeringUniversity of HullHullUK

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